This thesis examines the stability of the planetary system around υ Andromedae using numerical integration. The author tests the nominal orbital parameters from McArthur et al. (2010), finding the two outer planets become unstable after 357,000 years. Lower maximum planet masses of 1.645 and 1.206 MJUP allow stability for 1 Myr. Additionally, 174 random configurations within the published error ranges resulted in instability within 2.1 Myr. The author developed an N-body integrator to perform the simulations and tested it on the Pythagorean three-body problem.
Dust-trapping Vortices and a Potentially Planet-triggered Spiral Wake in the ...Sérgio Sacani
The radial drift problem constitutes one of the most fundamental problems in planet formation theory, as it predicts
particles to drift into the star before they are able to grow to planetesimal size. Dust-trapping vortices have been
proposed as a possible solution to this problem, as they might be able to trap particles over millions of years,
allowing them to grow beyond the radial drift barrier. Here, we present ALMA 0 04 resolution imaging of the pretransitional
disk of V1247 Orionis that reveals an asymmetric ring as well as a sharply confined crescent structure,
resembling morphologies seen in theoretical models of vortex formation. The asymmetric ring (at 0 17 = 54 au
separation from the star) and the crescent (at 0 38 = 120 au) seem smoothly connected through a one-armed
spiral-arm structure that has been found previously in scattered light. We propose a physical scenario with a planet
orbiting at ∼0 3 ≈ 100 au, where the one-armed spiral arm detected in polarized light traces the accretion stream
feeding the protoplanet. The dynamical influence of the planet clears the gap between the ring and the crescent and
triggers two vortices that trap millimeter-sized particles, namely, the crescent and the bright asymmetry seen in the
ring. We conducted dedicated hydrodynamics simulations of a disk with an embedded planet, which results in
similar spiral-arm morphologies as seen in our scattered-light images. At the position of the spiral wake and the
crescent we also observe 12CO(3-2) and H12CO+ (4-3) excess line emission, likely tracing the increased scaleheight
in these disk regions.
Direct Measure of Radiative And Dynamical Properties Of An Exoplanet AtmosphereSérgio Sacani
Two decades after the discovery of 51Pegb, the formation processes and atmospheres of short-period gas giants
remain poorly understood. Observations of eccentric systems provide key insights on those topics as they can
illuminate how a planet’s atmosphere responds to changes in incident flux. We report here the analysis of multi-day
multi-channel photometry of the eccentric (e ~ 0.93) hot Jupiter HD80606b obtained with the Spitzer Space
Telescope. The planet’s extreme eccentricity combined with the long coverage and exquisite precision of new
periastron-passage observations allow us to break the degeneracy between the radiative and dynamical timescales
of HD80606b’s atmosphere and constrain its global thermal response. Our analysis reveals that the atmospheric
layers probed heat rapidly (∼4 hr radiative timescale) from<500 to 1400 K as they absorb ~20% of the incoming
stellar flux during the periastron passage, while the planet’s rotation period is 93 35
85
-
+ hr, which exceeds the predicted
pseudo-synchronous period (40 hr).
Key words: methods: numerical – planet–star interactions – planets and satellites: atmospheres – planets and
satellites: dynamical evolution and stability – planets and satellites: individual (HD 80606 b) – techniques:
photometric
This document provides lecture notes on the topic of geophysics. It introduces gravimetry, which detects tiny differences in gravitational force to differentiate underground structures based on density variations. Key points covered include Newton's law of gravitation, factors that influence the gravity field of Earth, methods for reducing gravity data to correct for these factors (such as latitude, elevation, topography, tides, and subsurface density variations), and applications of gravimetry in geological mapping and exploration.
Finding Ourselves in the Universe_ A Mathematical Approach to Cosmic Crystall...Joshua Menges
This thesis discusses using mathematics to approach the concept of cosmic crystallography. It explores representing the universe as a 2-torus or 3-torus, which are topological shapes that repeat themselves. The paper examines what a cosmic crystallographer might observe in different scenarios within a 2D torus universe model, including stationary galaxy clusters, moving clusters, and aging clusters. It touches briefly on possibilities for future work, such as expanding the model to 3D and accounting for galaxy motion within clusters. The background provides context on the shapes of 2D and 3D tori, cosmic crystallography, galaxies in the Local Group including the Milky Way, and stellar classifications.
Another Force Effects On The Earth Moon Motion (III)Gerges francis
Paper Question
-Can the moon orbit regress and the Earth still in its same point in the space If the Earth moon distances after the regression still equal their values before it?
- The paper question tells us that….
- The moon orbit regression is done because of the moon vertical motion and both are done in consistency with a displacement done by Earth vertically for 1 km per solar day…
- I claim that, there are 3 motions done, but only one motion is seen, we have to conclude the 2 rest hidden motions….
o The seen motion is The Moon Orbit Regression
o The 1st hidden motion is the moon vertical motion…that means, the moon in its revolution around The Earth does a vertical motion, and this vertical motion is the reason of the Metonic Cycle (19 sidereal years)
o The 2nd hidden motion is the Earth motion, where the Earth moves daily a vertical displacement = 1 km
- These 3 motions are done in consistency with each other, and depends on each other (this dependency can be seen in a deep analysis for these 3 motions origin)
Paper Objective
- The paper tries to prove the moon vertical motion by using the moon motion data analysis, after this proof , The paper discusses if a vertical displacement of Earth is a necessary requirement for the moon orbit regression, which is done as a result of the moon vertical motion.
Paper 2nd Question
- Why it's necessary to know if the moon has a vertical motion?
- (1st) The moon motion has pauses can't be explained, as we have seen in our tests for (Gerges Equation for the moon orbital motion)… where the moon moves on a solar day a distance = 4000 km (in average) (for example from 384000 km to 388000 km) but we have found that, the moon in perigee & apogee top points stay for many days without change its orbit (for example during 28th, 29th and 30th January 2020, the moon stayed on (404425 km, 405333km, 405111 km)) – how to explain that?
Gerges Francis Tawdrous +201022532292
The Moon Orbit Geometrical Structure Proves The Following Conclusions:
Primary Conclusions
(1) Solar Group Can't be created neither by Big Bang Theory Nor Sun Gravity Concept.
(2) The Solar Group is created of Only One Energy travels through the group
(3) This one Energy creates planets matters (E=mc2 supports that) and planets orbital distances (because Space = Energy –my hypothesis)
(4) Solar Group can be similar to one train and each planet is a carriage of it.
(5) Solar Group can be similar to one machine and each planet is a gear in it
(6) Solar Group can be similar to one building and each planet is a part of it
(7) So, when a planet moves – means - this planet moves as a carriage in one train –all solar planets move together in one general motion
Paper Basic Conclusion:
Energy must be Transported from Jupiter to Earth Moon Orbit
The paper tries to prove this fact
Uma espetacular colisão de galáxias foi descoberta além da Via Láctea. O sistema mais próximo já descoberto, a identificação foi anunciada por uma equipe de astrônomos liderada pelo Professor Quentin Parker da Universidade de Hong Kong e pelo Professor Albert Zijlstra na Universidade de Manchester.
A galáxia está a 30 milhões de anos-luz de distância, o que significa que ela é relativamente próxima. Ela foi chamada de Roda de Kathryn, em homenagem à sua semelhança com o famoso fogo de artifício e também em homenagem à esposa do coautor do trabalho.
Esses sistemas são muito raros e nascem da colisão entre duas galáxias de tamanhos similares. As ondas de choque geradas na colisão comprimem o reservatório de gás em cada galáxia e disparam a formação de novas estrelas. Isso cria um espetacular anel de intensa emissão, e ilumina o sistema, do mesmo modo que a Roda Catherine ilumina a noite num show de fogos de artifício.
As galáxias crescem através de colisões, mas é raro registrar esse processo acontecendo, e é extremamente raro ver o anel da colisão em progresso. Pouco mais de 20 sistemas com anéis completos são conhecidos.
Discovery of a_probable_4_5_jupiter_mass_exoplanet_to_hd95086_by_direct_imagingSérgio Sacani
The document reports the discovery of a probable 4-5 Jupiter-mass exoplanet orbiting the young star HD 95086. Deep imaging observations using VLT/NaCo detected a faint source at a separation of 56 AU from the star. Follow-up observations over more than a year found the source to be co-moving with the star, suggesting it is bound. Its luminosity corresponds to a predicted mass of 4-5 Jupiter masses, making it the lowest mass exoplanet directly imaged around a star. If confirmed, this discovery could provide insights into giant planet formation and evolution.
Dust-trapping Vortices and a Potentially Planet-triggered Spiral Wake in the ...Sérgio Sacani
The radial drift problem constitutes one of the most fundamental problems in planet formation theory, as it predicts
particles to drift into the star before they are able to grow to planetesimal size. Dust-trapping vortices have been
proposed as a possible solution to this problem, as they might be able to trap particles over millions of years,
allowing them to grow beyond the radial drift barrier. Here, we present ALMA 0 04 resolution imaging of the pretransitional
disk of V1247 Orionis that reveals an asymmetric ring as well as a sharply confined crescent structure,
resembling morphologies seen in theoretical models of vortex formation. The asymmetric ring (at 0 17 = 54 au
separation from the star) and the crescent (at 0 38 = 120 au) seem smoothly connected through a one-armed
spiral-arm structure that has been found previously in scattered light. We propose a physical scenario with a planet
orbiting at ∼0 3 ≈ 100 au, where the one-armed spiral arm detected in polarized light traces the accretion stream
feeding the protoplanet. The dynamical influence of the planet clears the gap between the ring and the crescent and
triggers two vortices that trap millimeter-sized particles, namely, the crescent and the bright asymmetry seen in the
ring. We conducted dedicated hydrodynamics simulations of a disk with an embedded planet, which results in
similar spiral-arm morphologies as seen in our scattered-light images. At the position of the spiral wake and the
crescent we also observe 12CO(3-2) and H12CO+ (4-3) excess line emission, likely tracing the increased scaleheight
in these disk regions.
Direct Measure of Radiative And Dynamical Properties Of An Exoplanet AtmosphereSérgio Sacani
Two decades after the discovery of 51Pegb, the formation processes and atmospheres of short-period gas giants
remain poorly understood. Observations of eccentric systems provide key insights on those topics as they can
illuminate how a planet’s atmosphere responds to changes in incident flux. We report here the analysis of multi-day
multi-channel photometry of the eccentric (e ~ 0.93) hot Jupiter HD80606b obtained with the Spitzer Space
Telescope. The planet’s extreme eccentricity combined with the long coverage and exquisite precision of new
periastron-passage observations allow us to break the degeneracy between the radiative and dynamical timescales
of HD80606b’s atmosphere and constrain its global thermal response. Our analysis reveals that the atmospheric
layers probed heat rapidly (∼4 hr radiative timescale) from<500 to 1400 K as they absorb ~20% of the incoming
stellar flux during the periastron passage, while the planet’s rotation period is 93 35
85
-
+ hr, which exceeds the predicted
pseudo-synchronous period (40 hr).
Key words: methods: numerical – planet–star interactions – planets and satellites: atmospheres – planets and
satellites: dynamical evolution and stability – planets and satellites: individual (HD 80606 b) – techniques:
photometric
This document provides lecture notes on the topic of geophysics. It introduces gravimetry, which detects tiny differences in gravitational force to differentiate underground structures based on density variations. Key points covered include Newton's law of gravitation, factors that influence the gravity field of Earth, methods for reducing gravity data to correct for these factors (such as latitude, elevation, topography, tides, and subsurface density variations), and applications of gravimetry in geological mapping and exploration.
Finding Ourselves in the Universe_ A Mathematical Approach to Cosmic Crystall...Joshua Menges
This thesis discusses using mathematics to approach the concept of cosmic crystallography. It explores representing the universe as a 2-torus or 3-torus, which are topological shapes that repeat themselves. The paper examines what a cosmic crystallographer might observe in different scenarios within a 2D torus universe model, including stationary galaxy clusters, moving clusters, and aging clusters. It touches briefly on possibilities for future work, such as expanding the model to 3D and accounting for galaxy motion within clusters. The background provides context on the shapes of 2D and 3D tori, cosmic crystallography, galaxies in the Local Group including the Milky Way, and stellar classifications.
