In this presentation the following topics are covered:
- Active debris removal techniques
- Tethered space tug
- Mathematical model
- Numerical simulation and analysis
- Results and conclusion
Presentation for the 5th Eucass - European Conference for Aerospace Sciences - Munich, Germany, 1-4 July 2013.
THEOS (Thailand Earth Observation System)
THEOS is an Earth observation mission of Thailand, under development at EADS Astrium SAS, Toulouse, France. In July 2004, EADS Astrium SAS signed a contract for delivery of THEOS with GISTDA (Geo-Informatics and Space Technology Development Agency) of Bangkok, Thailand. GISTDA is Thailand's leading national organization (i.e., space agency) in the field of space activities and applications. The Thai Ministry of Science and Technology is funding the program.
The THEOS cooperative agreement includes the production and launch of one optical imaging satellite, as well as the development of the ground segment necessary to operate and control the satellite directly from Thailand. The contract also specifies on-the-job training of Thai engineers as part of the EADS Astrium development team. Also as part of the THEOS program, GISTDA earned the right to receive data from the SPOT-2, 4 and 5 spacecraft of CNES in Thailand, which have many features similar to those of THEOS. The prime objective of THEOS is to provide Thailand with an affordable access to space (i.e., a state-of-the-art Earth observation satellite for the near future), and to spawn through this program's operational experience the country's own capability and infrastructure an indigenous potential for the development of future space missions.
The science objectives call for the provision of:
1) Panchromatic (2 m) and multispectral (15 m) imagery from THEOS observations, and
2) The generation of geo-referenced image products and image processing capabilities for applications in the fields of cartography, land use, agricultural monitoring, forestry management, coastal zone monitoring and flood risk management.
The Thai government has also expressed its intention to offer THEOS data to the disaster mitigation efforts under the International Charter.
In this presentation the following topics are covered:
- Active debris removal techniques
- Tethered space tug
- Mathematical model
- Numerical simulation and analysis
- Results and conclusion
Presentation for the 5th Eucass - European Conference for Aerospace Sciences - Munich, Germany, 1-4 July 2013.
THEOS (Thailand Earth Observation System)
THEOS is an Earth observation mission of Thailand, under development at EADS Astrium SAS, Toulouse, France. In July 2004, EADS Astrium SAS signed a contract for delivery of THEOS with GISTDA (Geo-Informatics and Space Technology Development Agency) of Bangkok, Thailand. GISTDA is Thailand's leading national organization (i.e., space agency) in the field of space activities and applications. The Thai Ministry of Science and Technology is funding the program.
The THEOS cooperative agreement includes the production and launch of one optical imaging satellite, as well as the development of the ground segment necessary to operate and control the satellite directly from Thailand. The contract also specifies on-the-job training of Thai engineers as part of the EADS Astrium development team. Also as part of the THEOS program, GISTDA earned the right to receive data from the SPOT-2, 4 and 5 spacecraft of CNES in Thailand, which have many features similar to those of THEOS. The prime objective of THEOS is to provide Thailand with an affordable access to space (i.e., a state-of-the-art Earth observation satellite for the near future), and to spawn through this program's operational experience the country's own capability and infrastructure an indigenous potential for the development of future space missions.
The science objectives call for the provision of:
1) Panchromatic (2 m) and multispectral (15 m) imagery from THEOS observations, and
2) The generation of geo-referenced image products and image processing capabilities for applications in the fields of cartography, land use, agricultural monitoring, forestry management, coastal zone monitoring and flood risk management.
The Thai government has also expressed its intention to offer THEOS data to the disaster mitigation efforts under the International Charter.
Invited Seminar presented at the VIA Forum Astroparticle Physics Forum COSMOVIA
21 March 2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Author: O.M. Lecian
Speaker: O.M. Lecian
Abstract: The LHAASO experiment is aimed at detecting highly-energetic particles of cosmological origin within a large
range of energies.
The sensitivity of the experimental apparatus can within the frameworks of statistical fluctuations of the
background.
Acceleration and lower-energy particles can be analyzed.
The anisotropy mass composition of cosmic rays can analytically described.
