This document proposes a point pairing method to characterize unknown space objects using non-resolved photometry data. The method is based on the principle of material frame indifference from mechanics. It identifies pairs of observation points where the contribution of either the solar panel or body to the observed brightness is identical, enabling separation of these contributions. When a point pair is found where the body contribution is the same, and the solar panel vector directions change marginally, the method provides three equations and three unknowns that can be solved to determine the albedo-area products of the solar panel and body. The point pairing method allows characterization using multi-spectral data by equalizing the number of unknowns and equations.
Confirmation of the_planetary_microlensing_signal_and_star_and_planet_mass_de...Sérgio Sacani
O Telescópio Espacial Hubble e o Observatório W. M. Keck, no Havaí, fizeram confirmações independentes de um exoplaneta orbitando sua estrela central de uma distância bem grande. O planeta foi descoberto através de uma técnica chamada de microlente gravitacional.
Essa descoberta traz uma nova peça para o processo de caçada de exoplanetas: para descobrir planetas longe de suas estrelas, como Júpiter e Saturno estão do Sol. Os resultados obtidos pelo Hubble e pelo Keck apareceram em dois artigos da edição de 30 de Julho de 2015 do The Astrophysical Journal.
A grande maioria dos exoplanetas catalogados são aqueles localizados bem perto de suas estrelas, isso acontece porque as técnicas atuais de se caçar exoplanetas favorecem a descoberta de planetas com curtos períodos orbitais. Mas esse não é o caso da técnica de microlente gravitacional, que pode encontrar planetas mais frios e mais distantes com órbitas de longo período que outros métodos não são capazes de detectar.
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.
Imaging the dust_sublimation_front_of_a_circumbinary_diskSérgio Sacani
Aims. We present the first near-IR milli-arcsecond-scale image of a post-AGB binary that is surrounded by hot circumbinary dust.
Methods. A very rich interferometric data set in six spectral channels was acquired of IRAS 08544-4431 with the new RAPID camera
on the PIONIER beam combiner at the Very Large Telescope Interferometer (VLTI). A broadband image in the H-band was reconstructed
by combining the data of all spectral channels using the SPARCO method.
Results. We spatially separate all the building blocks of the IRAS 08544-4431 system in our milliarcsecond-resolution image. Our
dissection reveals a dust sublimation front that is strikingly similar to that expected in early-stage protoplanetary disks, as well as an
unexpected flux signal of 4% from the secondary star. The energy output from this companion indicates the presence of a compact
circum-companion accretion disk, which is likely the origin of the fast outflow detected in H.
Conclusions. Our image provides the most detailed view into the heart of a dusty circumstellar disk to date. Our results demonstrate
that binary evolution processes and circumstellar disk evolution can be studied in detail in space and over time.
Confirmation of the_ogle_planet_signature_and_its_characteristics_with_lens_s...Sérgio Sacani
O Telescópio Espacial Hubble e o Observatório W. M. Keck, no Havaí, fizeram confirmações independentes de um exoplaneta orbitando sua estrela central de uma distância bem grande. O planeta foi descoberto através de uma técnica chamada de microlente gravitacional.
Essa descoberta traz uma nova peça para o processo de caçada de exoplanetas: para descobrir planetas longe de suas estrelas, como Júpiter e Saturno estão do Sol. Os resultados obtidos pelo Hubble e pelo Keck apareceram em dois artigos da edição de 30 de Julho de 2015 do The Astrophysical Journal.
A grande maioria dos exoplanetas catalogados são aqueles localizados bem perto de suas estrelas, isso acontece porque as técnicas atuais de se caçar exoplanetas favorecem a descoberta de planetas com curtos períodos orbitais. Mas esse não é o caso da técnica de microlente gravitacional, que pode encontrar planetas mais frios e mais distantes com órbitas de longo período que outros métodos não são capazes de detectar.
Confirmation of the_planetary_microlensing_signal_and_star_and_planet_mass_de...Sérgio Sacani
O Telescópio Espacial Hubble e o Observatório W. M. Keck, no Havaí, fizeram confirmações independentes de um exoplaneta orbitando sua estrela central de uma distância bem grande. O planeta foi descoberto através de uma técnica chamada de microlente gravitacional.
Essa descoberta traz uma nova peça para o processo de caçada de exoplanetas: para descobrir planetas longe de suas estrelas, como Júpiter e Saturno estão do Sol. Os resultados obtidos pelo Hubble e pelo Keck apareceram em dois artigos da edição de 30 de Julho de 2015 do The Astrophysical Journal.
A grande maioria dos exoplanetas catalogados são aqueles localizados bem perto de suas estrelas, isso acontece porque as técnicas atuais de se caçar exoplanetas favorecem a descoberta de planetas com curtos períodos orbitais. Mas esse não é o caso da técnica de microlente gravitacional, que pode encontrar planetas mais frios e mais distantes com órbitas de longo período que outros métodos não são capazes de detectar.
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.
Imaging the dust_sublimation_front_of_a_circumbinary_diskSérgio Sacani
Aims. We present the first near-IR milli-arcsecond-scale image of a post-AGB binary that is surrounded by hot circumbinary dust.
Methods. A very rich interferometric data set in six spectral channels was acquired of IRAS 08544-4431 with the new RAPID camera
on the PIONIER beam combiner at the Very Large Telescope Interferometer (VLTI). A broadband image in the H-band was reconstructed
by combining the data of all spectral channels using the SPARCO method.
Results. We spatially separate all the building blocks of the IRAS 08544-4431 system in our milliarcsecond-resolution image. Our
dissection reveals a dust sublimation front that is strikingly similar to that expected in early-stage protoplanetary disks, as well as an
unexpected flux signal of 4% from the secondary star. The energy output from this companion indicates the presence of a compact
circum-companion accretion disk, which is likely the origin of the fast outflow detected in H.
Conclusions. Our image provides the most detailed view into the heart of a dusty circumstellar disk to date. Our results demonstrate
that binary evolution processes and circumstellar disk evolution can be studied in detail in space and over time.
Confirmation of the_ogle_planet_signature_and_its_characteristics_with_lens_s...Sérgio Sacani
O Telescópio Espacial Hubble e o Observatório W. M. Keck, no Havaí, fizeram confirmações independentes de um exoplaneta orbitando sua estrela central de uma distância bem grande. O planeta foi descoberto através de uma técnica chamada de microlente gravitacional.
Essa descoberta traz uma nova peça para o processo de caçada de exoplanetas: para descobrir planetas longe de suas estrelas, como Júpiter e Saturno estão do Sol. Os resultados obtidos pelo Hubble e pelo Keck apareceram em dois artigos da edição de 30 de Julho de 2015 do The Astrophysical Journal.