Another Force Effects On The Earth Moon Motion (III)Gerges francis
Paper Question
-Can the moon orbit regress and the Earth still in its same point in the space If the Earth moon distances after the regression still equal their values before it?
- The paper question tells us that….
- The moon orbit regression is done because of the moon vertical motion and both are done in consistency with a displacement done by Earth vertically for 1 km per solar day…
- I claim that, there are 3 motions done, but only one motion is seen, we have to conclude the 2 rest hidden motions….
o The seen motion is The Moon Orbit Regression
o The 1st hidden motion is the moon vertical motion…that means, the moon in its revolution around The Earth does a vertical motion, and this vertical motion is the reason of the Metonic Cycle (19 sidereal years)
o The 2nd hidden motion is the Earth motion, where the Earth moves daily a vertical displacement = 1 km
- These 3 motions are done in consistency with each other, and depends on each other (this dependency can be seen in a deep analysis for these 3 motions origin)
Paper Objective
- The paper tries to prove the moon vertical motion by using the moon motion data analysis, after this proof , The paper discusses if a vertical displacement of Earth is a necessary requirement for the moon orbit regression, which is done as a result of the moon vertical motion.
Paper 2nd Question
- Why it's necessary to know if the moon has a vertical motion?
- (1st) The moon motion has pauses can't be explained, as we have seen in our tests for (Gerges Equation for the moon orbital motion)… where the moon moves on a solar day a distance = 4000 km (in average) (for example from 384000 km to 388000 km) but we have found that, the moon in perigee & apogee top points stay for many days without change its orbit (for example during 28th, 29th and 30th January 2020, the moon stayed on (404425 km, 405333km, 405111 km)) – how to explain that?
Gerges Francis Tawdrous +201022532292
The Moon Orbit Geometrical Structure Proves The Following Conclusions:
Primary Conclusions
(1) Solar Group Can't be created neither by Big Bang Theory Nor Sun Gravity Concept.
(2) The Solar Group is created of Only One Energy travels through the group
(3) This one Energy creates planets matters (E=mc2 supports that) and planets orbital distances (because Space = Energy –my hypothesis)
(4) Solar Group can be similar to one train and each planet is a carriage of it.
(5) Solar Group can be similar to one machine and each planet is a gear in it
(6) Solar Group can be similar to one building and each planet is a part of it
(7) So, when a planet moves – means - this planet moves as a carriage in one train –all solar planets move together in one general motion
Paper Basic Conclusion:
Energy must be Transported from Jupiter to Earth Moon Orbit
The paper tries to prove this fact
Uma espetacular colisão de galáxias foi descoberta além da Via Láctea. O sistema mais próximo já descoberto, a identificação foi anunciada por uma equipe de astrônomos liderada pelo Professor Quentin Parker da Universidade de Hong Kong e pelo Professor Albert Zijlstra na Universidade de Manchester.
A galáxia está a 30 milhões de anos-luz de distância, o que significa que ela é relativamente próxima. Ela foi chamada de Roda de Kathryn, em homenagem à sua semelhança com o famoso fogo de artifício e também em homenagem à esposa do coautor do trabalho.
Esses sistemas são muito raros e nascem da colisão entre duas galáxias de tamanhos similares. As ondas de choque geradas na colisão comprimem o reservatório de gás em cada galáxia e disparam a formação de novas estrelas. Isso cria um espetacular anel de intensa emissão, e ilumina o sistema, do mesmo modo que a Roda Catherine ilumina a noite num show de fogos de artifício.
As galáxias crescem através de colisões, mas é raro registrar esse processo acontecendo, e é extremamente raro ver o anel da colisão em progresso. Pouco mais de 20 sistemas com anéis completos são conhecidos.
Discovery of a_probable_4_5_jupiter_mass_exoplanet_to_hd95086_by_direct_imagingSérgio Sacani
The document reports the discovery of a probable 4-5 Jupiter-mass exoplanet orbiting the young star HD 95086. Deep imaging observations using VLT/NaCo detected a faint source at a separation of 56 AU from the star. Follow-up observations over more than a year found the source to be co-moving with the star, suggesting it is bound. Its luminosity corresponds to a predicted mass of 4-5 Jupiter masses, making it the lowest mass exoplanet directly imaged around a star. If confirmed, this discovery could provide insights into giant planet formation and evolution.
This document presents a hypothesis that Earth's motion is the source of light energy in the solar system. The author proposes that Earth's velocity around the sun produces a beam of light equal to the supposed velocity of light. Various equations are presented analyzing distances, velocities, and time periods related to Earth's orbit and the orbits of other planets and celestial bodies. The author concludes that Earth is the source of energy for the entire solar system. References are provided for the author's other works on similar topics analyzing planetary motion and trajectories.
Why The Earth Moon Distance = The Planets Diameters Total (I) Gerges francis
The Earth Moon Motion has 4 basic points which are
Perigee radius (perigee is the nearest point, the moon can reach) =363000 km
Earth Moon Distance when the moon is in total solar eclipse point = 373000 km
The Moon Orbital Distance = 384000 km
Apogee radius (Apogee is the most far point, the moon can reach) = 406000 km
Paper Hypotheses
(1)
The Moon Motion 4 points are defined based on Pythagoras Rule
(2)
Jupiter & Saturn cooperate to build the Earth Moon Orbit
Paper Conclusion
There's A Geometrical Necessity Causes "The Earth Moon Distance = The Planets Diameters Total"
Gerges Francis Tawdrous +201022532292
The Internal Structure of Asteroid (25143) Itokawa as Revealed by Detection o...WellingtonRodrigues2014
- The authors detected an acceleration in the rotation rate of asteroid (25143) Itokawa through photometric observations spanning 2001 to 2013.
- By measuring rotational phase offsets between observed and modeled lightcurves, they found a YORP acceleration of 3.54 ± 0.38 × 10−8 rad day−2, equivalent to a decrease in the asteroid's rotation period of about 45 ms per year.
- Thermophysical modeling of the detailed shape model from the Hayabusa spacecraft could not reconcile the observed YORP strength unless the asteroid's center of mass is shifted by about 21 m along its long axis. This suggests Itokawa has two components with different densities that merged, either from a
Exocometary gas in_th_hd_181327_debris_ringSérgio Sacani
An increasing number of observations have shown that gaseous debris discs are not an
exception. However, until now we only knew of cases around A stars. Here we present the first
detection of 12CO (2-1) disc emission around an F star, HD 181327, obtained with ALMA
observations at 1.3 mm. The continuum and CO emission are resolved into an axisymmetric
disc with ring-like morphology. Using a Markov chain Monte Carlo method coupled with
radiative transfer calculations we study the dust and CO mass distribution. We find the dust is
distributed in a ring with a radius of 86:0 0:4 AU and a radial width of 23:2 1:0 AU. At
this frequency the ring radius is smaller than in the optical, revealing grain size segregation
expected due to radiation pressure. We also report on the detection of low level continuum
emission beyond the main ring out to 200 AU. We model the CO emission in the non-LTE
regime and we find that the CO is co-located with the dust, with a total CO gas mass ranging
between 1:2 10 6 M and 2:9 10 6 M, depending on the gas kinetic temperature and
collisional partners densities. The CO densities and location suggest a secondary origin, i.e.
released from icy planetesimals in the ring. We derive a CO cometary composition that is
consistent with Solar system comets. Due to the low gas densities it is unlikely that the gas is
shaping the dust distribution.
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
- The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
-The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
-The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
This document discusses the orbital geometry of the moon through multiple equations and figures. Some key points:
- The moon's orbit uses Pythagorean theorem, with the distance between perigee and apogee (43,000 km) as the base unit to create all other orbital distances.
- The 43,000 km distance is fundamental to the moon's orbital structure and motion, as it is used to concentrate energy into the orbit via Pythagorean relationships.
- Equations show the moon's creation and motion are related to light behavior, with an initial "supposed" light velocity of 1.16 mkm/sec that reduces to the known 0.3 mkm/sec after the moon
This document analyzes the "Moon Orbital Triangle" in an attempt to better understand the moon's motion. It provides details of the triangle, including defining the distances between points and calculating angles. The analysis explores how Pythagorean theorem relates to the moon's daily displacement and orbital inclination. It is suggested that interactions between Venus and Mars affect the moon's regression and create differences in the rate of time, concentrating planetary motion energies into sunlight. References are provided for further related research.
This paper tries to summarize the main ideas and questions in my previous papers -
It's just a guide through my papers – and I add some data for references which can be used in planets data analysis
We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of
the 870 m continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that
trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal
a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli
(1{6AU) with modest contrasts (5{30%). We associate these features with concentrations of solids
that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima.
No signicant non-axisymmetric structures are detected. Some of the observed features occur near
temperatures that may be associated with the condensation fronts of major volatile species, but the
relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the
so-called zonal
ows). Other features, particularly a narrow dark annulus located only 1 AU from the
star, could indicate interactions between the disk and young planets. These data signal that ordered
substructures on AU scales can be common, fundamental factors in disk evolution, and that high
resolution microwave imaging can help characterize them during the epoch of planet formation.
Keywords: protoplanetary disks | planet-disk interactions | stars: individual (TW Hydrae)
The identification of_93_day_periodic_photometric_variability_for_yso_ylw_16aSérgio Sacani
This study identifies a 93 day periodic photometric variability in the Class I young stellar object (YSO) YLW 16A in the Rho Ophiuchus star forming region. Light curve analysis reveals variations of ~0.5 magnitudes in the Ks band over this period. The authors propose a triple system model consisting of an inner binary with a 93 day period eclipsed by a warped circumbinary disk, with a tertiary companion at ~40 AU responsible for warping the disk. This model is similar to one previously proposed for another YSO, WL 4, and may indicate such triple systems with eclipsing disks are common around young stars. Understanding these systems can provide insights into stellar and planetary formation and evolution.
Paper Hypothesis
-There's Another Similar Orbit For The Moon Motion
The Hypothesis explanation
- The triangle ACE shows that, a double value of the triangle perimeter is used for geometrical necessities in the moon orbital motion
- i.e.
- While the (ACE) triangle perimeter = 943817 km, the geometrical structure of the moon orbit uses the value 1887634 km (= 2 x 943817 km) as one of the basic motion values.
- There's one more reason for this hypothesis, because the moon orbital motion space area contains (50%) of the Jupiter Whole Energy, that tells if the energy is transported to the moon orbit why just (50%) only?
- I suggest that
- Another similar orbit of the moon must be found which we can't see. This idea is supported by our previous argument, where the moon moves daily 2.58 mkm (as Earth) and because of the contraction this value became 2.41 mkm, So the tries to cover this difference (0.17 mkm) by its daily displacement (88000km) which is not enough and the moon needs to move another displacement (88000km) to cover the different distance, where this last displacement (88000km) we can't see, and based on that I suppose the moon must have another similar orbit through which the moon moves this additional displacement (88000km).
- The paper tries to prove this fact
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) Gerges francis
The document discusses the moon's orbital motion and proposes that it uses Pythagorean triangles. It argues that the moon's four basic orbital points (perigee, apogee, eclipse radius, orbital distance) are defined by Pythagorean equations using 86,000 km as the constant leg length. This suggests the moon employs Pythagorean triangles in its orbit. The triangles allow the moon to move in closer orbits while maintaining its daily 88,000 km displacement. The real displacement through its orbit depends on the angle θ, which defines orbital height. The motion is proposed to change daily by 0.985 degrees due to needing to match the Earth's motion. There are hints of a second force and orbit affecting the moon.
The atacama cosmology_telescope_measuring_radio_galaxy_bias_through_cross_cor...Sérgio Sacani
A radiação cósmica de micro-ondas aponta para a matéria escura invisível, marcando o ponto onde jatos de material viajam a velocidades próximas da velocidade da luz, de acordo com uma equipe internacional de astrônomos. O principal autor do estudo, Rupert Allison da Universidade de Oxford apresentou os resultados no dia 6 de Julho de 2015 no National Astronomy Meeting em Venue Cymru, em Llandudno em Wales.