The LHAASO Experiment is also suited for detecting particles of cosmological origin originated from the breach
(and/or other kinds of modifications) of particle theories paradigms comprehending other symmetry groups.
Some physical implications of anisotropies can be looked for.
The study of anisotropy distribution for particles of cosmological origin as well as the anisotropies of their velocities
both in the case of a flat Minkowskian background as well as in the case of curved space-time can be investigated,
as far as the theoretical description of the cross-section is concerned, as well as for the theoretical expressions of
such quantities to be analyzed.
The case of a geometrical phase of particles can be schematized by means of a geometrical factor.
Particular solutions are found under suitable approximations.
A comparison with the study of ellipsoidal galaxies is achieved.
The case of particles with anisotropies in velocities falling off faster than dark matter (DM) is compared.
The study of possible anisotropies in the spatial distribution of cosmological particles can therefore be described
also deriving form the interaction of cosmic particles with the gravitational field, arising at quantum distances, at
the semiclassical level and at the classical scales, within the framework of the proper description of particles
anisotropies properties.
Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missi...Winston Sanks
This report outlines the rationale, procedures, technical feasibility, risk assessment, and cost-benefit
analysis of utilizing a Near-Earth Object, 101955 Bennu (provisional designation 1999 RQ36 - the target of
the OSIRIS-REx mission), as a source of energy to minimize the propulsion requirements of an
interplanetary spacecraft. The planet Mars is the target body in this study and the outbound Trans-Mars
injection in the years between 2175 and 2199 will be analyzed (within this timeframe Bennu’s orbit is
predicted to approach Earth within two Earth radii on at least 80 occasions). The Mars orbit insertion burn,
Trans-Earth injection burn, and Earth orbit insertion burn are assumed to be achieved with propulsive
maneuvers outlined in standard manned interplanetary mission architectures. To accomplish this mission,
two methods of transferring kinetic energy are examined: direct capture and release of the asteroid by a
spacecraft using a Kevlar net and an inertial reel, and indirect capture by establishing a station on the
asteroid to manufacture compressed material from the carbonaceous regolith in order to fire a mass stream
to be captured by the spacecraft. This mission architecture analysis takes into account the associated safety
risks of perturbations within Bennu’s orbit (which could result in inaccurate rendezvous location
predictions), the implications of altering the orbit of 101955 Bennu after transferring a portion of its energy
(since there is a possibility of collision with Earth in the late 22nd century if the asteroid is slowed too
significantly), g-limit restrictions of the spacecraft and its occupants during an acceleration by the asteroid,
and the possibility of a collision between Bennu and the spacecraft. In addition, the cost-benefit
considerations of this mission architecture are weighed. This examination concludes that a direct capture Net
and Reel system aboard the spacecraft is not a viable capture method due to an insufficient maximum ΔV
available through a best-case perfectly elastic collision (capture) with the asteroid, as well as a prohibitive
weight penalty aboard the spacecraft due to the Net and Reel system. However, this report finds that the
method of establishing a station on Bennu with the capability to separate mass from the asteroid and fire it at
a spacecraft is a plausible (if costly) means of transferring a significant ΔV. A KETNEO-FIMM Asteroid
Station mission architecture could also be used in subsequent interplanetary missions providing cost-sharing
over many decades for future interplanetary missions.
Ultra-fast Outflows from Active Galactic Nuclei of Seyfert I GalaxiesAshkbiz Danehkar
High Energy Phenomena Seminar, Harvard CfA, Cambridge, USA, September 7, 2016, https://doi.org/10.6084/m9.figshare.13699048 https://youtu.be/7q_wv61ou1E
mpact of Urbanization on Land Surface Temperature - A Case Study of Kolkata N...theijes
Land Surface Temperature depends on the nature of land surface. Water bodies, green fields remain cooler than bare ground and built-up area. Kolkata New Town is emerging in agricultural area through filling of big water bodies and converting cultivated lands into built up area. This study aims to analyse the changes in land surface temperature with advent of the town. It is found that the land surface temperature is increasing sharply. The mean temperature of the area was 22.8°C in 1996 which became 24.9°C in 2004 and 26.4°C in 2014. Spatial variation was sharp during early stage of project i.e. 1996-2004. Besides The relation of built-up (NDBI) and LST is found positively co-related with a r value of 0.76 in 2004 and 0.73 in 2014 and the relation with vegetation (NDVI) is negatively related and the r value is -.0.35 in both the years of 2004 and 2014. Several patches of heat zones are now being popped up these zones have been identified on the map of Kolkata New Town. The study suggests toconsider the possible micro-climatic changes in town planning for the sustainable development.