A grande maioria dos exoplanetas catalogados são aqueles localizados bem perto de suas estrelas, isso acontece porque as técnicas atuais de se caçar exoplanetas favorecem a descoberta de planetas com curtos períodos orbitais. Mas esse não é o caso da técnica de microlente gravitacional, que pode encontrar planetas mais frios e mais distantes com órbitas de longo período que outros métodos não são capazes de detectar.
GPS Datum Conversion and Improvement in GPS Accuracyijsrd.com
GPS Positioning has numerous applications in the field of navigation and Geodesy.GPS positioning is mainly based on the different Geodetic Datum. This paper mainly discusses the improved datum conversion equations for the conversion of World Geodetic System (WGS-84) to Universal Transverse Mercator (UTM), vice versa and the reduction of errors introduced while datum conversion. By applying the different filters like Least Squares Algorithm (LSA), Kalman Filter (KF) and Modified Kalman Filter (MKF) a considerable improvement in consistency has been observed. Comparatively Modified Kalman Filter gives better accuracy in positioning.GPS coordinates data samples are collected in different environments like heavy traffic area, tall buildings area are taken to validate the results.
Further analysis of the References- part 2. Some further analyses about directional recoil, cross sections, galaxy Physics and experiment-optimizations techniques.
VIA Forum Astroparticle Physics Forum COSMOVIA
Author: O.M. Lecian.
Title: LHAASO Further references- part2.
28/03/2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Serendipitous discovery of an extended xray jet without a radio counterpart i...Sérgio Sacani
A recent Chandra observation of the nearby galaxy cluster Abell 585 has led to the discovery of
an extended X-ray jet associated with the high-redshift background quasar B3 0727+409, a luminous
radio source at redshift z = 2:5. This is one of only few examples of high-redshift X-ray jets known
to date. It has a clear extension of about 1200, corresponding to a projected length of 100 kpc, with
a possible hot spot located 3500 from the quasar. The archival high resolution VLA maps surprisingly
reveal no extended jet emission, except for one knot about 1:400 from the quasar. The high X-ray to
radio luminosity ratio for this source appears consistent with the / (1 + z)4 amplication expected
from the inverse Compton radiative model. This serendipitous discovery may signal the existence
of an entire population of similar systems with bright X-ray and faint radio jets at high redshift, a
selection bias which must be accounted for when drawing any conclusions about the redshift evolution
of jet properties and indeed about the cosmological evolution of supermassive black holes and active
galactic nuclei in general.
The discovery of_lensed_radio_and_x-ray_sources_behind_the_frontier_fields_cl...Sérgio Sacani
We report on high-resolution JVLA and Chandra observations of the Hubble Space Telescope (HST) Frontier Cluster
MACSJ0717.5+3745. MACSJ0717.5+3745 offers the largest contiguous magnified area of any known cluster,
making it a promising target to search for lensed radio and X-ray sources. With the high-resolution 1.0–6.5 GHz
JVLA imaging in A and B configuration, we detect a total of 51 compact radio sources within the area covered by the
HST imaging. Within this sample, we find sevenlensed sources with amplification factors larger than two. None of
these sources are identified as multiply lensed. Based on the radio luminosities, the majority of these sources are
likely star-forming galaxies with star-formation rates (SFRs) of 10–50 M: yr−1 located at 1 1 z 1 2. Two of the
lensed radio sources are also detected in the Chandra image of the cluster. These two sources are likely active galactic
nuclei, given their 2–10 keV X-ray luminosities of ∼1043–44 erg s−1. From the derived radio luminosity function, we
find evidence for an increase in the number density of radio sources at 0.6 z 2.0, compared to a z 0.3 sample.
Our observations indicate that deep radio imaging of lensing clusters can be used to study star-forming galaxies, with
SFRs as low as ∼10Me yr−1, at the peak of cosmic star formation history.
A Simplified and Robust Surface Reflectance Estimation Method (SREM) for Use ...Muhammad Bilal
Advantages of SREM:
1. SREM is the simplest method compared to the existing surface reflectance (SR) estimation methods.
2. SREM performs SR inversion based on the 6S Radiative Transfer Model (RTM) equations.
3. SREM does not depend on RTM simulation and a comprehensive lookup table (LUT).
4. SREM does not use the following parameters:
a. aerosol optical depth (AOD),
b. aerosol model,
c. water vapor concentration,
d. ozone concertation, and
e. other gases.
5. SREM can provide SR retrievals over diverse land surfaces including urban, vegetated, and desert surfaces.
6. SREM SR values are comparable with the following satellite SR products:
a. Landsat SR product (LEDAPS & LaSRC) at 30 m resolution,
b. Sentinel-2A SR product at 10 m resolution,
c. MODIS (MOD09) SR product at 500 m resolution, and
d. Planet satellite at 3 m resolution.
7. SREM can be applied to other Multispectral as well as Hyperspectral satellite data.
SREM ENVI/IDL CODE:
SREM IDL codes for Multispectral and Hyperspectral satellite data are available on demand, please email me at muhammad.bilal@connect.polyu.hk with the subject “SREM_SatelliteName_Code” if anyone is interested, and please provide the following information:
a. Full name,
b. Position,
c. Affiliation,
d. Research application.
PDF Version: https://www.mdpi.com/2072-4292/11/11/1344/pdf
https://www.researchgate.net/project/Simplified-and-Robust-Surface-Reflectance-Estimation-Method-SREM
Comparative Study of Selective Locations (Different region) for Power Generat...ijceronline
The sun is the primary source of energy. The sun, which is the largest member of the solar system,is a sphere of intensely hot gaseous matter having a diameter of 1.30 x 109 m, and at an average distance 1.495 x 1011 from the earth. An definite knowledge of the solar radiation distribution at a particular geographical location is of huge importance for the progress and development of many solar energy devices and for estimates of their performance as well as install new solar power plant. In this study, the measured or estimate data of global solar radiation on a horizontal surface and number of Bright Sunshine Hours (BSH) for Gujarat was analyzed of different locations. The solar energy potential (BSH) of several locations in Gujarat is received by compiling data from Agricultural Universities,Anand, S.K.Nagar, Navsari and Junagadh. These Universities are located in different region central Gujarat,North Gujarat,South Gujarat and Saurashtra respectively. Forecasting of power generation from weibull probability density function. Measured data put in the equation of weibull probability density function and find out shape parameter and scale parameter. After apply the Statistical test Corelation-coefficient (R2 ) and analysis the data for preference of selective locations.