Atualmente, ninguém sabe ao certo do que a matéria escura é feita, mas ela é responsável por cerca de 26% do conteúdo de energia do universo, com galáxias massivas se formando em densas regiões de matéria escura. Embora invisível, a matéria escura se mostra através do efeito gravitacional – uma grande bolha de matéria escura puxa a matéria normal (como elétrons, prótons e nêutrons) através de sua própria gravidade, eventualmente se empacotando conjuntamente para criar as estrelas e galáxias inteiras.
Muitas das maiores dessas são galáxias ativas com buracos negros supermassivos em seus centros. Alguma parte do gás caindo diretamente na direção do buraco negro é ejetada como jatos de partículas e radiação. As observações feitas com rádio telescópios mostram que esses jatos as vezes se espalham por milhões de anos-luz desde a galáxia – mais distante até mesmo do que a extensão da própria galáxia.
Os cientistas esperam que os jatos possam viver em regiões onde existe um excesso de concentração da matéria escura, maior do que o da média. Mas como a matéria escura é invisível, testar essa ideia não é algo tão direto.
"Research Hypothesis"
Solar Planets Data Are Created Based On One Equation Only
The Hypothesis Explanation
Solar planets data such as Planet Diameter – Orbital Distance – Orbital Period - Orbital Inclination- Axial Tilt…..etc
All this data is created based on One Equation Only
This paper has 3 objectives which are:
1st to prove the research hypothesis
2nd to explain "how to analyze planets data to conclude the geometrical rules behind it"
3rd to discuss the theoretical basics, on which this one equation is created
EXTINCTION AND THE DIMMING OF KIC 8462852Sérgio Sacani
To test alternative hypotheses for the behavior of KIC 8462852, we obtained measurements of the star
over a wide wavelength range from the UV to the mid-infrared from October 2015 through December
2016, using Swift, Spitzer and at AstroLAB IRIS. The star faded in a manner similar to the longterm
fading seen in Kepler data about 1400 days previously. The dimming rate for the entire period
reported is 22.1 ± 9.7 milli-mag yr−1
in the Swift wavebands, with amounts of 21.0 ± 4.5 mmag in
the groundbased B measurements, 14.0 ± 4.5 mmag in V , and 13.0 ± 4.5 in R, and a rate of 5.0 ± 1.2
mmag yr−1 averaged over the two warm Spitzer bands. Although the dimming is small, it is seen at
& 3 σ by three different observatories operating from the UV to the IR. The presence of long-term
secular dimming means that previous SED models of the star based on photometric measurements
taken years apart may not be accurate. We find that stellar models with Tef f = 7000 - 7100 K and
AV ∼ 0.73 best fit the Swift data from UV to optical. These models also show no excess in the
near-simultaneous Spitzer photometry at 3.6 and 4.5 µm, although a longer wavelength excess from
a substantial debris disk is still possible (e.g., as around Fomalhaut). The wavelength dependence of
the fading favors a relatively neutral color (i.e., RV & 5, but not flat across all the bands) compared
with the extinction law for the general ISM (RV = 3.1), suggesting that the dimming arises from
circumstellar material
WHERE IS THE FLUX GOING? THE LONG-TERM PHOTOMETRIC VARIABILITY OF BOYAJIAN’S ...Sérgio Sacani
We present ∼ 800 days of photometric monitoring of Boyajian’s Star (KIC 8462852) from the AllSky
Automated Survey for Supernovae (ASAS-SN) and ∼ 4000 days of monitoring from the All Sky
Automated Survey (ASAS). We show that from 2015 to the present the brightness of Boyajian’s Star
has steadily decreased at a rate of 6.3 ± 1.4 mmag yr−1
, such that the star is now 1.5% fainter than it
was in February 2015. Moreover, the longer time baseline afforded by ASAS suggests that Boyajian’s
Star has also undergone two brightening episodes in the past 11 years, rather than only exhibiting a
monotonic decline. We analyze a sample of ∼ 1000 comparison stars of similar brightness located in
the same ASAS-SN field and demonstrate that the recent fading is significant at & 99.4% confidence.
The 2015 − 2017 dimming rate is consistent with that measured with Kepler data for the time period
from 2009 to 2013. This long-term variability is difficult to explain with any of the physical models
for the star’s behavior proposed to date
Abstract
Paper Question
How to form the required hypothesis?
The Question Explanation
- The data analysis method 1st step is (The Directed Data Definition)
- The data analysis method 2nd step is (The hypothesis formation)
- The hypothesis is the task without which the data can't create any meaning.
- The hypothesis basically tries to answer (How the directed data is created?)
- Sometimes the data be so difficult to enable any hypothesis to be formed but the hypothesis is a basic step can't be canceled, in this case such data can not be used.
Gerges Francis Tawdrous +201022532292
This document summarizes the key differences between mitosis and meiosis. Mitosis involves the division of somatic cells, resulting in two identical daughter cells. It progresses through interphase, prophase, metaphase, anaphase and telophase. Meiosis produces gametes through two divisions and results in four daughter cells each with half the number of chromosomes as the original parent cell. The stages of mitosis are described in more detail.
The document provides an overview of the Laps for CF communication plan including:
- An introduction of the team developing the plan.
- A situation analysis reviewing Laps for CF's organizational profile, past events, website, social media presence, and competitive landscape.
- Details on the plan's goals of increasing awareness of Laps for CF at UA and increasing attendance and funding at events.
- An outline of research conducted, a SWOT analysis, and strategic recommendations to meet the plan's objectives.
This document presents a hypothesis that Earth's motion is the source of light energy in the solar system. The author proposes that Earth's velocity around the sun produces a beam of light equal to the supposed velocity of light. Various equations are presented analyzing distances, velocities, and time periods related to Earth's orbit and the orbits of other planets and celestial bodies. The author concludes that Earth is the source of energy for the entire solar system. References are provided for the author's other works on similar topics analyzing planetary motion and trajectories.
Why The Earth Moon Distance = The Planets Diameters Total (I) Gerges francis
The Earth Moon Motion has 4 basic points which are
Perigee radius (perigee is the nearest point, the moon can reach) =363000 km
Earth Moon Distance when the moon is in total solar eclipse point = 373000 km
The Moon Orbital Distance = 384000 km
Apogee radius (Apogee is the most far point, the moon can reach) = 406000 km
Paper Hypotheses
(1)
The Moon Motion 4 points are defined based on Pythagoras Rule
(2)
Jupiter & Saturn cooperate to build the Earth Moon Orbit
Paper Conclusion
There's A Geometrical Necessity Causes "The Earth Moon Distance = The Planets Diameters Total"
Gerges Francis Tawdrous +201022532292
The Internal Structure of Asteroid (25143) Itokawa as Revealed by Detection o...WellingtonRodrigues2014
- The authors detected an acceleration in the rotation rate of asteroid (25143) Itokawa through photometric observations spanning 2001 to 2013.
- By measuring rotational phase offsets between observed and modeled lightcurves, they found a YORP acceleration of 3.54 ± 0.38 × 10−8 rad day−2, equivalent to a decrease in the asteroid's rotation period of about 45 ms per year.
- Thermophysical modeling of the detailed shape model from the Hayabusa spacecraft could not reconcile the observed YORP strength unless the asteroid's center of mass is shifted by about 21 m along its long axis. This suggests Itokawa has two components with different densities that merged, either from a
Exocometary gas in_th_hd_181327_debris_ringSérgio Sacani
An increasing number of observations have shown that gaseous debris discs are not an
exception. However, until now we only knew of cases around A stars. Here we present the first
detection of 12CO (2-1) disc emission around an F star, HD 181327, obtained with ALMA
observations at 1.3 mm. The continuum and CO emission are resolved into an axisymmetric
disc with ring-like morphology. Using a Markov chain Monte Carlo method coupled with
radiative transfer calculations we study the dust and CO mass distribution. We find the dust is
distributed in a ring with a radius of 86:0 0:4 AU and a radial width of 23:2 1:0 AU. At
this frequency the ring radius is smaller than in the optical, revealing grain size segregation
expected due to radiation pressure. We also report on the detection of low level continuum
emission beyond the main ring out to 200 AU. We model the CO emission in the non-LTE
regime and we find that the CO is co-located with the dust, with a total CO gas mass ranging
between 1:2 10 6 M and 2:9 10 6 M, depending on the gas kinetic temperature and
collisional partners densities. The CO densities and location suggest a secondary origin, i.e.
released from icy planetesimals in the ring. We derive a CO cometary composition that is
consistent with Solar system comets. Due to the low gas densities it is unlikely that the gas is
shaping the dust distribution.
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
- The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
-The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) (Revised) Gerges francis
Paper hypothesis:
-The moon orbital motion causes the moon orbit regression 19 degrees per sidereal year (365.25 days)
Paper Argument:
The Moon Orbital Triangle Basic Uses:
(1) The moon uses Pythagoras triangle as one of its orbital motion techniques, based on that, the triangle supports the moon motion equation definition.
(2) There's 2nd force effects on the moon orbital motion and this force can be concluded from the moon orbital triangle
(3) There's 2nd orbit for the moon motion, and this orbit can be discovered by the moon orbital triangle data analysis
(4) The moon orbital triangle declination angle (1.1 degrees) on the horizontal level has a massive geometrical effect on the moon motion.
(5) The triangle shows that, the moon daily displacement (88000 km) is defined based on geometrical rules.
(6) The Triangle shows why the moon can't move beyond apogee orbit (r= 0.406 mkm).
Paper conclusion:
1. Earth Does A Displacement As A Result Of The Moon Orbit Regression.
2. Earth and its moon motions are interacted with each deeply
Gerges Francis Tawdrous +201022532292
This document discusses the orbital geometry of the moon through multiple equations and figures. Some key points:
- The moon's orbit uses Pythagorean theorem, with the distance between perigee and apogee (43,000 km) as the base unit to create all other orbital distances.
- The 43,000 km distance is fundamental to the moon's orbital structure and motion, as it is used to concentrate energy into the orbit via Pythagorean relationships.
- Equations show the moon's creation and motion are related to light behavior, with an initial "supposed" light velocity of 1.16 mkm/sec that reduces to the known 0.3 mkm/sec after the moon
This document analyzes the "Moon Orbital Triangle" in an attempt to better understand the moon's motion. It provides details of the triangle, including defining the distances between points and calculating angles. The analysis explores how Pythagorean theorem relates to the moon's daily displacement and orbital inclination. It is suggested that interactions between Venus and Mars affect the moon's regression and create differences in the rate of time, concentrating planetary motion energies into sunlight. References are provided for further related research.
This paper tries to summarize the main ideas and questions in my previous papers -
It's just a guide through my papers – and I add some data for references which can be used in planets data analysis
We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of
the 870 m continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that
trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal
a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli
(1{6AU) with modest contrasts (5{30%). We associate these features with concentrations of solids
that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima.
No signicant non-axisymmetric structures are detected. Some of the observed features occur near
temperatures that may be associated with the condensation fronts of major volatile species, but the
relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the
so-called zonal
ows). Other features, particularly a narrow dark annulus located only 1 AU from the
star, could indicate interactions between the disk and young planets. These data signal that ordered
substructures on AU scales can be common, fundamental factors in disk evolution, and that high
resolution microwave imaging can help characterize them during the epoch of planet formation.
Keywords: protoplanetary disks | planet-disk interactions | stars: individual (TW Hydrae)
The identification of_93_day_periodic_photometric_variability_for_yso_ylw_16aSérgio Sacani
This study identifies a 93 day periodic photometric variability in the Class I young stellar object (YSO) YLW 16A in the Rho Ophiuchus star forming region. Light curve analysis reveals variations of ~0.5 magnitudes in the Ks band over this period. The authors propose a triple system model consisting of an inner binary with a 93 day period eclipsed by a warped circumbinary disk, with a tertiary companion at ~40 AU responsible for warping the disk. This model is similar to one previously proposed for another YSO, WL 4, and may indicate such triple systems with eclipsing disks are common around young stars. Understanding these systems can provide insights into stellar and planetary formation and evolution.