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...Sérgio Sacani
Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens
of thousands of field stars. Tests against independent estimates of these properties are however
scarce, especially in the metal-poor regime. Here, we report the detection of solar-like
oscillations in 8 stars belonging to the red-giant branch and red-horizontal branch of the globular
cluster M4. The detections were made in photometric observations from the K2 Mission
during its Campaign 2. Making use of independent constraints on the distance, we estimate
masses of the 8 stars by utilising different combinations of seismic and non-seismic inputs.
When introducing a correction to the Δν scaling relation as suggested by stellar models, for
RGB stars we find excellent agreement with the expected masses from isochrone fitting, and
with a distance modulus derived using independent methods. The offset with respect to independent
masses is lower, or comparable with, the uncertainties on the average RGB mass
(4 − 10%, depending on the combination of constraints used). Our results lend confidence to
asteroseismic masses in the metal poor regime. We note that a larger sample will be needed
to allow more stringent tests to be made of systematic uncertainties in all the observables
(both seismic and non-seismic), and to explore the properties of RHB stars, and of different
populations in the cluster.
Invited Seminar presented at the VIA Forum Astroparticle Physics Forum COSMOVIA
21 March 2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Author: O.M. Lecian
Speaker: O.M. Lecian
Abstract: The LHAASO experiment is aimed at detecting highly-energetic particles of cosmological origin within a large
range of energies.
The sensitivity of the experimental apparatus can within the frameworks of statistical fluctuations of the
background.
Acceleration and lower-energy particles can be analyzed.
The anisotropy mass composition of cosmic rays can analytically described.
The LHAASO Experiment is also suited for detecting particles of cosmological origin originated from the breach
(and/or other kinds of modifications) of particle theories paradigms comprehending other symmetry groups.
Some physical implications of anisotropies can be looked for.
The study of anisotropy distribution for particles of cosmological origin as well as the anisotropies of their velocities
both in the case of a flat Minkowskian background as well as in the case of curved space-time can be investigated,
as far as the theoretical description of the cross-section is concerned, as well as for the theoretical expressions of
such quantities to be analyzed.
The case of a geometrical phase of particles can be schematized by means of a geometrical factor.
Particular solutions are found under suitable approximations.
A comparison with the study of ellipsoidal galaxies is achieved.
The case of particles with anisotropies in velocities falling off faster than dark matter (DM) is compared.
The study of possible anisotropies in the spatial distribution of cosmological particles can therefore be described
also deriving form the interaction of cosmic particles with the gravitational field, arising at quantum distances, at
the semiclassical level and at the classical scales, within the framework of the proper description of particles
anisotropies properties.
Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missi...Winston Sanks
This report outlines the rationale, procedures, technical feasibility, risk assessment, and cost-benefit
analysis of utilizing a Near-Earth Object, 101955 Bennu (provisional designation 1999 RQ36 - the target of
the OSIRIS-REx mission), as a source of energy to minimize the propulsion requirements of an
interplanetary spacecraft. The planet Mars is the target body in this study and the outbound Trans-Mars
injection in the years between 2175 and 2199 will be analyzed (within this timeframe Bennu’s orbit is
predicted to approach Earth within two Earth radii on at least 80 occasions). The Mars orbit insertion burn,
Trans-Earth injection burn, and Earth orbit insertion burn are assumed to be achieved with propulsive
maneuvers outlined in standard manned interplanetary mission architectures. To accomplish this mission,
two methods of transferring kinetic energy are examined: direct capture and release of the asteroid by a
spacecraft using a Kevlar net and an inertial reel, and indirect capture by establishing a station on the
asteroid to manufacture compressed material from the carbonaceous regolith in order to fire a mass stream
to be captured by the spacecraft. This mission architecture analysis takes into account the associated safety
risks of perturbations within Bennu’s orbit (which could result in inaccurate rendezvous location
predictions), the implications of altering the orbit of 101955 Bennu after transferring a portion of its energy
(since there is a possibility of collision with Earth in the late 22nd century if the asteroid is slowed too
significantly), g-limit restrictions of the spacecraft and its occupants during an acceleration by the asteroid,
and the possibility of a collision between Bennu and the spacecraft. In addition, the cost-benefit
considerations of this mission architecture are weighed. This examination concludes that a direct capture Net
and Reel system aboard the spacecraft is not a viable capture method due to an insufficient maximum ΔV
available through a best-case perfectly elastic collision (capture) with the asteroid, as well as a prohibitive
weight penalty aboard the spacecraft due to the Net and Reel system. However, this report finds that the
method of establishing a station on Bennu with the capability to separate mass from the asteroid and fire it at
a spacecraft is a plausible (if costly) means of transferring a significant ΔV. A KETNEO-FIMM Asteroid
Station mission architecture could also be used in subsequent interplanetary missions providing cost-sharing
over many decades for future interplanetary missions.