Merging galaxy clusters leave long-lasting signatures on the baryonic and non-baryonic cluster constituents,
including shock fronts, cold fronts, X-ray substructure, radio halos, and offsets between the dark matter (DM) and
the gas components. Using observations from Chandra, the Jansky Very Large Array, the Giant Metrewave Radio
Telescope, and the Hubble Space Telescope, we present a multiwavelength analysis of the merging Frontier Fields
cluster MACS J0416.1-2403 (z = 0.396), which consists of NE and SW subclusters whose cores are separated on
the sky by ∼250 kpc. We find that the NE subcluster has a compact core and hosts an X-ray cavity, yet it is not a
cool core. Approximately 450 kpc south–southwest of the SW subcluster, we detect a density discontinuity that
corresponds to a compression factor of ∼1.5. The discontinuity was most likely caused by the interaction of the
SW subcluster with a less massive structure detected in the lensing maps SW of the subclusterʼs center. For both
the NE and the SW subclusters, the DM and the gas components are well-aligned, suggesting that MACS J0416.1-
2403 is a pre-merging system. The cluster also hosts a radio halo, which is unusual for a pre-merging system. The
halo has a 1.4 GHz power of (1.3 ± 0.3) × 1024WHz−1, which is somewhat lower than expected based on the
X-ray luminosity of the cluster if the spectrum of the halo is not ultra-steep. We suggest that we are either
witnessing the birth of a radio halo, or have discovered a rare ultra-steep spectrum halo.
GPS Datum Conversion and Improvement in GPS Accuracyijsrd.com
GPS Positioning has numerous applications in the field of navigation and Geodesy.GPS positioning is mainly based on the different Geodetic Datum. This paper mainly discusses the improved datum conversion equations for the conversion of World Geodetic System (WGS-84) to Universal Transverse Mercator (UTM), vice versa and the reduction of errors introduced while datum conversion. By applying the different filters like Least Squares Algorithm (LSA), Kalman Filter (KF) and Modified Kalman Filter (MKF) a considerable improvement in consistency has been observed. Comparatively Modified Kalman Filter gives better accuracy in positioning.GPS coordinates data samples are collected in different environments like heavy traffic area, tall buildings area are taken to validate the results.
Further analysis of the References- part 2. Some further analyses about directional recoil, cross sections, galaxy Physics and experiment-optimizations techniques.
VIA Forum Astroparticle Physics Forum COSMOVIA
Author: O.M. Lecian.
Title: LHAASO Further references- part2.
28/03/2020
http://viavca.in2p3.fr/2010c_o_s_m_o_v_i_a__forum_sd24fsdf4zerfzef4ze5f4dsq34sdteerui45788789745rt7yr68t4y54865h45g4hfg56h45df4h86d48h48t7uertujirjtiorjhuiofgrdsqgxcvfghfg5h40yhuyir/viewtopic.php?f=73&t=3705&sid=c56cbf76f87536fc4c3ff216d9edaba2
Serendipitous discovery of an extended xray jet without a radio counterpart i...Sérgio Sacani
A recent Chandra observation of the nearby galaxy cluster Abell 585 has led to the discovery of
an extended X-ray jet associated with the high-redshift background quasar B3 0727+409, a luminous
radio source at redshift z = 2:5. This is one of only few examples of high-redshift X-ray jets known
to date. It has a clear extension of about 1200, corresponding to a projected length of 100 kpc, with
a possible hot spot located 3500 from the quasar. The archival high resolution VLA maps surprisingly
reveal no extended jet emission, except for one knot about 1:400 from the quasar. The high X-ray to
radio luminosity ratio for this source appears consistent with the / (1 + z)4 amplication expected
from the inverse Compton radiative model. This serendipitous discovery may signal the existence
of an entire population of similar systems with bright X-ray and faint radio jets at high redshift, a
selection bias which must be accounted for when drawing any conclusions about the redshift evolution
of jet properties and indeed about the cosmological evolution of supermassive black holes and active
galactic nuclei in general.
The discovery of_lensed_radio_and_x-ray_sources_behind_the_frontier_fields_cl...Sérgio Sacani
We report on high-resolution JVLA and Chandra observations of the Hubble Space Telescope (HST) Frontier Cluster
MACSJ0717.5+3745. MACSJ0717.5+3745 offers the largest contiguous magnified area of any known cluster,
making it a promising target to search for lensed radio and X-ray sources. With the high-resolution 1.0–6.5 GHz
JVLA imaging in A and B configuration, we detect a total of 51 compact radio sources within the area covered by the
HST imaging. Within this sample, we find sevenlensed sources with amplification factors larger than two. None of
these sources are identified as multiply lensed. Based on the radio luminosities, the majority of these sources are
likely star-forming galaxies with star-formation rates (SFRs) of 10–50 M: yr−1 located at 1 1 z 1 2. Two of the
lensed radio sources are also detected in the Chandra image of the cluster. These two sources are likely active galactic
nuclei, given their 2–10 keV X-ray luminosities of ∼1043–44 erg s−1. From the derived radio luminosity function, we
find evidence for an increase in the number density of radio sources at 0.6 z 2.0, compared to a z 0.3 sample.
Our observations indicate that deep radio imaging of lensing clusters can be used to study star-forming galaxies, with
SFRs as low as ∼10Me yr−1, at the peak of cosmic star formation history.
A Simplified and Robust Surface Reflectance Estimation Method (SREM) for Use ...Muhammad Bilal
Advantages of SREM:
1. SREM is the simplest method compared to the existing surface reflectance (SR) estimation methods.
2. SREM performs SR inversion based on the 6S Radiative Transfer Model (RTM) equations.
3. SREM does not depend on RTM simulation and a comprehensive lookup table (LUT).
4. SREM does not use the following parameters:
a. aerosol optical depth (AOD),
b. aerosol model,
c. water vapor concentration,
d. ozone concertation, and
e. other gases.
5. SREM can provide SR retrievals over diverse land surfaces including urban, vegetated, and desert surfaces.
6. SREM SR values are comparable with the following satellite SR products:
a. Landsat SR product (LEDAPS & LaSRC) at 30 m resolution,
b. Sentinel-2A SR product at 10 m resolution,
c. MODIS (MOD09) SR product at 500 m resolution, and
d. Planet satellite at 3 m resolution.