Paper Hypothesis
-There's Another Similar Orbit For The Moon Motion
The Hypothesis explanation
- The triangle ACE shows that, a double value of the triangle perimeter is used for geometrical necessities in the moon orbital motion
- i.e.
- While the (ACE) triangle perimeter = 943817 km, the geometrical structure of the moon orbit uses the value 1887634 km (= 2 x 943817 km) as one of the basic motion values.
- There's one more reason for this hypothesis, because the moon orbital motion space area contains (50%) of the Jupiter Whole Energy, that tells if the energy is transported to the moon orbit why just (50%) only?
- I suggest that
- Another similar orbit of the moon must be found which we can't see. This idea is supported by our previous argument, where the moon moves daily 2.58 mkm (as Earth) and because of the contraction this value became 2.41 mkm, So the tries to cover this difference (0.17 mkm) by its daily displacement (88000km) which is not enough and the moon needs to move another displacement (88000km) to cover the different distance, where this last displacement (88000km) we can't see, and based on that I suppose the moon must have another similar orbit through which the moon moves this additional displacement (88000km).
- The paper tries to prove this fact
Gerges Francis Tawdrous +201022532292
The Moon Orbital Triangle (General discussion) (V) Gerges francis
The document discusses the moon's orbital motion and proposes that it uses Pythagorean triangles. It argues that the moon's four basic orbital points (perigee, apogee, eclipse radius, orbital distance) are defined by Pythagorean equations using 86,000 km as the constant leg length. This suggests the moon employs Pythagorean triangles in its orbit. The triangles allow the moon to move in closer orbits while maintaining its daily 88,000 km displacement. The real displacement through its orbit depends on the angle θ, which defines orbital height. The motion is proposed to change daily by 0.985 degrees due to needing to match the Earth's motion. There are hints of a second force and orbit affecting the moon.
The atacama cosmology_telescope_measuring_radio_galaxy_bias_through_cross_cor...Sérgio Sacani
A radiação cósmica de micro-ondas aponta para a matéria escura invisível, marcando o ponto onde jatos de material viajam a velocidades próximas da velocidade da luz, de acordo com uma equipe internacional de astrônomos. O principal autor do estudo, Rupert Allison da Universidade de Oxford apresentou os resultados no dia 6 de Julho de 2015 no National Astronomy Meeting em Venue Cymru, em Llandudno em Wales.
Atualmente, ninguém sabe ao certo do que a matéria escura é feita, mas ela é responsável por cerca de 26% do conteúdo de energia do universo, com galáxias massivas se formando em densas regiões de matéria escura. Embora invisível, a matéria escura se mostra através do efeito gravitacional – uma grande bolha de matéria escura puxa a matéria normal (como elétrons, prótons e nêutrons) através de sua própria gravidade, eventualmente se empacotando conjuntamente para criar as estrelas e galáxias inteiras.
Muitas das maiores dessas são galáxias ativas com buracos negros supermassivos em seus centros. Alguma parte do gás caindo diretamente na direção do buraco negro é ejetada como jatos de partículas e radiação. As observações feitas com rádio telescópios mostram que esses jatos as vezes se espalham por milhões de anos-luz desde a galáxia – mais distante até mesmo do que a extensão da própria galáxia.
Os cientistas esperam que os jatos possam viver em regiões onde existe um excesso de concentração da matéria escura, maior do que o da média. Mas como a matéria escura é invisível, testar essa ideia não é algo tão direto.
"Research Hypothesis"
Solar Planets Data Are Created Based On One Equation Only
The Hypothesis Explanation
Solar planets data such as Planet Diameter – Orbital Distance – Orbital Period - Orbital Inclination- Axial Tilt…..etc
All this data is created based on One Equation Only
This paper has 3 objectives which are:
1st to prove the research hypothesis
2nd to explain "how to analyze planets data to conclude the geometrical rules behind it"
3rd to discuss the theoretical basics, on which this one equation is created
EXTINCTION AND THE DIMMING OF KIC 8462852Sérgio Sacani
To test alternative hypotheses for the behavior of KIC 8462852, we obtained measurements of the star
over a wide wavelength range from the UV to the mid-infrared from October 2015 through December
2016, using Swift, Spitzer and at AstroLAB IRIS. The star faded in a manner similar to the longterm
fading seen in Kepler data about 1400 days previously. The dimming rate for the entire period
reported is 22.1 ± 9.7 milli-mag yr−1
in the Swift wavebands, with amounts of 21.0 ± 4.5 mmag in
the groundbased B measurements, 14.0 ± 4.5 mmag in V , and 13.0 ± 4.5 in R, and a rate of 5.0 ± 1.2
mmag yr−1 averaged over the two warm Spitzer bands. Although the dimming is small, it is seen at
& 3 σ by three different observatories operating from the UV to the IR. The presence of long-term
secular dimming means that previous SED models of the star based on photometric measurements
taken years apart may not be accurate. We find that stellar models with Tef f = 7000 - 7100 K and
AV ∼ 0.73 best fit the Swift data from UV to optical. These models also show no excess in the
near-simultaneous Spitzer photometry at 3.6 and 4.5 µm, although a longer wavelength excess from
a substantial debris disk is still possible (e.g., as around Fomalhaut). The wavelength dependence of
the fading favors a relatively neutral color (i.e., RV & 5, but not flat across all the bands) compared
with the extinction law for the general ISM (RV = 3.1), suggesting that the dimming arises from
circumstellar material
WHERE IS THE FLUX GOING? THE LONG-TERM PHOTOMETRIC VARIABILITY OF BOYAJIAN’S ...Sérgio Sacani
We present ∼ 800 days of photometric monitoring of Boyajian’s Star (KIC 8462852) from the AllSky
Automated Survey for Supernovae (ASAS-SN) and ∼ 4000 days of monitoring from the All Sky
Automated Survey (ASAS). We show that from 2015 to the present the brightness of Boyajian’s Star
has steadily decreased at a rate of 6.3 ± 1.4 mmag yr−1
, such that the star is now 1.5% fainter than it
was in February 2015. Moreover, the longer time baseline afforded by ASAS suggests that Boyajian’s
Star has also undergone two brightening episodes in the past 11 years, rather than only exhibiting a
monotonic decline. We analyze a sample of ∼ 1000 comparison stars of similar brightness located in
the same ASAS-SN field and demonstrate that the recent fading is significant at & 99.4% confidence.
The 2015 − 2017 dimming rate is consistent with that measured with Kepler data for the time period
from 2009 to 2013. This long-term variability is difficult to explain with any of the physical models
for the star’s behavior proposed to date
Abstract
Paper Question
How to form the required hypothesis?
The Question Explanation
- The data analysis method 1st step is (The Directed Data Definition)
- The data analysis method 2nd step is (The hypothesis formation)
- The hypothesis is the task without which the data can't create any meaning.
- The hypothesis basically tries to answer (How the directed data is created?)
- Sometimes the data be so difficult to enable any hypothesis to be formed but the hypothesis is a basic step can't be canceled, in this case such data can not be used.
Gerges Francis Tawdrous +201022532292
This document summarizes the key differences between mitosis and meiosis. Mitosis involves the division of somatic cells, resulting in two identical daughter cells. It progresses through interphase, prophase, metaphase, anaphase and telophase. Meiosis produces gametes through two divisions and results in four daughter cells each with half the number of chromosomes as the original parent cell. The stages of mitosis are described in more detail.
The document provides an overview of the Laps for CF communication plan including:
- An introduction of the team developing the plan.
- A situation analysis reviewing Laps for CF's organizational profile, past events, website, social media presence, and competitive landscape.
- Details on the plan's goals of increasing awareness of Laps for CF at UA and increasing attendance and funding at events.
- An outline of research conducted, a SWOT analysis, and strategic recommendations to meet the plan's objectives.
HR Driving the Business of the BusinessAnil Saxena
This is a presentation built around a session I lead. The purpose of this session is to support the movement that HR is a unique position to be a primal force in driving organizational performance:
o Increasing Market-share
o Driving customer loyalty
o Enabling positive public perception
o and so much more
“The senior HR executive [needs to be] a business person first and an HR leader second. They need to decipher and deliver.” - Claude Balthazard and Susan Robinson
Senior HR leaders drive and create the nexus of the where the business and the only resource that appreciates meet, its people.
But how does that happen? How does all of HR become an integral tool to drive overall organizational performance in measures that matter to business leaders - increased revenue, increased sales per customer, lower customer acquisition costs, and all the other measures that senior leaders make decisions based upon?
By leading the effort to become a Culture of Performance.
Teaching strategies for disabled students 2diegolopezhtg
This document discusses best practices for giving instructions to students, particularly those with special needs. It emphasizes that instructions should be explicit, clear, simple, and given in "bite-sized chunks". It also stresses the importance of having students repeat back instructions to ensure understanding, giving both written and verbal instructions, and repeating instructions multiple times. Chunking instructions into smaller pieces and having students tell or show what they are supposed to do helps reduce confusion and frustration for students with special needs. Overall, the document provides guidance on structuring instructions in a way that makes them easiest for all students to understand.
Tiga kalimat ringkasan dokumen tersebut adalah:
Dokumen tersebut membahas tentang sokongan dan pergerakan pada manusia dan haiwan, termasuk struktur dan fungsi rangka manusia, peranan otot dan ligamen dalam pergerakan, serta mekanisme pergerakan cacing tanah, belalang, dan ikan.
Dokumen tersebut membahas tempat-tempat wisata di Jawa Barat yang layak dikunjungi, seperti Pantai Pelabuhan Ratu dengan ombak besar untuk berselancar, Curug Cikaso dengan tiga air terjun setinggi 80 meter, dan Taman Wisata Mekarsari seluas 264 hektar yang kaya akan tanaman.
The document discusses different types of radiation and their interaction with matter. It describes four main types: alpha particles, beta particles, x-rays and gamma rays, and neutrons. It provides details on each type, including their penetration abilities, the processes by which they interact with atoms like ionization and excitation, and the effects they can cause like damage from energy deposition.
This document is the GNU Library General Public License which guarantees users' freedom to share and change libraries. It allows developers to use free libraries in non-free programs while preserving users' freedom to modify libraries. The license requires libraries distributed under it to provide users with complete source code and ensure modified versions remain freely distributable.
This document provides information about T. Rowe Price's European equity funds and investment approach. It discusses:
- T. Rowe Price's global reach and local expertise in managing over $478 billion in assets.
- Their investment process focuses on fundamental research, a collaborative culture, and disciplined process. They have 20 analysts dedicated to researching European companies.
- Their European equity fund range includes funds focused on various market caps and regions within Europe, managed by experienced portfolio managers following a bottom-up stock selection strategy.
- The funds aim to outperform benchmarks with similar risk, through identifying undervalued quality businesses and avoiding style constraints. Research is a core strength with over 130 analysts worldwide.
This document discusses identity, diaspora, and the future in a changing world. It notes that the traditional view of a clearly defined identity and culture may no longer exist as globalization and new technologies have led to constant shifting over time. Diaspora groups are going more global due to factors like increased population mobility, growth and immigration, rising remittances, and improved communications. While new social organizing and access to other cultures is easier in this environment, it also makes privacy and intellectual property harder to protect. Overall, the structures that determine our behaviors and identities are rapidly changing in complex, non-linear ways.
Investigation of the Tidal Migration of 'Hot' Jupiters Calum Hervieu
This document is a thesis written by Calum Hervieu that investigates the formation of "hot Jupiters" through N-body simulations. It first provides background on hot Jupiters and their traditional formation theory involving migration through the protoplanetary disk. However, recent observations have found some hot Jupiters on inclined orbits, inconsistent with this theory. The thesis then proposes an alternative formation mechanism involving three-body Kozai-Lidov cycles that can tilt the orbits. It describes developing an N-body code to simulate this process and test its ability to reproduce the observations. The results agree with the hypotheses, implying the code and underlying physics are valid.