Ultra-fast Outflows from Active Galactic Nuclei of Seyfert I GalaxiesAshkbiz Danehkar
High Energy Phenomena Seminar, Harvard CfA, Cambridge, USA, September 7, 2016, https://doi.org/10.6084/m9.figshare.13699048 https://youtu.be/7q_wv61ou1E
mpact of Urbanization on Land Surface Temperature - A Case Study of Kolkata N...theijes
Land Surface Temperature depends on the nature of land surface. Water bodies, green fields remain cooler than bare ground and built-up area. Kolkata New Town is emerging in agricultural area through filling of big water bodies and converting cultivated lands into built up area. This study aims to analyse the changes in land surface temperature with advent of the town. It is found that the land surface temperature is increasing sharply. The mean temperature of the area was 22.8°C in 1996 which became 24.9°C in 2004 and 26.4°C in 2014. Spatial variation was sharp during early stage of project i.e. 1996-2004. Besides The relation of built-up (NDBI) and LST is found positively co-related with a r value of 0.76 in 2004 and 0.73 in 2014 and the relation with vegetation (NDVI) is negatively related and the r value is -.0.35 in both the years of 2004 and 2014. Several patches of heat zones are now being popped up these zones have been identified on the map of Kolkata New Town. The study suggests toconsider the possible micro-climatic changes in town planning for the sustainable development.
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...Sérgio Sacani
Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens
of thousands of field stars. Tests against independent estimates of these properties are however
scarce, especially in the metal-poor regime. Here, we report the detection of solar-like
oscillations in 8 stars belonging to the red-giant branch and red-horizontal branch of the globular
cluster M4. The detections were made in photometric observations from the K2 Mission
during its Campaign 2. Making use of independent constraints on the distance, we estimate
masses of the 8 stars by utilising different combinations of seismic and non-seismic inputs.
When introducing a correction to the Δν scaling relation as suggested by stellar models, for
RGB stars we find excellent agreement with the expected masses from isochrone fitting, and
with a distance modulus derived using independent methods. The offset with respect to independent
masses is lower, or comparable with, the uncertainties on the average RGB mass
(4 − 10%, depending on the combination of constraints used). Our results lend confidence to
asteroseismic masses in the metal poor regime. We note that a larger sample will be needed
to allow more stringent tests to be made of systematic uncertainties in all the observables
(both seismic and non-seismic), and to explore the properties of RHB stars, and of different
populations in the cluster.
An Earth-sized exoplanet with a Mercury-like compositionSérgio Sacani
Earth, Venus, Mars and some extrasolar terrestrial planets1
have a mass and radius that is consistent with a mass fraction
of about 30% metallic core and 70% silicate mantle2
. At the
inner frontier of the Solar System, Mercury has a completely
different composition, with a mass fraction of about 70%
metallic core and 30% silicate mantle3
. Several formation or
evolution scenarios are proposed to explain this metal-rich
composition, such as a giant impact4, mantle evaporation5
or the depletion of silicate at the inner edge of the protoplanetary
disk6. These scenarios are still strongly debated.