7. SREM can be applied to other Multispectral as well as Hyperspectral satellite data.
SREM ENVI/IDL CODE:
SREM IDL codes for Multispectral and Hyperspectral satellite data are available on demand, please email me at muhammad.bilal@connect.polyu.hk with the subject “SREM_SatelliteName_Code” if anyone is interested, and please provide the following information:
a. Full name,
b. Position,
c. Affiliation,
d. Research application.
PDF Version: https://www.mdpi.com/2072-4292/11/11/1344/pdf
https://www.researchgate.net/project/Simplified-and-Robust-Surface-Reflectance-Estimation-Method-SREM
Comparative Study of Selective Locations (Different region) for Power Generat...ijceronline
The sun is the primary source of energy. The sun, which is the largest member of the solar system,is a sphere of intensely hot gaseous matter having a diameter of 1.30 x 109 m, and at an average distance 1.495 x 1011 from the earth. An definite knowledge of the solar radiation distribution at a particular geographical location is of huge importance for the progress and development of many solar energy devices and for estimates of their performance as well as install new solar power plant. In this study, the measured or estimate data of global solar radiation on a horizontal surface and number of Bright Sunshine Hours (BSH) for Gujarat was analyzed of different locations. The solar energy potential (BSH) of several locations in Gujarat is received by compiling data from Agricultural Universities,Anand, S.K.Nagar, Navsari and Junagadh. These Universities are located in different region central Gujarat,North Gujarat,South Gujarat and Saurashtra respectively. Forecasting of power generation from weibull probability density function. Measured data put in the equation of weibull probability density function and find out shape parameter and scale parameter. After apply the Statistical test Corelation-coefficient (R2 ) and analysis the data for preference of selective locations.
Merging galaxy clusters leave long-lasting signatures on the baryonic and non-baryonic cluster constituents,
including shock fronts, cold fronts, X-ray substructure, radio halos, and offsets between the dark matter (DM) and
the gas components. Using observations from Chandra, the Jansky Very Large Array, the Giant Metrewave Radio
Telescope, and the Hubble Space Telescope, we present a multiwavelength analysis of the merging Frontier Fields
cluster MACS J0416.1-2403 (z = 0.396), which consists of NE and SW subclusters whose cores are separated on
the sky by ∼250 kpc. We find that the NE subcluster has a compact core and hosts an X-ray cavity, yet it is not a
cool core. Approximately 450 kpc south–southwest of the SW subcluster, we detect a density discontinuity that
corresponds to a compression factor of ∼1.5. The discontinuity was most likely caused by the interaction of the
SW subcluster with a less massive structure detected in the lensing maps SW of the subclusterʼs center. For both
the NE and the SW subclusters, the DM and the gas components are well-aligned, suggesting that MACS J0416.1-
2403 is a pre-merging system. The cluster also hosts a radio halo, which is unusual for a pre-merging system. The
halo has a 1.4 GHz power of (1.3 ± 0.3) × 1024WHz−1, which is somewhat lower than expected based on the
X-ray luminosity of the cluster if the spectrum of the halo is not ultra-steep. We suggest that we are either
witnessing the birth of a radio halo, or have discovered a rare ultra-steep spectrum halo.
Orbital configurations of spaceborne interferometers for studying photon ring...Sérgio Sacani
Recent advances in technology coupled with the progress of observational
radio astronomy methods resulted in achieving a major milestone of astrophysics - a direct image of the shadow of a supermassive black hole, taken
by the Earth-based Event Horizon Telescope (EHT). The EHT was able to
achieve a resolution of ∼20 µas, enabling it to resolve the shadows of the
black holes in the centres of two celestial objects: the supergiant elliptical
galaxy M87 and the Milky Way Galaxy. The EHT results mark the start of a
new round of development of next generation Very Long Baseline Interferometers (VLBI) which will be able to operate at millimetre and sub-millimetre
wavelengths. The inclusion of baselines exceeding the diameter of the Earth
and observation at as short a wavelength as possible is imperative for further development of high resolution astronomical observations. This can be
achieved by a spaceborne VLBI system. We consider the preliminary mission
design of such a system, specifically focused on the detection and analysis
of photon rings, an intrinsic feature of supermassive black holes. Optimised
Earth, Sun-Earth L2 and Earth-Moon L2 orbit configurations for the space
interferometer system are presented, all of which provide an order of magnitude improvement in resolution compared to the EHT. Such a space-borne
Present of the torsion pendulum of Cavendish (CTB) and the radiometer
on heat fluxes (RHF). First instrument is the best for fundamental science for example new discovery affect
ANRI and expect - AGRI ; second – intend to applied research at first time thermo nuclear fields at natural
conditions
Present of the torsion pendulum of Cavendish (CTB) and the radiometer
on heat fluxes (RHF). First instrument is the best for fundamental science for example new discovery affect
ANRI and expect - AGRI ; second – intend to applied research at first time thermo nuclear fields at natural
conditions .
Fusion of Multispectral And Full Polarimetric SAR Images In NSST DomainCSCJournals
Polarimetric SAR (POLSAR) and multispectral images provide different characteristics of the imaged objects. Multispectral provides information about surface material while POLSAR provides information about geometrical and physical properties of the objects. Merging both should resolve many of object recognition problems that exist when they are used separately. Through this paper, we propose a new scheme for image fusion of full polarization radar image (POLSAR) with multispectral optical satellite image (Egyptsat). The proposed scheme is based on Non-Subsampled Shearlet Transform (NSST) and multi-channel Pulse Coupled Neural Network (m-PCNN). We use NSST to decompose images into low frequency and band-pass sub- band coefficients. With respect to low frequency coefficients, a fusion rule is proposed based on local energy and dispersion index. In respect of sub-band coefficients, m-PCNN is used to guide how the fused sub-band coefficients are calculated using image textural information.
The proposed method is applied on three batches of Egyptsat (Red-Green-infra-red) and radarsat2 (C-band full-polarimetric HH-HV and VV-polarization) images. The batches are selected to react differently with different polarization. Visual assessment of the obtained fused image gives excellent information on clarity and delineation of different objects. Quantitative evaluations show the proposed method can superior the other data fusion methods.
Imaging the Milky Way with Millihertz Gravitational WavesSérgio Sacani
Modern astronomers enjoy access to all-sky images across a wide range of the electromagnetic spectrum from
long-wavelength radio to high-energy gamma rays. The most prominent feature in many of these images is our
own Galaxy, with different features revealed in each wave band. Gravitational waves (GWs) have recently been
added to the astronomers’ toolkit as a nonelectromagnetic messenger. To date, all identified GW sources have been
extra-Galactic and transient. However, the Milky Way hosts a population of ultracompact binaries (UCBs), which
radiate persistent GWs in the milliHertz band that is not observable with today’s terrestrial gravitational-wave
detectors. Space-based detectors such as the Laser Interferometer Space Antenna will measure this population and
provide a census of their location, masses, and orbital properties. In this work, we will show how this data can be
used to form a false-color image of the Galaxy that represents the intensity and frequency of the gravitational
waves produced by the UCB population. Such images can be used to study the morphology of the Galaxy, identify
interesting multimessenger sources through cross-matching, and for educational and outreach purposes.