This document is a thesis that analyzes the fundamental plane of 203 early type galaxies in the Coma cluster across multiple wavelength bands. It finds a fundamental plane in the r-band with coefficients a3D = 1.22, b3D = -0.82, and aXFP = 1.05. A positive correlation is seen between galaxy properties like Sérsic index and velocity dispersion. The fundamental plane is successfully plotted across ugrizJHK bands and a color-magnitude relation is observed peaking in the H-band. Coefficients a and intrinsic scatter are found to relate to wavelength, agreeing with previous studies. Ellipticals and S0 galaxies produce similar fundamental planes.
Jupiter atmosphere and magnetosphere exploration satelliteReetam Singh
The document describes the Jupiter Atmosphere and Magnetosphere Exploration Satellite (JAMES) mission. JAMES aims to study Jupiter's atmosphere, magnetosphere, moons and radiation environment. Its scientific goals are to investigate atmospheric conditions on Jupiter, the possibility of habitable environments within the Jovian system, and to map and study Jupiter's magnetosphere and auroras. JAMES will carry instrumentation including a camera, magnetometer, energetic particle detector, plasma wave detector, and dust detector to achieve these goals and provide data on Jupiter's formation and evolution.
This document is a student thesis on star formation studies using the Herschel space observatory. It provides background on pre-stellar cores, the core mass function (CMF), and how the CMF relates to the initial mass function (IMF). The student analyzed data from Herschel to locate pre-stellar cores in the Aquila rift and construct a CMF. Comparing their CMF to a previous study, they found their calculated CMF was five orders of magnitude smaller, likely due to errors in their mass calculation method and aperture size/shape used.
This document is a master's thesis that conducts an asteroseismic study of the binary star system α Centauri. It begins with introductions to asteroseismology and stellar oscillations. It then describes the stellar system α Centauri and previous studies of its components. The thesis presents an observational study of α Centauri A using time series photometry and spectroscopy. Frequencies of stellar oscillations are extracted from this data and compared to theoretical stellar models. This allows constraints to be placed on the internal structure and evolutionary state of α Centauri A.
This document summarizes research on the habitable zones around stars and the habitability of exoplanets. It discusses how the habitable zone is defined as the region where liquid water could exist on a planet's surface. The inner and outer edges of the habitable zone are modeled based on factors like the runaway greenhouse effect and CO2 condensation limits. Current exoplanet detection methods are also overviewed. While over 20 potentially habitable exoplanets have been identified, confirming life remains difficult due to natural phenomena creating false biosignatures. However, an inhabited exoplanet may be confirmed in the near future as detection capabilities continue advancing rapidly.
This document summarizes research determining the orbit of the potentially hazardous asteroid 2102 Tantalus. Four sets of images of the asteroid were taken using ground-based telescopes. The images were analyzed to determine the asteroid's position over time. Its right ascension and declination were calculated using a least squares plate reduction program. Photometry of the images found apparent magnitudes ranging from 16.0 to 17.5. The orbital elements of the asteroid, including eccentricity, semimajor axis, and inclination, were computed using the method of Gauss. The research provides an improved model of 2102 Tantalus' long-term trajectory.
Locating Hidden Exoplanets in ALMA Data Using Machine LearningSérgio Sacani
Exoplanets in protoplanetary disks cause localized deviations from Keplerian velocity in channel
maps of molecular line emission. Current methods of characterizing these deviations are time consuming, and there is no unified standard approach. We demonstrate that machine learning can quickly
and accurately detect the presence of planets. We train our model on synthetic images generated from
simulations and apply it to real observations to identify forming planets in real systems. Machine
learning methods, based on computer vision, are not only capable of correctly identifying the presence
of one or more planets, but they can also correctly constrain the location of those planets.
Study of mars and mars retrograde from the year 2000 – 2022 and the brief stu...IRJET Journal
1. Retrogrades are an optical illusion where Mars appears to move backwards in its orbit from Earth's frame of reference, occurring every 26 months. They are caused by the difference in orbital speeds between Earth and Mars.
2. Recent Mars retrogrades were observed and captured in images in 2003, 2005, 2006, 2016, and 2020. The 2016 retrograde was also observed from Mars by the Curiosity rover, showing Earth in retrograde motion.
3. Retrogrades are not actual changes in orbital paths but illusions due to the relative positions and motions of Earth and Mars in their elliptical orbits around the Sun, which have different distances and speeds. Pseudoscientific claims about their effects have
Locating Hidden Exoplanets in ALMA Data Using Machine LearningSérgio Sacani
Exoplanets in protoplanetary disks cause localized deviations from Keplerian velocity in channel maps of
molecular line emission. Current methods of characterizing these deviations are time consuming,and there is no
unified standard approach. We demonstrate that machine learning can quickly and accurately detect the presence of
planets. We train our model on synthetic images generated from simulations and apply it to real observations to
identify forming planets in real systems. Machine-learning methods, based on computer vision, are not only
capable of correctly identifying the presence of one or more planets, but they can also correctly constrain the
location of those planets.
This document describes a C++ program called CRadtran that calculates microwave radiance from the atmosphere. It presents the radiative transfer equation that models how intensity changes as light travels through atmospheric layers. The atmosphere is divided into thin slices where temperature, pressure, and attenuation are constant. The change in intensity is calculated for each slice using the radiative transfer equation, accounting for emission and absorption. Integrating the intensity changes across all slices allows determining the upwelling microwave radiance from the top of the atmosphere. This program improves on an older FORTRAN model by being more readable and usable.
This dissertation consists of two projects related to microlensing and dark energy:
1) The first project uses microlensing population models and color-magnitude diagrams to constrain the locations of 13 microlensing source stars and lenses detected in the Large Magellanic Cloud. The analysis suggests the source stars are in the LMC disk and the lenses are in the Milky Way halo.
2) The second project uses Markov chain Monte Carlo analysis of an inverse power law quintessence model to study constraints from future dark energy experiments. Simulated data sets representing different experiments are used to examine how well experiments can constrain the model and distinguish it from a cosmological constant. Stage 4 experiments may exclude a cosmological constant at the 3σ
The Sparkler: Evolved High-redshift Globular Cluster Candidates Captured by JWSTSérgio Sacani
This document discusses compact red sources detected around a strongly lensed galaxy ("the Sparkler") at a redshift of 1.378 using JWST data. Photometry and morphological fits of the sources suggest they are spatially unresolved, very red, and consistent with old stellar populations. Spectroscopy shows emission from the galaxy but no signs of star formation in the red sources. The sources are most likely evolved globular clusters dating back to formation redshifts between 7-11, corresponding to ages of 3.9-4.1 billion years at the time of observation. If confirmed, these would be the first observed globular clusters at high redshift, opening a window into early globular cluster formation in the first billion years of
Dynamical instabilities among giant planets are thought to be nearly ubiquitous, and culminate in the ejection of one or more
planets into interstellar space. Here we perform N-body simulations of dynamical instabilities while accounting for torques from
the galactic tidal field. We find that a fraction of planets that would otherwise have been ejected are instead trapped on very wide
orbits analogous to those of Oort cloud comets. The fraction of ejected planets that are trapped ranges from 1-10%, depending
on the initial planetary mass distribution. The local galactic density has a modest effect on the trapping efficiency and the orbital
radii of trapped planets. The majority of Oort cloud planets survive for Gyr timescales. Taking into account the demographics of
exoplanets, we estimate that one in every 200-3000 stars could host an Oort cloud planet. This value is likely an overestimate, as
we do not account for instabilities that take place at early enough times to be affected by their host stars’ birth cluster, or planet
stripping from passing stars. If the Solar System’s dynamical instability happened after birth cluster dissolution, there is a ∼7%
chance that an ice giant was captured in the Sun’s Oort cloud.
This document is a senior thesis submitted by Taylor Hugh Morgan to Brigham Young University investigating the post-Newtonian three-body problem. It explores the chaotic nature of three-body gravitational interactions using a numerical integration of the post-Newtonian equations of motion. The author finds that including gravitational radiation and general relativistic effects leads to more black hole formations than in Newtonian gravity. The author also looks at systems discovered by the Kepler Space Telescope to refine mass bounds of stability, finding that the post-Newtonian approximation does not significantly change the bounds.
The Possible Tidal Demise of Kepler’s First Planetary SystemSérgio Sacani
We present evidence of tidally-driven inspiral in the Kepler-1658 (KOI-4) system, which consists of a giant planet
(1.1RJ, 5.9MJ) orbiting an evolved host star (2.9Re, 1.5Me). Using transit timing measurements from Kepler,
Palomar/WIRC, and TESS, we show that the orbital period of Kepler-1658b appears to be decreasing at a rate = -
+ P 131 22
20 ms yr−1
, corresponding to an infall timescale P P » 2.5 Myr. We consider other explanations for the
data including line-of-sight acceleration and orbital precession, but find them to be implausible. The observed
period derivative implies a tidal quality factor
¢ = ´ -
+ Q 2.50 10 0.62
0.85 4, in good agreement with theoretical
predictions for inertial wave dissipation in subgiant stars. Additionally, while it probably cannot explain the entire
inspiral rate, a small amount of planetary dissipation could naturally explain the deep optical eclipse observed for
the planet via enhanced thermal emission. As the first evolved system with detected inspiral, Kepler-1658 is a new
benchmark for understanding tidal physics at the end of the planetary life cycle
The internal structure_of_asteroid_itokawa_as_revealed_by_detection_of_yorp_s...Sérgio Sacani
The study detected an acceleration in the rotation rate of asteroid (25143) Itokawa through long-term photometric monitoring between 2001-2013. By measuring rotational phase offsets between observed and modeled lightcurves, a YORP acceleration of 3.54 ± 0.38 × 10−8 rad day−2 was measured, equivalent to a decrease in the asteroid's rotation period of about 45 ms per year. Thermophysical analysis of the detailed shape model from the Hayabusa spacecraft found that the center-of-mass must be offset by about 21 m along the long axis to reconcile the observed and theoretical YORP strengths, suggesting Itokawa is composed of two separate bodies with densities of 1750 ± 110 kg m
This dissertation examines the stability and nonlinear evolution of an idealized hurricane model. The author uses the quasi-geostrophic shallow water equations to model the hurricane as a simple axisymmetric annular vortex with a predefined potential vorticity distribution. Both single-layered and two-layered models are considered. For the single-layer case, linear stability analysis reveals barotropic and baroclinic instabilities that depend on parameters like the potential vorticity within the core and the Rossby deformation length. Nonlinear simulations then show how the annular structure breaks down in different ways depending on these parameters. For the two-layer case, linear stability is found to be identical to the single-layer case, and phase diagrams
Learning Geometric Algebra by Modeling Motions of the Earth and Shadows of Gn...James Smith
Because the shortage of worked-out examples at introductory levels is an obstacle to widespread adoption of Geometric Algebra (GA), we use GA to calculate Solar azimuths and altitudes as a function of time via the heliocentric model. We begin by representing the Earth's motions in GA terms. Our representation incorporates an estimate of the time at which the Earth would have reached perihelion in 2017 if not affected by the Moon's gravity. Using the geometry of the December 2016 solstice as a starting point, we then employ GA's capacities for handling rotations to determine the orientation of a gnomon at any given latitude and longitude during the period between the December solstices of 2016 and 2017. Subsequently, we derive equations for two angles: that between the Sun's rays and the gnomon's shaft, and that between the gnomon's shadow and the direction ``north" as traced on the ground at the gnomon's location. To validate our equations, we convert those angles to Solar azimuths and altitudes for comparison with simulations made by the program Stellarium. As further validation, we analyze our equations algebraically to predict (for example) the precise timings and locations of sunrises, sunsets, and Solar zeniths on the solstices and equinoxes. We emphasize that the accuracy of the results is only to be expected, given the high accuracy of the heliocentric model itself, and that the relevance of this work is the efficiency with which that model can be implemented via GA for teaching at the introductory level. On that point, comments and debate are encouraged and welcome.