Here, we report the discovery of a multiple transiting planetary
system (K2-229) in which the inner planet has a radius
of 1.165 ± 0.066 Earth radii and a mass of 2.59 ± 0.43 Earth
masses. This Earth-sized planet thus has a core-mass fraction
that is compatible with that of Mercury, although it was
expected to be similar to that of Earth based on host-star
chemistry7
. This larger Mercury analogue either formed with
a very peculiar composition or has evolved, for example, by
losing part of its mantle. Further characterization of Mercurylike
exoplanets such as K2-229 b will help to put the detailed
in situ observations of Mercury (with MESSENGER and
BepiColombo8) into the global context of the formation and
evolution of solar and extrasolar terrestrial planets.
Science with small telescopes - exoplanetsguest8aa6ebb
The search for extrasolar planets has become one of the most attractive problems in modern astrophysics. The biggest observatories in the world are involved in this task as well as little amateur instruments. There is also a huge variety of astronomical methods used for their investigation. Here I present the projects for searching for exoplanets by transit method and our observations of the planet WASP-2b. We observed a transit on 3/4 August 2008 with a 354 mm Schmidt-Cassegrain Celestron telescope and CCD SBIG STL 11000M camera. By precise photometry made using MaximDL software we obtained the light curve of the star system. Decrease of brightness by 0.02m is detected. Analyzing our data we estimate the radius of the planet and inclination of its orbit. Our results are in good correlation with the published information in literature.
First discovery of_a_magnetic_field_in_a_main_sequence_delta_scuti_star_the_k...Sérgio Sacani
Coralie Neiner do Laboratory for Space Studies and Astrophysics Instrumentation, LESIA (CNRS/Observatoire de Paris/UPMC/Université Paris Diderot) e Patricia Lampens (Royual OIbservatory of Belgium), descobriram a primeira estrela magnética do tipo delta Scuti, através de observações espectropolarimétricas, realizadas com o telescópio CFHT. As estrelas do tipo delta Scuti, são estrelas pulsantes, sendo que algumas delas mostram assinaturas atribuídas para um segundo tipo de pulsação. A descoberta mostra que isso é na verdade a assinatura de um campo magnético. Essa descoberta tem importantes implicações para o entendimento do interior das estrelas.
Dois tipos de estrelas pulsantes existem entre as estrelas com massa entre 1.5 e 2.5 vezes a massa do Sol: as estrelas do tipo delta Scuti e as estrelas do tipo gamma Dor. A teoria nos diz que as estrelas com temperatura entre 6900 e 7400 graus Kelvin podem ter ambos os tipos de pulsação. Essas são então chamadas de estrelas híbridas. Contudo, o satélite Kepler da NASA tem detectado um grande número de estrelas híbridas com temperaturas maiores ou menores do que esse limite pensado anteriormente. A existência dessas estrelas híbridas com temperaturas maiores é algo muito controverso, já que desafia o nosso entendimento sobre as estrelas pulsantes do tipo delta Scuti e gamma Dor.
A new universal formula for atoms, planets, and galaxiesIOSR Journals
In this paper a new universal formula about the rotation velocity distribution of atoms, planets, and galaxies is presented. It is based on a new general formula based on the relativistic Schwarzschild/Minkowski metric, where it has been possible to obtain expressions for the rotation velocity - and mass distribution versus the distance to the atomic nucleus, planet system centre, and galactic centre. A mathematical proof of this new formula is also given. This formula is divided into a Keplerian(general relativity)-and a relativistic(special relativity) part. For the atomic-and planet systems the Keplerian distribution is followed, which is also in accordance with observations.
According to the rotation velocity distribution of the galaxies the rotation velocity increases very rapidly from the centre and reaches a plateau which is constant out to a great distance from the centre. This is in accordance with observations and is also in accordance with the main structure of rotation velocity versus distance from different galaxy measurements.
Computer simulations were also performed to establish and verify the rotation velocity distributions in the atomic – planetary- and galaxy system, according to this paper. These computer simulations are in accordance with observations in two and three dimensions. It was also possible to study the matching percentage in these calculations showing a much higher matching percentage between theoretical and observational values by this new formula.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Astronomy from the Moon: From Exoplanets to Cosmology and Beyond in Visible L...Sérgio Sacani
We review what could be astronomy from the Moon in the next decades in the visible domain.