Polarized reflected light from the Spica binary systemSérgio Sacani
Close binary systems often show linear polarization varying
over the binary period, usually attributed to light scattered
from electrons in circumstellar clouds1–3
. One of the brightest
close binary systems is Spica (alpha Virginis) consisting of
two B-type stars orbiting with a period of just over four days.
Past observations of Spica have shown low polarization with
no evidence for variability4–6. Here we report new high-precision polarization observations of Spica that show variation
with an amplitude of about 200 parts per million. By including
polarized radiative transfer in a binary star model, we show
that the phase-dependent polarization is mainly due to light
reflected from the primary component of the binary system
off the secondary component and vice versa. The stars reflect
only a few per cent of the incident light, but the reflected light
is very highly polarized. The polarization results show that the
binary orbit is clockwise and the position angle of the line of
nodes is 130.4° ± 6.8°, in agreement with intensity interferometer results7
. We suggest that reflected light polarization
may be much more important in binary systems than has previously been recognized and may be a way of detecting previously unrecognized close binaries.
ASTRONOMICAL OBJECTS DETECTION IN CELESTIAL BODIES USING COMPUTER VISION ALGO...csandit
Computer vision, astronomy, and astrophysics function quite productively together to the point where they are completely logical for each other. Out of computer vision algorithms the
progress of astronomy and astrophysics would have slowed down to reasonably a deadlock. The new researches and calculations can lead to more information as well as higher quality of data. Consequently, an organized view on planetary surfaces can change all in the long run. A new
discovery would be a puzzling complexity or a possible branching of paths, yet the quest to know more about the celestial bodies by dint of computer vision algorithms will continue. The detection of astronomical objects in celestial bodies is a challenging task. This paper presents
an implementation of how to detect astronomical objects in celestial bodies using computer vision algorithm with satisfactory performance. It also puts forward some observations linked
among computer vision, astronomy, and astrophysics.
Similar to Characterization of unknown space objects (20)
1. Point Pairing Method Based on the Principle of Material Frame Indifference for the
Characterization of Unknown Space Objects using Non-Resolved Photometry Data
Anil B. Chaudhary, Tamara E. Payne, Keith Lucas, Shaylah Mutschler,
Tim Vincent
Applied Optimization, Inc.
Phan Dao, Jeremy Murray-Krezan
Air Force Research Laboratory /RVBY
ABSTRACT
The point pairing method in this paper is based on a set of simple physical truths for three-axis stabilized space
objects in the geosynchronous orbit (GEO). It defines a method for the calculation of pairs of observation
conditions (i.e. point pairs) that have a special property for three-axis stabilized GEO object characterization. An
observation condition is defined to be the geometry of illumination for the solar panel and the body of the satellite
and the geometry of its observation by a sensor. The physical truths are due to observation conditions that are
equivalent with respect to either the solar panel or body for a pair of points, which can be identified analytically.
When the observation conditions are equivalent for the solar panel, the contribution to the GEO object brightness by
the solar panel at that pair of points is identical. Then the difference between the pair of brightness values cancels
the solar panel contribution unconditionally, and the remainder is only due to the body. Similarly, when the
contribution of the body to the observed brightness is the same for the point pair, the difference between the two
brightness values cancels the body contribution unconditionally and the remainder is only due to the solar panels.
This enables separation of the observed brightness data into contributions by the solar panels and the body, which is
fundamental to space-object characterization. This separation of the solar panel or body contributions is feasible in
each waveband of observation. Thus point pairing is useful for the analysis of panchromatic as well as multi-spectral
data. The desired conditions for point pairing occur routinely, typically within weeks of each other.
1. INTRODUCTION
The principle of material frame indifference (PMFI) is one of the basic principles in the mechanics of materials that
is utilized for the characterization of the intrinsic, physical, constitutive behavior of materials. Reference [1]
describes this principle as follows: “Physical laws, if they really describe the physical world, should be independent
of the position and orientation of the observer. That is, if two scientists using different coordinate systems observe
the same physical point, it should be possible to state a physical law governing the event in such a way that if the
law is true for one observer, it is also true for the other. For this reason, the equations of physical laws are vector
equations or tensor equations, since vectors and tensors transform from one coordinate system to another in such a
way that if a vector of a tensor equation holds in one coordinate system, it holds in any other coordinate system not
moving relative to the first one, i.e., in any other coordinate system in the same reference frame.”
Fig. 1-1: Nadir Facing 3-Axis Stabilized Body and Sunward Articulating Solar Panels
The present paper applies PMFI to analyze the reflection of incident sunlight by a space object and to determine
conditions under which the observations taken at two distinct instants of time possess a special property that is
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14. ABSTRACT
The point pairing method in this paper is based on a set of simple physical truths for three-axis stabilized
space objects in the geosynchronous orbit (GEO). It defines a method for the calculation of pairs of
observation conditions (i.e. point pairs) that have a special property for three-axis stabilized GEO object
characterization. An observation condition is defined to be the geometry of illumination for the solar panel
and the body of the satellite and the geometry of its observation by a sensor. The physical truths are due to
observation conditions that are equivalent with respect to either the solar panel or body for a pair of
points, which can be identified analytically. When the observation conditions are equivalent for the solar
panel, the contribution to the GEO object brightness by the solar panel at that pair of points is identical.
Then the difference between the pair of brightness values cancels the solar panel contribution
unconditionally, and the remainder is only due to the body. Similarly, when the contribution of the body to
the observed brightness is the same for the point pair, the difference between the two brightness values
cancels the body contribution unconditionally and the remainder is only due to the solar panels. This
enables separation of the observed brightness data into contributions by the solar panels and the body,
which is fundamental to space-object characterization. This separation of the solar panel or body
contributions is feasible in each waveband of observation. Thus point pairing is useful for the analysis of
panchromatic as well as multispectral data. The desired conditions for point pairing occur routinely,
typically within weeks of each other.
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Prescribed by ANSI Std Z39-18
4. useful in the analysis of non-resolved photometric data. The two materials of interest are those that constitute the
solar panel and the body of a 3-axis stabilized geosynchronous satellite, respectively [Fig. 1-1].