Similar to Irina Goriatcheva - Stability Analysis of Companions Ups And (20)
Learning Geometric Algebra by Modeling Motions of the Earth and Shadows of Gn...
Irina Goriatcheva - Stability Analysis of Companions Ups And
1. UNIVERSITY of CALIFORNIA
SANTA CRUZ
STABILITY ANALYSIS OF THE COMPANIONS OF υ
ANDROMEDAE
A thesis submitted in partial satisfaction of the
requirements for the degree of
BACHELOR OF SCIENCE
in
ASTROPHYSICS
by
Irina Goriatcheva
10 June 2012
The thesis of Irina Goriatcheva is approved by:
Greg Laughlin
Advisor
Adriane Steinacker
Theses Coordinator
Michael Dine
Chair, Department of Physics
3. Abstract
Stability Analysis of the Companions of υ Andromedae
by
Irina Goriatcheva
We present a baseline analysis of the stability of the nominal best-fit υ Andromedae model as
presented in McArhur et al. (2010). We find that the nominal two-planet fit for υ Andromedae
becomes violently unstable after 357,000 years after the start of integration. To find a region of
stability for the proposed fit, we show that maximum masses required for a stable evolution for 1
Myr begin at 1.645 and 1.206 MJUP for υ And c and d, respectively, which are much lower than
the allowed minimum masses of 1.96 ± 0.05 and 4.33 ± 0.11 MJUP for the outer two planets.
Finally, we test 174 randomly selected configurations within the error range of the model presented
in McArthur et al. (2010) and find that all of these configurations resulted in violent instability
within 2.1 Myr since the start of integration. In addition to the study of the υ Andromedae system
that constitutes the primary result of this thesis, we also present a synopsis of preliminary work on
dynamical evolution of self-gravitating bodies. To this end, we develop a 4th
order Runge-Kutta
N-body integrator with energy and angular momentum conservation tracking. Using the integrator,
we solve the Pythagorean 3-body problem and test for accuracy of the produced solution using a
parallel integration with half the specified time-step.
5. v
List of Figures
2.1 [Murray and Dermott (2000)] A description of an elliptical orbit positioned in the
reference plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 A visual representation of an orbit with respect to a chosen reference plane [Murray
and Dermott (2000)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 [McArthur et al. (2010)] Left: a view of the υ And c and d orbits projected on the
plane of the sky. The darker circles indicate the portion of the orbit that is above the
plane of the sky, while the light circles represent the portion that is below. The trace
of the segments are proportional to the masses of the companions. Right: view of the
two outer orbits projected on the orthogonal axis . . . . . . . . . . . . . . . . . . . . 9
4.1 The trajectory of the solution to the three body Pythagorean problem. The blue,
green, and red lines trace out the motion of bodies with masses of three, four, and
five, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1 Graph of time vs. semi-major axis for the McArthur nominal astrometric fit for the
two outer planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Graph of time vs. eccentricity for the nominal McArthur astrometric fit for the two
outer planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.3 Plots of randomly selected values of the orbital parameters from within the error
range provided in McArthur et al. (2010) that resulted in instability. Each value
was individually modified one at a time and the modified parameter was input into
the nominal configuration which was then tested for stability. The circles represent
the values of the randomly selected parameters while the solid triangle indicates the
nominal fit for υ Andromedae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6. vi
List of Tables
2.1 the values for the orbital elements given by McArthur et al. (2010). [1] TBJD =
T − 2400000 JD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8. 1
1 Introduction
In 1999, when the fourth grade class from Moscow, Idaho, was informed of the discovery of
the first multiple-planet system, which had recently been detected in orbit around a nearby star, υ
Andromedae, they enthusiastically suggested charming, intuitive names: Twopiter, Fourpiter, and
Dinky. After learning of the planets, the children wrote to Dr. Debra Fischer of San Francisco State
University, who was on the team that discovered the system, to say that they had arrived at this
conclusion through the use of paper plates as a scale model for the companions of υ Andromedae.
In their scheme, the planet orbiting υ Andromedae which was twice the mass of Jupiter was named
“Twopiter”, the one four times as massive was dubbed “Fourpiter”, and the third, lowest mass
member of the system was to be called “Dinky”.
Sadly, it now appears that the engaging names may no longer apply. Following a detailed
analysis of astrometric data taken with the Fine Guidance Sensor of the Hubble Space Telescope,
McArthur et al. (2010) report that the planetary masses are several times larger than previously
believed. The two outer planets might more appropriately be called Tenpiter and Fourteenpiter (no
update was given on the innermost planet, so presumably the name Dinky still holds). These rather
revisions, apart from being a mouthful, suggest that the first multiple planet system found orbiting
a nearby star is profoundly unlike our own solar system, and indeed, may not be a planetary system
at all. The massive υ Andromedae planets orbit at distances of 0.06, 0.8, and 2.5 that of the distance
from the Earth to the Sun, and the orbits of the outer two, which may, in fact be brown dwarfs
rather than planets, are significantly eccentric. In addition, the two outer bodies have a mutual
9. 2
inclination, Φcd, of Φcd = 29o
.917 ± 1o
. Following the established convention, we will refer to the
companions of υ Andromedae as υ And b, c, and d.
Furthermore, the innermost planet in the υ Andromedae system was discovered in 1996,
using high precision radial velocity (RV) measurements. The McArthur et al. 2010 paper indicates
that, despite a decade of study, the configuration of its companions remains a mystery. Given that υ
Andromedae is the first non-pulsar multiple planet extrasolar system found orbiting a main sequence
star (Butler et al. 1999), its planetary orbits and masses are a matter of both scientific and historical
importance.
The motion of the companions of υ Andromedae are so strange and chaotic that the system
has been the focus of a great deal of attention over the years, and indeed, more effort has gone into
studying its dynamics than has been expended on any other extrasolar multiple planet system.
A brief recap of the research to date might run as follows: Shortly after its discovery, Laughlin
& Adams (1999) produced a study that allowed planet d deviate from a circle to the observed
eccentricity. They found that N-body interactions alone could not have altered the orbit into its
current eccentricity. It was also concluded that the system experienced chaotic evolution. Some
time later, Stepinski et al. (2000) found that the mutual angle of inclination, Φcd, of the two outer
orbits must be Φcd < 60o
while the mean inclination relative to the plane of the sky, icd, must be
icd > 13o
. Also, it was found that the difference between the arguments of pericenter of υ And c
and d librates around zero (Chiang et al. 2011). The orbits are thus compelled, over long periods
of time, to precess at the same rate around the star.
The unusually large eccentricities of the υ And system demand an explanation. Our own
Solar system houses planets in nearly circular orbits, and so it is startling that the planets in this
neighboring system have developed such high eccentricities. If we assume that planet formation arises
via disk accretion, then there is seemingly little reason for an orbit to deviate far from circularity.
According to the detailed analysis done by Ford et al. (2005), the companions of υ Andromedae
started out in nearly circular orbits (as expected if the planets evolved via accretion and coagulation
10. 3
of the protostellar disk). Subsequent gravitational interactions with a fourth planet, which has been
ejected from the system, caused the eccentricity of υ And d to undergo a significant increase due
to their close encounter. The fourth planet was then ejected from the system and the gravitational
interactions of υ And d and υ And c have caused the second planet to evolve a higher eccentricity.
υ And b, however, is found to be in a near circular orbit that is much detached from the
chaotic behavior of the outer two companions. A study of the effects of general relativity performed
by Adams & Laughlin (2006) found that general relativity damps the maximum the eccentricity of
planet b bserved in a secular cycle from about 0.4 to 0.016. In addition, Lissauer & Rivera (2001)
discovered that the inner orbit is strongly detached from interactions with the other two.
The peculiar configuration of the outer two orbits makes the system very susceptible to
instabilities. If planets c and d are 13.98+2.3
−5.3 MJUP and 10.25+0.7
−3.3 MJUP , respectively, in addition
to having a 29o
.917 ± 1o
mutual inclination angle (McArthur et al. 2010), then the system is likely
to be unstable. The angle of mutual inclination introduces a z-component for the motion, which is
very unusual for planetary orbits, and hence provides an avenue for instability that does not exist
in co-planar systems.
McArthur et al. used data from the high-cadence radial velocity (RV) measurements ob-
tained at the Hobby-Eberly Telescope, as well as the measurements from the Lick, Elodie, Harlan
J. Smith, and Whipple 60” telescopes. As mentioned above, they also used astrometric data from
the Hubble Space Telescope Fine Guidance Sensors to inform their derived fit for the υ Andromedae
system. The resulting system model (see Table 2.1) is driven largely by the astrometric data, and
suggests that the star is being pulled by planets whose orbits lie almost entirely in the plane of the
sky. Note that the McArthur et al. (2010) model of the system is based on the observed assumption
that that the astrocenteric variations are due solely to the planets’ gravitational pull on the star.
A reasonable working hypothesis is that the companions of υ Andromedae were initially
coplanar (Hubickyj 2010) and were later disturbed by some unknown phenomena or dynamical
interaction to produce high eccentricities and inclinations for planets c and d (Barnes et al. 2011).
11. 4
In this thesis, we will explicitly test the stability of the orbital elements and the masses of υ And
c and d as presented by McArthur et al. The system will be considered stable if no ejections or
collisions occur during an appropriately long-term integration.
To test the presented model of the υ Andromedae system for long-term stability, we must
use numerical methods. Empirical solutions to the equations of motion exist only for the two body
problem, the solutions to which are conic sections (circles, ellipses, the parabola, and hyperbolae).
To solve for the evolution of the motion of three or more bodies, empirical solutions to which are
not known, numerical integrations must be performed. It is important to note that the nature of
the three body problem is chaotic, meaning that it is highly sensitive to initial conditions. This
phenomenon is more widely known as the “butterfly effect”, where a minimal variation in the initial
conditions causes a drastic difference in the long term behavior of the motion.
In order to investigate the sensitivity to initial conditions of the multiple-body problem,
we have developed an N-body integrator that uses the 4th
order Runge-Kutta algorithm of solving
differential equations, and monitors energy and angular momentum conservation. To prove accuracy
of the solution, the code runs a parallel integration using a temporal half-step to check for convergence
of the two solutions. The three-body Pythogarean Problem was solved as a check of the accuracy of
the integrator. While using the N-body code, it was observed that, indeed, slight variation in the
initial conditions produced drastic differences in the orbital evolutions of the bodies.
In the next sections, we present a baseline analysis of the stability of the nominal best-fit υ
Andromedae planetary system model as presented by McArhur et al. (2010). From the analysis, the
system became unstable after 357,000 years since the start of integration. Furthermore, a systematic
decrease in mass was performed to establish maximum masses for the two outer companions, provided
that the rest of the McArthur elements presented were left unchanged. We found that the masses
had to be reduced to 1.645 MJUP and 1.206 MJUP for υ And c and υ And d, respectively, for the
system to remain stable for 1 Myr. In addition, values from within the error range of all the elements
and masses produced by McArthur et al. were randomly selected and tested for stability. We show
12. 5
that out of 174 runs, all of the configuratioins went unstable whithin 2.1 Myr.
Because a stable solution resulted when the masses of the two outer planets were reduced to
values less than the minimum masses, M sin i, presented by McArthur et al. (which equal Mc sin ic =
1.96 ± 0.05 and Md sin id = 4.33 ± 0.11 Jupiter masses), it is likely that the actual masses of the
companions are much smaller than presented. In fact, the stable masses derived in this thesis suggest
that the names given by the fourth graders from Moscow, Idaho, may in fact be appropriate. In
addition, instabilities of the nominal solution, as well as the modified configurations with elements
selected from whithin the error presented by McArthur et al. (2010) call the model into question.
That we observe the planets orbiting a 2 Billion year-old star suggests that the configuration is
vastly less extreme than McArthur et al. (2010) have found.