After a short review observational approaches, from photometry to high contrast and high angular
resolution imaging, We essentially focus on some promising scientific objectives, from Solar
System to the extragalactic domain. At the end, I add a proposal to use the Earth-Moon system to
test fundamental physics. Since this meeting is dedicated to the next decades of Astronomy from
the Moon, we consider projects and science objectives for several decades from now.
Irina Goriatcheva - Stability Analysis of Companions Ups And
Progress_on_Understanding_Satellite_Clus
1. Progress on Understanding Satellite Cluster Flight
About Oblate Planets
Dr. Vladimir Martinusi
Joint Work with Prof. Pini Gurfil
Distributed Space Systems Lab
Faculty of Aerospace Engineering
Technion – Israel Institute of Technology
http://dssl.technion.ac.il/
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 1 / 23
3. Introduction: Cluster Flight
Cluster Flight: two or more satellites flying somewhat loose
Min/max range fixed by mission specifications
No strict formation geometry required
Applications:
Geolocation
Space networks
SAR Interferometry
Disaggregated spacecraft
Related technologies:
High-resolution imaging
Data relaying
Interferometry
In-situ gravitometry
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 3 / 23
4. Framework
Goal: mitigate the effects of the gravity field perturbations
Real problem: the potential of the geoid (see figure)
V (r) =
Q∈D
dm
r − rQ
=
Q∈D
dm (r)
r2
Q − 2r · rQ + r2
; (1)
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 4 / 23
5. Basic Physical Gravitational Models
The homogenous spherical model
leads to the Newtonian potential
analytic equations of motion
inaccurate for realistic scenarios
widely used as a nominal orbit
Ellipsoid
the potential has analytic expression
Legendre polynomials expansion
accurate for realistic scenarios
equations of motion are non-integrable
widely used for numerical propagators
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 5 / 23
6. Mathematical Models
The Newtonian potential – homogenous spherical model:
V0 (r) = −
µm
r
(2)
Geoid: Spherical harmonics model:
V (r) = V0 (r) −
∞
∑
k=1
rk
AkPk (cos φ) −
∞
∑
k=1
rk
k
∑
m=1
(Bkm sin mθ + Ckm cos mθ) Pkm (sin φ) (3)
φ = colatitude; θ = argument of latitude
Pk, Pkm = Legendre polynomials
Ak, Bkm, Ckm = spherical harmonics, 1 ≤ m ≤ k
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 6 / 23
7. Spherical Harmonics – A Visualization
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 7 / 23
8. Classical Approximate Models
Brouwer, Garfinkel, Kozai methods (1959)
Fourier series expansion of the geoid potential
Truncates the series ⇒ averaging
Analytic solution for the equations of motion
The Vinti potential (1959)
Integrable approximation (St¨ackel-type dynamical system)
Uses oblate spheroidal coordinates
Drawback: stands only for J2
2 ≈ J4 (Earth)
Analytic solution for the equations of motion
The two fixed centers (Izs´ak, Aksenov, Grebenikov)(1960s)
First approached by Euler, Lagrange, Jacobi
Applied in the context of celestial motion
Analytic solution for the equations of motion
The Cid–Lahulla radial intermediary (1960s)
Integrable approximation
Closed-form solution with elliptic integrals
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 8 / 23
9. New Approximation Proposal
The main perturbation is due to the J2 zonal harmonic
Approximating the gravitational model by considering only the J2
term is reasonably accurate
The J2 potential has the expression
VJ2 (r) = −
µm
r
1 − J2
req
r
2
3 cos2
φ − 1 = VJ2 (r, φ) (4)
The term in φ causes the problem to be non-integrable
Ignore the term in φ:
The problem becomes integrable
Physical meaning: motion in the equatorial plane
The J2–central potential has the expression:
VJ2 (r) = −
µm
r
1 + J2
req
r
2
= VJ2 (r) (5)
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 9 / 23
10. Analytic Solutions
The Absolute Motion
Falls in the general case of motion in a central force field
Potential of type A/r + B/r3 ⇒ solution with elliptic integrals
Closed form expression for (r,v) [Jezewski 1989, Martinusi and
Gurfil 2011]
Has five independent first integrals ⇒ maximal super-integrability
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 10 / 23
11. Analytic Solutions (cont’d)
The Absolute Motion (cont’d)
The orbit is contained in a fixed plane, defined by (r0,v0)
The orbit is bounded between two concentric circles
Unique shape defined by: the radial period T; the orbital angle ϕ
There exist several pericenters and apocenters
A main pericenter may be defined based on the ICs [Martinusi and
Gurfil 2012]
A set of 6 orbital elements may be defined (5
are constant)
Regularization of the equations of motion
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 11 / 23
12. Analytic Solutions (cont’d)
The Relative Motion
Based on the general solution for the relative motion in a central
force field [Condurache and Martinusi 2007]
Closed form expression for (r, v) [Martinusi and Gurfil 2011]
Explicit periodicity conditions
Particular case – 1:1 commensurability
Theorem
The relative motion in a central force
field is 1:1 periodic if and only if the
radial periods T1,2 and the orbital
angles ϕ1,2 of the absolute motions are
equal.