The sizes for the solar panel and the body are assumed to be unknown. The observer is the sensor that measures the
sunlight reflected by the solar panel and the body along the direction of the line of sight from the sensor to the
satellite. The material constitutive laws of interest are the bidirectional reflectance distribution functions (BRDF)
for diffuse and specular reflectances of the solar panel and the body. The reference frame is the Earth-Centered
Inertial (ECI) reference frame [2]. The purpose of this analysis is to characterize the albedo-Area product of the
panel and the body.
Any surface may be viewed as a collection of planar facets. An individual facet may be 2-D simplex (i.e. triangle)
or a quadrilateral, which is a combination of two triangles. The size (area) of a triangle is half the magnitude of the
cross-product of it sides. In geometry, the vector area can be defined for a finite planar surface using the scalar area
and a unit vector that is normal to the plane of the surface. Albedo is a dimensionless quantity that equals the ratio
of the reflected sunlight to incident sunlight. The albedo is defined in terms of a BRDFthat defines optical
reflectance with respect to two vector directions; namely the vector direction of incident sunlight and the vector
direction of the line of sight of the sensor. Thus, we may interpret the albedo-Area product as a vector. Or, in other
words, the albedo-Area product of a satellite is a function of its pose with respect to the observer and not a scalar,
constant value. We can also consider the albedo-Area product of a satellite as the sum of the albedo-Area products
for the solar panels and the body.
The solar panel of a 3-axis stabilized satellite tracks the sun’s projection in the equatorial plane. The axis of the
solar panel is normal to the orbital plane of the satellite. The normal to the solar panel typically has an offset angle
with respect to the direction of incident sunlight, which is assumed herein to remain constant over the duration of
interval in which the observation data is analyzed. However, in reality, the solar panel offset angle may be changed
by its operators from time-to-time. The body points to nadir in order to communicate with the terrestrial stations or
customers. Thus, a 3-axis stabilized satellite can be visualized as an articulating assembly of the solar panels and the
body. The relative orientation of the body with respect to the solar panels depends on the orbital position of the
satellite. Thus, the satellite may be considered as an object with a periodic geometry.
The vector directions of incident and reflected sunlight can be defined in terms of the azimuth and elevation angles
in a spherical coordinate frame attached to the center of mass of the satellite. These two vector directions are
defined with respect to the normal of the particular surface under consideration, either the panel or the body.
Consider the body’s reference frame, Fig. 1-2. Let the first axis of the spherical coordinate frame be perpendicular
to the orbital plane of the satellite and the second axis point to nadir. The third axis is defined to complete the
orthogonal triad. Since the orbital position of the satellite and its geometry change continuously, the definition of
the spherical coordinate frame with respect to the ECI reference frame changes continuously as well. As this
coordinate frame is tied to nadir, the frame accommodates the angles relative to the body component, labeled as 휓
and 휂. A similar coordinate frame tied to the solar panel normal may be established to accommodate the angles
relative to the panel component, labeled 휔 and 휃, shown in Fig. 1-3.1
Consider two instants of time. In general, for the two instants, the azimuth and elevation angles for the vector
directions of incident and reflected sunlight with respect to the normal vectors to its solar panels and the body will
be different. This change in the angles is due to two reasons, namely due to change in the relative position of the
satellite with respect to the sensor and the sun and also due to the geometry and ephemerides of the satellite. Then,
as per the PMFI, the optical reflectance behavior of the solar panel and body can only be a function of the vector
1 The angles of observation, 휓, 휂,휔, 푎푛푑 휃, are defined more precisely in Section 2.
5. directions of the incident and reflected sunlight with respect to the normal vectors to the solar panel and the body. It
is insufficient to define the optical reflectance only as a function of azimuth angle or the elevation angle.
Furthermore, finite angles are not vectors and thus we cannot define components of optical reflectance in terms of
the azimuth angle or elevation angle.
Fig. 1-2: Rotating Coordinate Frame Specific to the Body
Fig. 1-3: Rotating Coordinate Frame Specific to the Panel
Once again, consider two instants of time that are distinct from each other. If the vector directions of the incident
and reflected sunlight with respect to the normal to solar panel are identical at these two instants, then the
contribution of the solar panel to the brightness of the GEO satellite at these two instants is identical. Or alternately,
6. the fraction of the albedo-Area for the satellite due to the solar panel will be identical at these two instants. This
condition is denoted as an occurrence of a point pair for the solar panel. Similarly, if the two vector directions are
identical at another two instants of time with respect to the normal vector to the body, then the contribution of the
body to the brightness (or the albedo-Area) of the GEO satellite at these second two instants of time will be
identical. This condition is denoted as an occurrence of a point pair for the body.
Consider that the albedo-Area of a satellite is a sum of the albedo-Areas of the solar panel and the body. Since the
albedo-Area of the solar panel and body depend on the changing vector directions of the incident and reflected
sunlight, the projected albedo-Area of the satellite changes continuously. The measured brightness of the satellite
can be converted into its albedo-Area product. A convenient mathematical procedure for this conversion is
described in[3]. Thus, each observation renders an equation that consists of one known (i.e. the projected albedo-
Area of the satellite) and two unknowns (i.e., the intrinsic albedo-Areas of the solar panel and the body).
Consider a situation when we have observation data at two instants of time. If the two instants are close to each
other, the two equations rendered by the two observations embody significant linear dependence and we cannot
reliably solve for the two unknowns. If the two instants are distinct from each other, the two equations are linearly
independent, but the projected albedo-Areas of the solar panel and the body change as well. Thus we are left with
two equations and four unknowns, which is not useful. This difficulty is not resolved by collecting data in multiple
wavebands because the number of independent equations grows in proportion to the number of wavebands, and the
number of unknowns grows in proportion to twice the number of wavebands. The use of point pairing is meant to
equalize the number of unknowns to the number of independent equations irrespective of the number of wavebands
in which the data is collected.
Consider the situation when we have data at a point pair for the body. The location of a point pair can be found by
mining an archive of brightness observations for a satellite. For example, such data is routinely collected in the open
filter (panchromatic data) by the metric-photometric sensors as a part of their astrometry mission. Or a desired point
pair of panchromatic or multi-color data may be collected by a priori determination of sensor tasking. With a point
pair, we have two independent equations and three unknowns. It is necessary to eliminate one additional unknown.