13. 6
2 Orbital Dynamics
2.1 Orbital Elements
Figure 2.1: [Murray and Dermott (2000)] A description of an elliptical orbit positioned in the
reference plane
In order to understand the configuration of a planetary system, we begin with a description
of orbital parameters as well as the reference system for the orientation of an orbit relative to
a standard reference plane. We are interested in stable systems, thus we focus our attention on
elliptical orbits. The radius of an ellipse at any point is given by
r =
a(1 − e2
)
1 + e cos f
, (2.1)
where a is the semi-major axis of the ellipse, f, the true anomaly, is the angle between the orbiting
14. 7
body and the pericenter (the point of closest approach of the ellipse to the focus), and e is the
eccentricity of the ellipse, which is defined to be
e ≡ 1 −
b2
a2
. (2.2)
In defining e, we used the minor axis of the ellipse, 2b (Figure 2.1). For the initial conditions, we
assume elliptical orbits that have some eccentricity, e, and a semi-major axis, a. In addition to the
true anomaly, f, we must define the eccentric anomaly, E, which is obtained by drawing a normal
to a through the position of the body in the orbit. E is defined as the angle from the pericenter to
the intersection of the described line and a circle of radius a, or in terms of f:
cos E =
e + cos f
1 + e cos f
. (2.3)
At this point in our model, we have a description of a Keplerian orbit lying in a reference plane. Next,
we need to tilt the orbit such that we can describe the trajectory with respect to a chosen reference
plane. To position an orbit in the correct spacial orientation, we perform a series of transformations:
Figure 2.2: A visual representation of an orbit with respect to a chosen reference plane [Murray and
Dermott (2000)]
We first rotate each orbit through a positive argument of pericenter, ω, with respect to
the Z-axis. This angle is the angle between the ascending node, the point where the orbit crosses
15. 8
the reference plane from below to above, to the pericenter. Next, we incline the orbit by rotating
around the X-axis by the inclination, i, which is the angle between the general orbital plane and
the reference plane with the X-axis pointing in the reference direction. Finally, we rotate by the
longitude of the ascending node, Ω, about the Z-axis. This is the angle between the reference line and
the ascending node (Murray and Dermott 1999). The transformation angles are illustrated in Figure
2.2. Now that we have established the orientation of an orbit, we can analyze the configuration of
υ Andromedae as presented by McArthur et al.
2.2 McArthur et al. (2010) Model
McArthur et al. (2010)
Orbital Parameters and Masses
υ And b υ And c υ And d
a (AU) 0.0594 ± 0.0003 0.829 ± 0.043 2.53 ± 0.014
e 0.012 ± 0.005 0.245 ± 0.006 0.316 ± 0.006
P (days) 4.617111 ± 0.000014 240.9402 ± 0.047 1281.507 ± 1.055
T[1]
(days) 50034.053 ± 0.328 49922.532 ± 1.17 50059.382 ± 3.495
i (deg) 7.868 ± 1.003 23.758 ± 1.316
Ω (deg) 236.853 ± 7.528 4.073 ± 3.301
ω (deg) 44.106 ± 25.561 247.659 ± 1.76 252.991 ± 1.311
mass (MJ ) 13.98+2.3
−5.3 10.25+0.7
−3.3
M sin i (MJ ) 0.69 ± 0.016 1.96 ± 0.05 4.33 ± 0.11
Table 2.1: the values for the orbital elements given by McArthur et al. (2010). [1] TBJD =
T − 2400000 JD
The McArthur et al. (2010) derived orbital elements and masses are listed in Table 2.1.
We note that the two outer massive planets, with masses of almost 14 and 10 MJUP , respectively,
have unusually high eccentricities, and lie almost entirely in the plane of the sky. The orbital
configuration is shown in Figure 2.3. It is also important to mention that the two outer planets
have a reported mutual inclination, Φcd = 29.917o
± 1o
, which, apart from being unusually large,
immediately introduces the potential for a Z-instability into the system. In addition, the minimum
possible masses with unknown inclination for υ And c and d are 1.96 ± 0.05 and 4.33 ± 0.11 MJUP ,
16. 9
respectively, which closely correspond to the “Twopiter” and “Fourpiter” model introduced in the
beginning of this thesis. The mass, inclination, and the longitude of the ascending node of υ And b
were not provided in the paper. McArthur et al. reported that this model evolved regularly for 100
Myr.
Figure 2.3: [McArthur et al. (2010)] Left: a view of the υ And c and d orbits projected on the plane
of the sky. The darker circles indicate the portion of the orbit that is above the plane of the sky,
while the light circles represent the portion that is below. The trace of the segments are proportional
to the masses of the companions. Right: view of the two outer orbits projected on the orthogonal
axis
17. 10
3 Methods
3.1 Orbital Parameters
Ambiguities occasionally occur in definitions of orbital elements. For example, inclination
can be defined in reference to the plane of the sky or the line of sight. When such ambiguities occur,
it is helpful to fall back on concrete definitions. To be confident that the interpretation of the orbital
elements is unambiguous, we developed a routine to convert orbital elements to cartesian positions
and velocities using explicit definitions for orbital parameters.
3.1.1 Obtaining Cartesian Position and Velocity from Orbital Elements
We begin our routine assuming that we are equipped with knowledge of a, e, masses of the
star and planet, M∗ andMp, the time at which the given parameters are relevant, tstart, and the
time of the pericenter passage, Tperi. We start with an orbit that lies in the plane of the sky. First,
we define the mean anomaly
M = n(tstart − Tperi) , (3.1)
where n is the mean motion defined as 2π
P where P is the period of the planet found by using Kepler’s
Third law:
P2
=
4π2
G(M∗ + Mp)
a3
. (3.2)
18. 11
Here, G is the gravitational constant. Next, we want to obtain the value for the eccentric anomaly,
E, by using
M = E − e sin E . (3.3)
In order to obtain a value for E, we carry out a simple iterative procedure until the value of E
converges:
Ei+1 = M + e sin Ei , (3.4)
where E0 = M. Now that we have determined E, we can calculate the values for the cartesian
position coordinates:
x = a(cos E − e) , (3.5)
as well as
y = a 1 − e2 sin E . (3.6)
Next, we define the true anomaly, f, as
f = 2 arctan(
1 + e
1 − e
tan
E
2
) . (3.7)
Using the true anomaly, we can find the cartesian velocity vectors
˙x = −
2πa
P
√
1 − e2
sin f , (3.8)
and
˙y =
2πa
P
√
1 − e2
(e + cos f) . (3.9)
We now have successfully constructed an orbit in terms of cartesian positions and velocities
relative to the reference plane. Next, we must rotate our cartesian vectors such that the orbit is in
the correct spacial orientation.
Right now, the orbit plane is normal to the specific angular momentum vector, j = ˆx × ˆv.
To orient the orbit such that it lies in an orientation demanded by the orbital elements Ω, i, and
19. 12
ω, we rotate x = (x, y, z), v = ( ˙x, ˙y, ˙z), and ˆz = (0, 0, 1) through an angle i about the axis,
ˆΩ = (cos Ω, sin Ω, 0), which is defined as the line of nodes of the orbit. In to order rotate x into the
true orbital plane, we perform
x
y
z
=
cos i + cos2
Ω(1 − cos i) cos Ω sin Ω(1 − cos i) sin Ω sin i
sin Ω sin Ω(1 − cos i) cos i + sin2
Ω(1 − cos i) − cos Ω sin i
− sin Ω sin i cos Ω sin i cos i
(3.10)
where x = (x , y , z ) is the position vector in the true orbital plane. Similar rotations are done to
v and ˆz to obtain v and ˆz , respectively. This transformation also outputs the updated pericenter
direction, ˆx .
Our next step is to get the correct orbital orientation by rotating the new pericenter
direction, ˆx , by an amount about the ˆz - axis (where is defined to be = Ω + ω) . This way,
we can account for the Ω and ω rotations to get the right angle between the reference line and the
ascending node. Thus, we transform x by the rotation matrix, R :
R =
cos + z 2
x (1 − cos ) zxzy(1 − cos ) − zz sin zxzz(1 − cos ) + zy sin
zyzx(1 − cos ) + zz sin cos + z 2
y (1 − cos ) zyzz(1 − cos ) − zx sin
zzzx(1 − cos ) − zy sin zzzy(1 − cos ) + zx sin cos + z 2
z (1 − cos )
(3.11)
where ˆz = (zx, zy, zz). As before, similar transformations are performed on v and ˆx to obtain v
and ˆx , respectively. These resulting cartesian vectors have the specified e, M, Ω, i, and ω. Thus,
x and v describe the correctly oriented orbit and define the motion of the planet relative to the
central star. As a check to confirm that proper transformations were performed we find that
sgn[(ˆΩ × ˆx ) · ˆz ] arccos(ˆΩ · ˆx ) ∈ (−π, π] (3.12)
was true for the above series of transformations.
20. 13
3.1.2 Jacobi Coordinates
The cartesian positions and velocities obtained from the appropriate transformations of
the orbital elements listed in McArthur et. al (2010) may be converted into Jacobi coordinates for
the three orbiting planets. Jacobi coordinates are used to simplify mathematical formulation and
often times provide more natural and also stable description of the system. This process builds a
“binary tree” model to connect the orbiting bodies via the preceding barycenter of the system. The
transformation to Jacobi coordinates is accomplished using the following prescription:
The center of mass for each orbiting body is calculated using
Ri =
1
Mi
i
j=0
mjrj , (3.13)
with
Mi =
i
j=0
mj , (3.14)
where ri is the vector from the origin to the ith
body. When converting to Jacobi coordinates we
assign the fist Jacobian vector to the position vector of the mass of the entire system,
˜r0 = RN−1 , (3.15)
where N is the number of bodies in the system (including the central star). When looking at the
υ Andromedae system, the fist Jacobi vector corresponds to R2. The remaining Jacobian position
vectors become
˜ri = ri − Ri−1 , (3.16)
where ˜ri is the vector denoting the position of the ith
mass with respect to the center of mass vector
Ri−1 .
To have the same origin for each position vector, we subtract the center of mass vectors
from the Jacobi coordinates, such that the new position vector, r , describes the Jacobi vectors of
each body with respect to one origin:
21. 14
ri = ˜ri + Ri . (3.17)
The same analysis was done to obtain the Jacobi coordinates of the velocity vectors by
integrating equations 3.13 and 3.15 with respect to time. Once the Jacobi positions and velocities
were obtained, the values for ri and vi were loaded into the integrator and a long-term stability
analysis of the system was performed.
22. 15
4 Procedures
4.1 N-Body Integration and Preliminary Experiments
When examining the evolution of multiple body systems, we must note that an analytic
solution exists only for the two body problem, where the allowed orbits are all conic sections.
When three or more bodies are involved, numerical integrations are required to obtain the dynamic
evolution of the system. Due to the chaotic evolution of planetary orbits, the long-term behavior is
highly dependent on initial conditions (a concept widely known as the ”butterfly effect”). Therefore,
slight variations in the initial conditions cause vast divergences in the outcome of the integration.
4.1.1 Runge-Kutta 4th
Order Method of Solving Ordinary Differential
Equations
The unpredictable and vastly complicated motion of many massive bodies that arise in
orbital dynamics are governed by Newton’s 2nd law. In its elegant and simple form, the law tells us
that the force between two massive bodies is governed by
F1 = m1¨r = −
Gm1m2
r2
, (4.1)
where F1 is the force on body 1, m1 and m2 are the masses of the two bodies and r is the distance from
the centers of the two bodies. For a system of N bodies, we consider the gravitational contribution
from each neighboring mass, and find that the force on a given body of mass mi is the sum of all
23. 16
the forces involved in the system acting on mi given by
Fij =
N−1
j=1
−
Gmimj
r2
ij
, (4.2)
where rij is the distance between the centers of mi and mj. To model the long-term evolution of a
three-body problem, we numerically solve equation 4.2 via a high-accuracy integration.