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 12 / 23
13. Application: Cluster Initialization
Algorithm for adjusting the inertial initial conditions [Martinusi and
Gurfil 2011]
Equatorial periodic relative motion
Bounded relative motion in inclined orbits
Relative distance remains within
the desired limits for up to one
year
Simulations were performed in
STK® with HPOP propagator
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 13 / 23
15. Application: Impulsive Maneuvers
Formation-keeping / Station-keeping impulsive maneuvers
Maneuvers should be made in order to reach the periodicity /
boundedness conditions
Single maneuver correction possible only if the desired orbit is
reachable by only one maneuver
Figure: yellow – actual orbit; orange – desired orbit
the desired orbit must intersect the min/max radii of the actual orbit
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 15 / 23
16. Application: Impulsive Maneuvers (cont’d)
Closed form expression for the impulsive maneuver velocity vector
[Martinusi and Gurfil 2012]:
∆v =
1
r−
1
2
h+
1 × r−
1 ±
1
r−
1
2E+
1 +
2µ
r−
1
+
µJ2r2
eq
r−
1
3
−
h+
1
r−
1
2
r−
1 − v−
1 .
Algorithm to select the the best maneuver moment
Equatorial orbits: possible anyway within the allowed area
Inclined orbits: at the equatorial plane passage
Maneuver moment depends on: impulse magnitude, drift rate (time
window), other mission specifications
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19. Additional Results – Open Orbits
Analytic closed-form solution for the open orbits in the equatorial
plane (with J2) [Martinusi and Gurfil 2013]
New orbit revealed: the “fish” orbit
Fly-by’s: explicit computation of:
Deflection angles
Pericenter position
Differences between the J2– central and Keplerian models
Numerical simulations run on actual real missions (Voyager,
Pioneer, Cassini)
A Laplace-Runge-Lenz-like vector revealed
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 19 / 23
20. Additional Results – Open Orbits (cont’d)
The “fish” orbit
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 20 / 23
21. Additional Results – Open Orbits (cont’d)
Differences J2–central versus Keplerian fly-by models:
v∞ [km/sec] ∆δ [deg] [deg] ∆rP [km] |∆rP| [km]
Pioneer 10 11.218 0.052 0.026 156.02 181.44
Pioneer 11 14.894 0.164 0.082 275.49 320.32
Voyager 2 5.653 0.003 0.001 39.59 46.05
Ulysses 7.118 0.008 0.004 62.78 73.00
Comparison – Jupiter flybys – Keplerian versus J2 – central
∆δ – difference in deflection angles;
– pericenter angular shift;
∆rP : difference in pericenter altitudes;
|∆rP| : distance between the J2 and the Keplerian pericenters
Could be incorporated into the analytical models of flybys
Vladimir Martinusi (DSSL) Cluster Flight About Oblate Planets 02/13/2013 21 / 23
22. Ongoing & Prospective Research
1 New set of orbital elements for the J2–central model
Based on the problem super-integrability
Possibility to derive new variational equations
2 Encke-like orbit propagator based on J2 – central nominal orbits
3 Two point boundary value problem in a Cid-Lahulla potential
(closed-form solution for inclined orbits)
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