To this end, consider that the solar declination changes continuously. Its range is -23.5o to +23.5o. Due to the
Earth’s elliptical orbit, the variation of the solar declination changes faster in January than July. Since the perihelion
and aphelion do not occur at the solstices, the maxima and minima are slightly asymmetrical [4] This results in the
maximum change of declination at the equinoxes of roughly 0.4 deg/day and at the solstices there is virtually no
change. Thus, we have a satellite with a periodic geometry and a gradual change in the vector direction of
illumination. The definition of a body point pair is narrowed to include an additional condition that the equalization
of body contribution be accompanied by a marginal change (~ 5o) in the vector direction of reflected sunlight for the
solar panel. This marginal change need only be as large as that required to render the two equations linearly
independent.
With the narrowed definition of a body point pair, we still have two independent equations and three unknowns.
However, since the change in the vector directions for the solar panel is marginal, the two unknowns corresponding
to the albedo-Area of the solar panel can be related to each other using the BRDF definition. This creates a set of
three independent equations and three unknowns, which can be readily solved. The definition and solution
procedure using a solar panel point pair is the counterpart of the logic described above for a body point pair [5].
The organization for the remainder of this paper is as follows. Section 2 describes the geometry of observation for a
GEO satellite. Section 3 describes a two-facet model that represents the satellite in terms of a sun-tracking facet and
a nadir-facing facet. Section 4 describes the reflectance and albedo-Area expressions based on the two-facet model.
Section 5 describes the procedure for the solution of albedo-Area values for the solar panel and the body. Section 5
7. also shows a notional example for the identification of point-pairing conditions using the satellite two-line element
(TLE) data. Section 6 lists the conclusions.
2. GEOMETRY OF TERRESTRIAL BASED OBSERVATION OF A GEOSTATIONARY RSO
Before proceeding further, a picture of the geometry of observation is useful. Consider the following diagram, Fig.
2-1. Note that the depiction is not to scale and is in 3D. The reference frame is ECI coordinates, where the origin is
the earth’s center, the vertical axis corresponds to celestial north, the horizontal axis passes through the equinoxes,
and the third axis completes the orthogonal triad [2]. The observation station, shown as a purple point labeled
“Obs,” is at approximately 30°푁 latitude and at approximately 45° longitude off of the RSO’s nadir vector, shown
as a dotted black line. The RSO, shown as a blue point, is in a geostationary orbit, shown as a black circle, and its
sunward articulating panel component is shown as a blue segment.
As the RSO orbits the earth, the panel component maintains alignment with respect to the sun’s projection in the
equatorial plane. The panel’s normal (푃!), shown as a green dashed vector, is offset by angle 훼 from the projection
of the sun. The light incident to the object arrives along the RSO-Sun vector (푅푆), shown as an orange line. The
angle between 푅푆 and 푃!, labeled 휔, determines the panel’s illumination per unit area, and the angle between the
RSO-Observer vector (푅푂) and 푃!, labeled 휃, determines the panel’s projected area from the observer’s perspective.
The angle, labeled 훽, between the panel specular reflection vector (푃!"#$), shown as a light blue dot-dashed line, and
푅푂 determines the strength of the panel’s specular glint from the observer’s perspective.
While the panel component maintains constant alignment with the sun’s projection into the equatorial plane, the
RSO’s body maintains a nadir facing orientation (퐸). The angle between 푅푆 and 퐸, labeled 휓, determines the
body’s illumination per unit area, and the angle between 푅푂 and 퐸, labeled 휂, determines the body’s projected area
from the observer’s perspective.
Fig. 2-1: Terrestrial Observation Geometry
8. 3. TWO FACET MODEL OF A RESIDENT SPACE OBJECT (RSO) IN GEOSYNCHRONOUS ORBIT
Due to the complexity of a satellite’s shape and motion, the system of equations that describe the satellite’s
properties is underdetermined, i.e. there are fewer equations than unknowns. However, most of these properties are
negligible or can be aggregated to form a more accessible and universal model. It has been found that, in the case of
three-axis stabilized satellites in a geosynchronous orbit, a two facet model performs adequately. In this section, the
assumptions underlying this model are outlined.
3.1 ASSUMPTIONS
1. The space object has a three-axis stabilized, nadir-pointing body.
2. The space object has sunward facing, articulating solar panels that maintain a constant alignment with the
projection of the sun in the equatorial plane, barring an operator maneuver or other non-nominal behavior.
3. The space object is represented by a two-facet model, in which one facet represents the solar panels and the
other represents the body.
4. The panel facet is approximately planar and possesses both specular and Lambertian reflectance properties.
Because it tends to zero away from the vector of specular reflection (glint), the specular component is only
dominant within a glint region. Otherwise, the panel’s contribution is dominated by Lambertian
reflectance.
5. The body is a complex three-dimensional shape with approximately Lambertian aggregate reflectance. It
has a different observed pose (due to self-occlusion) at each phase angle.
4. INTENSITY OF REFLECTANCE AND ALBEDO-AREA
Consider the solar energy in a certain waveband incident on the RSO and the intensity of its reflectance off of the
RSO. If the RSO is observed as an unresolved point source, then the radiant power2 of its reflection, denoted 훷
(note this is an uppercase phi), is the total reflected solar energy per unit time originating from that point source,
measured in units of [푊] [6]. The observed intensity, denoted 퐼, of this reflectance, then, is the energy flowing
through a solid angle centered at the source per unit time, measured in units of [푊/푠푟].
The intensity of an RSO’s reflectance depends on three parameters that are assumed, at least in the near term, to be
constant. These parameters are the incident solar flux in a certain waveband, denoted 푓!"# !
!" !! and sometimes
referred to as the “solar constant,” the area of the RSO’s reflecting facets measured in units of [푚!], and the albedo
of the facets, which is unit-less. The last two parameters listed, area and albedo, are qualities intrinsic to the RSO’s
material. While it is impossible to determine those parameters individually without specific insight into the RSO’s
construction, their product, albedo-Area (푎퐴), can be determined from photometric and astrometric data [3].
While 푎퐴 is a property that is intrinsic to an object, the observed 푎퐴 of an object at any given moment is a
projection of its geometry of observation with respect to the source of illumination and the observer. “Projected”
푎퐴 of an object, then, refers to its observed value based on the current geometry of the observation. “Intrinsic” 푎퐴
of an object, on the other hand, refers to its value independent of the geometry of observation. For clarity, the
symbol 푎퐴! is used to represent an object 푥’s projected 푎퐴, while the symbol 풂푨풙 is used to represent its intrinsic
푎퐴.
4.1 COMPOSITION OF THE TOTAL PHOTOMETRIC SIGNATURE
The power of the RSO’s total reflectance at the point source is an aggregate of the respective powers of the panel
and body reflectances, as shown next in (4-1).