Equation 4.2 is a second order differential equation with constant coefficients, which may
be reduced to a series of coupled first order differential equations. To do so, we note that
˙x = v , (4.3)
where x = (x, y, z) and v = (vx, vy, vz). Reducing equation 4.2 to a first order differential equation
we obtain
˙v = −
N−1
j=1
Gmj
r2
ij
. (4.4)
To get the trajectory of the orbiting bodies, we must solve the system composed of equations
4.3 and 4.4. To do so, we organize the position and velocity components into an array given by
C = [x0, v0, x1, v1, x2, v2, ..., xN−1, vN−1] , (4.5)
and allow this vector to run through the 4th order Runge-Kutta method for solving differential
equations. We start out with defining
k1 =
dCi
dt
, (4.6)
such that the derivative solves equations 4.3 and 4.4 for x and v, respectively. We then proceed
with the Runge-Kutta algorithm:
b1 = Ci + k1
∆t
2
, (4.7)
k2 =
db1
dt
, (4.8)
b2 = Ci + k2
∆t
2
, (4.9)
k2 =
db2
dt
, (4.10)
b3 = Ci + k3∆t , (4.11)
24. 17
k4 =
db3
dt
, (4.12)
so that we obtain the value for Ci+1 via the expression
Ci+1 = Ci +
∆t
6
(k1 + 2k2 + 2k3 + k4) . (4.13)
This procedure can be repeated indefinitely to get the full solution for an N-body problem.
As an additional check, the energy and angular momentum conservation were monitored
during the integration, specifically with respect to close encounters. The fractional change in energy
and angular momentum was required to be at a minimum to provide the correct solution.
Figure 4.1: The trajectory of the solution to the three body Pythagorean problem. The blue, green,
and red lines trace out the motion of bodies with masses of three, four, and five, respectively.
As a numerical check, we integrated the Pythogarean 3 body problem where the Pythog-
arean 3, 4, 5, traingle was set up such that on the vertex opposite of side of length 3, a point mass
25. 18
of mass 3 was placed. Likewise point masses of mass 4 and 5 were placed at the vertices opposite of
sides 4 and 5, respectively. To confirm the accuracy of the solution, a parallel integration was run
using a time-step of ∆t
2 . The difference between the two solutions was was found to be minimal as
the integrations drew the same trajectory of the moving bodies to within a resolution element on
the display. Thus, the accuracy of our result to the degree required by the problem was confirmed
(see Figure 4.1).
4.2 Testing the McArthur et al. (2010) Model
4.2.1 Nominal Solution
The orbital elements of the two outer planets were converted into the cartesian position and
velocity components and loaded into the integrator. Because the mass, inclination, and longitude
of the ascending node were missing from the McArthur et al. data, and because of the “detached”
nature of υ And b, as well as the drastic reduction in the computational burden, the first planet
was not included in the integration. By using a two planet model, we can carry out more extensive
parameter studies.
Using the routine for converting from orbital elements to cartesian position and velocities
(which are outlined in Section 3.1.1), we transformed the results derived by McArhtur et al. into
cartesian values to avoid ambiguities due to variations in definitions of orbital elements (specifically
variations in the definition of inclination). The cartesian vectors were then tested for stability using
an N-body Bulirsh-Stoer integrator which was configured to have an 1.0e-13 individual timestep
accuracy for Bulirsch-Stoer. The system was considered unstable if the eccentricity of one or more
planets rapidly approached 1 or if there was a sharp increase in a such the resulting a is more than
1.25 times greater than the value at the start of the integration. All integrations for υ Andromedae
configurations had a common starting epoch at 240000 JD.
26. 19
4.2.2 Reducing the Nominal Mass
Provided that the nominal solution was unstable, the mass was systematically reduced to
identify the range when a reduction in the masses resulted in a drastically less chaotic evolution of
the system. For this procedure, instability was considered to occur when the semi-major axis, a,
exceeded 5% change in a at the start of the integration. This relatively strict definition of instability
was enforced because drastic changes in a will occur at exponentially later time when masses are
systematically reduced. To avoid using unnecessary computer time to observe vast variations in a,
we restricted the definition of instability, as our overall goal is to determine the masses at which the
evolution is no longer violently unstable.
We perform integrations using the reduced masses for 1 Million years and monitor the
decrease in the chaotic behavior of e. When mass reduction yields a oscillating evolution of the
eccentricities we consider the resulting configuration as stable.
4.2.3 Stability Within the Error Range
For completeness of our stability analysis, we test values provided within the error range of
the model by McArhur et al. We modify one of the elements provided and replace it by a randomly
selected value that is within the error range determined by McArhur et al. We test the modified
configuration for stability for 1Myr. The stable results will be tested for longer to determine the
time at which a exceeds a change of 25% of the initial value. For this analysis, 174 runs were carried
out using configurations with randomly modified elements that were within the error range.
27. 20
5 Results
5.1 Nominal Result
With the starting epoch of the integration chosen to be 240000 Julian Days, a long-term
integration of the orbital parameters was performed. The results of the nominal integration showed
that system participated in a dynamically active trajectory for 357,000 years following the starting
epoch. The behavior of the planets then became violently unstable, and as a consequence, the
eccentricity of planet d approached unity (Figure 5.2). In addition, the semi-major axis increased to
over 10 AU (Figure 5.1) which resulted in the ejection planet d. This behavior is very characteristic
of an unstable configuration - the system experiences a relatively short period of stability during
which the eccentricities display an evolution suggestive of orbital resonance. Eventually, repeated
planet interaction causes the orbits to become unstable and result in an ejection of a planet or a
collision between two bodies. With an ejection of a planet d, the system is declared manifestly
unstable, and the integration is halted.
5.2 Reduced Masses and Configurations Within the Error
Range
Since the nominal configuration resulted a violent instability, the masses at which the
McArthur et al. orbital model remained in a stable configuration were called to be determined. To
28. 21
Figure 5.1: Graph of time vs. semi-major axis for the McArthur nominal astrometric fit for the two
outer planets
Figure 5.2: Graph of time vs. eccentricity for the nominal McArthur astrometric fit for the two
outer planets
find a stable configuration, we systematically decreased the masses of υ and c and d to 1.645 MJUP
and 1.206 MJUP , respectively. These masses were the maximum masses that yielded smooth, stable
evolution of the eccentricity, and, as a consequence, the semi-major axis, for 1 Myr.
29. 22
In addition to the nominal result, 174 configurations (which included a modified parameter
that was within the range of error provided in McArthur et al. (2010)) were tested for stability. The
randomly selected parameters that were included in the stability analysis can be found in Figures
5.3.
These results are shown for an assumption that an instability is considered to be a 25%
change in the semi-major axis. A much tighter definition of instability would have sufficed with only
a 5% change in the semi-major axis. If this definition of instability was adopted, the systems that
we have tested would have gone unstable much earlier in the integration than we have allowed for.
This suggests that even with our liberal definition of instability that allows much room for change
in the semi-major axis and eccentricities, the system still went unstable within only 1 Myr.
30. 23
2.515
2.52
2.525
2.53
2.535
2.54
2.545
0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86
ad(AU)
ac (AU)
0.31
0.312
0.314
0.316
0.318
0.32
0.322
0.237 0.24 0.243 0.246 0.249 0.252
ed
ec
1280.6
1280.8
1281
1281.2
1281.4
1281.6
1281.8
1282
1282.2
1282.4
1282.6
240.875 240.9 240.925 240.95 240.975 241
Pd(days)
Pc (days)
50056
50057
50058
50059
50060
50061
50062
50063
49921.5 49922 49922.5 49923 49923.5 49924
Td(days)
Tc (days)
22.5
23
23.5
24
24.5
25
6.5 7 7.5 8 8.5 9
id
ic
251
252
253
254
255
245 246 247 248 249 250
!2(degrees)
!1 (degrees)
0
1
2
3
4
5
6
7
230 232 234 236 238 240 242 244
!2(degrees)
!1 (degrees)
7
8
9
10
11
9 10 11 12 13 14 15 16
Md(MJUP)
Mc (MJUP)
Figure 5.3: Plots of randomly selected values of the orbital parameters from within the error range
provided in McArthur et al. (2010) that resulted in instability. Each value was individually modified
one at a time and the modified parameter was input into the nominal configuration which was then
tested for stability. The circles represent the values of the randomly selected parameters while the
solid triangle indicates the nominal fit for υ Andromedae
31. 24
6 Summary and Conclusions
In this thesis, we have adopted the orbital model derived by McArthur et al. (2010). We
converted their reported orbital elements to cartesian position and velocities using a Jacobian scheme
and integrated the system starting at 240000 JD. From the results of the integration, it was shown
that the model presented by McArthur et al. became dramatically unstable 357,000 years after the
start of the integration.
In addition, the minimum masses required to produce a significant decrease in the violence
of the stability of the system for 2 Myr years were 1.645 MJUP and 1.206 MJUP , respectively, which
were 16.1% and 72.1% smaller than the allowed minimum masses, M sin i, of 1.96 ± 0.05 and 4.33
± 0.11 MJUP for υ And c and d, respectively. The M sin i measurements provide a cap on the
minimum allowed masses, yet our integrations demonstrated that the maximum mass required for
stability using the proposed orbital elements are less than the M sin i measurements. This important
inconsistency suggests that the orbital elements of the system, particularly e and i, are vastly less
exotic than proposed by McArthur et al. The large eccentricities provice more opportunity for
planet-planet orbital perturbations if the periods are not in resonance. In addition, the odds for
instability would be greatly reduced by eliminating the allowed Z-instability induced by the nonzero
Φcd in the McArhtur et al. model. Thus, it is most probable that the eccentricities of the outer two
plants as well as Φcd are significantly smaller than the values put forth by McArthur et al.
It is possible that some of the astrometric signal that McArthur et al. employed to derive
their fit may not be due to orbiting planets. The signal, for example, may be due to bodies outside of
32. 25
the υ Andromedae system. Other possible sources of the observed positional changes of the star on
the sky may be due to jitter, or systematic errors arising from inadequate removal of the constant
trajectory of the center of mass of the system. Astrometry, which requires careful attention and
construction of a reference grid of comparison stars, is notoriously difficult to carry out when one
requires cutting-edge percision. At this point, we believe that a further analysis is warranted in
order to establish that the signals are, in fact, due to orbiting planets.
It has been over a decade since the discovery of the υ And system. With more attention
devoted to this unusual configuration of planets than any other multi-planet system, the naive
expectations would be that a stable configuration that agrees with the data would have been long
since established. Yet the system still remains a mystery. More work is required to sort out what is
actually going on, and the fourth graders from Moscow, Idaho, many of whom are now likely college
graduates, like myself, can only hope that it will look remotely like our own!
33. 26
Bibliography
[1] Adams, F. C., & Laughlin, G. 2006, ApJ, 649, 992
[2] Barnes, R., Greenberg, R., Quinn, T. R., McArthur, B. E., Fritz Benedict, G. 2011, ApJ, 726,
71
[3] Butler, R. P., Marcy, G. W., Fischer, D. A., Brown, T. M., Contos, A. R., Korzennik, S. G.,
Nisenson, P., & Noyes, R. W. 1999, ApJ, 526, 916
[4] Chiang, E. I., Tabachnik, S., & Tremaine, S. 2001, AJ, 1607, 1607
[5] Ford, D. A., Lystad, V., & Rasio, F. A. 2005, Nature, 434, 873
[6] Hubickyj, O. 2010, in Formation and Evolution of Exoplanets, ed. R. Barnes (Berlin: Wiley-
VCH), 101
[7] Laughlin, G., & Adams, F. 1999, ApJ, 526, 881
[8] Lissauer, J. J., & Rivera, E. J. 2001, ApJ, 554, 1141
[9] McArthur, B. E., Benedict, G. F., Barnes, R., Martioli, E., Korzennik, S., Nelan, E., & Butler,
R. P. 2010, ApJ, 715, 1213
[10] Murray, C. D. & Dermott, S. F. 2000, Solar System Dynamics, ed. Murray, C. D. & Dermott,
S. F.
[11] Stepinski, T. F., Malhorta, R., & Black, D. C. 2000, ApJ, 545, 1044