훷!"# = 훷! + 훷! [푾] (4-1)
2 Although this quantity is based in emissive radiometry, it is adapted for the reflectance photometry.
9. The RSO’s observed intensity, however, is a projection through a solid angle of observation, shown next in (4-2).
퐼!"# = 퐼! + 퐼! 푾/풔풓 (4-2)
By the assumptions in Section 3.1, the panel’s reflectance has both a Lambertian and specular component, as it is a
roughly planar surface. The body, on the other hand, is a complex three dimensional object and is assumed to
possess roughly Lambertian reflectance (as an aggregate of many small specular reflections). Equation (4-2) is now
re-written as (4-3) with this in mind, where subscripts 퐿 and 푆 denote “Lambertian” and “specular” respectively.
퐼!"# = 퐼!" + 퐼!" + 퐼!" [푾/풔풓] (4-3)
A specular reflection (sometimes called a “glint”) may be thought of as a near perfect mirror-like reflection of the
incident light, where the angle of reflection is equal to the angle of incidence. The strength of this reflection from
the observer’s point of view depends on the angle between the observer and the vector of specular reflection, defined
earlier as 훽, where !
! > 훽 > 0. Let 퐼!", then, be written as a function of 훽, denoted 퐼!"(훽). As 훽 → 0, the specular
contribution 퐼!"(훽) quickly becomes large since the vector of specular reflectance is aligning with the observation
vector. As 훽 → !
!, however, the vector of specular reflectance and the observation vector are diverging, so, from the
observer’s perspective, the specular contribution 퐼!"(훽) decreases sharply. Equation (4-3) is now re-written in (4-4)
as such a function of 훽.
퐼!"# 훽 = 퐼!" + 퐼!" 훽 + 퐼!" [푾/풔풓] (4-4)
The strength of the Lambertian reflectance of the panel is proportional to its projected brightness, contributing a
factor of cos (휔). It is also proportional to the projected area from the observer’s perspective, contributing a factor
of cos (휃). Similarly, the strength of the Lambertian reflectance of the body is proportional to its projected
brightness, contributing a factor of cos (휓), and to its projected area from the observer’s perspective, contributing a
factor of cos (휂). Equation (4-4) is now updated in (4-5).
퐼!"# 훽,휔, 휃,휓, 휂 = 퐼!"cos (휔)cos (휃) + 퐼!" 훽 + 퐼!" cos 휓 cos (휂) [푾/풔풓] (4-5)
Rather than consider the intensity of the RSO’s reflectance, however, a transformation to projected albedo-Area
(푎퐴!"#) is performed from the photometric and astrometric data (apparent magnitude and position vectors).
Because this method is defined for Lambertian only reflectance, only observations where 훽 is not close to 0° are
considered so that the specular contribution of the panel 퐼!" 훽 drops to near zero. This transformation, derived in
previous work, is performed on (4-5) to obtain (4-6) [3].
푎퐴!"# ≈ 푎퐴! cos 휔 cos 휃 + 푎퐴! cos 휓 cos 휂 풎ퟐ | 푤ℎ푖푙푒 훽 푖푠 푛표푡 푐푙표푠푒 푡표 0° (4-6)
Decomposing the total projected albedo-Area of an RSO (푎퐴!"#) into component intrinsic albedo-Areas
(푎퐴! 푎푛푑 푎퐴!) is a task fundamental to the characterization of the RSO. In the next section, a method of
performing such a decomposition from both space based observations and a single ground based sensor is proposed.
5. POINT PAIRING
The fundamental goal of Point-Pairing is to obtain a pair of observation data points that possess a certain geometric
compatibility allowing for the cancellation of either the body or panel component, leaving only the other component.
The two observations should meet the following basic criteria.
In the case of Body Point-Pairing, in which the body’s contribution cancels out, leaving only the panel’s
contribution, the following conditions must be met.
1. The body’s contribution to the total projected albedo-Area should be identical for each observation.
2. The panel’s contribution to the total projected albedo-Area should be different for each observation.
3. The observations must be made at identical longitudinal phase angles so that the body’s poses are identical.
10. In the case of Panel Point-Pairing, in which the panel’s contribution cancels out, leaving only the body’s
contribution, the following conditions must be met.
1. The panel’s contribution to the total projected albedo-Area should be identical for each observation.
2. The body’s contribution to the total projected albedo-Area should be different for each observation, while
the body’s observed pose should be identical.
3. The observations must be made at identical longitudinal phase angles so that the body’s poses are identical.
An example of body point-pairing will be given from a simulated data set using a single ground based observer,
while an example of panel point-pairing will be given from a simulated data set with a space based observer.
BODY POINT-5.1 PAIRING METHODOLOGY
Body Point-Pairing relies on the proposition that, for nearly every observation, another observation exists for which
the projected body component is equal (within a certain tolerance), while the projected panel component is different.
Furthermore, the body’s poses in each of these observations must be identical. If two such observations are known,
then the difference between the two observations is an expression containing only a projection of the panel
component. Consider two such observations of the same RSO, defined mathematically next in (5-1).
푎퐴!"#! = 푎퐴! cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! [풎ퟐ]
푎퐴!"#! = 푎퐴! cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! [풎ퟐ]
푠푢푐ℎ 푡ℎ푎푡
휓! ≈ 휓! 푎푛푑 휂! ≈ 휂!
휔! ≠ 휔! 표푟 휃! ≠ 휃!
(5-1)
The observations are subtracted, shown next in (5-2).
푎퐴!"#! − 푎퐴!"#!
=
푎퐴! cos 휔! cos 휃! − cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! − cos 휓! cos 휂! [풎ퟐ]
(5-2)
Since cos 휓! cos 휂! ≈ cos 휓! cos 휂! by equation (5-1), the difference between the trigonometric products for
the body is very close to zero. This allows the body component to drop out nearly completely when the difference is
computed. Equation (5-2) may now be re-written in terms of just the panel’s component, allowing the panel’s
intrinsic albedo-Area to be computed directly in equation (5-3).
푎퐴!"#! − 푎퐴!"#! ≈ 푎퐴! cos 휔! cos 휃! − cos 휔! cos 휃! [풎ퟐ]
⇓
푎퐴! ≈
푎퐴!"#! − 푎퐴!"#!
cos 휔! cos 휃! − cos 휔! cos 휃!
[풎ퟐ]
(5-3)
Since the body angles of observation, 휓 and 휂, are very close from one observation to the next, the algebraic
condition for the body’s contribution to cancel out is met within a certain tolerance. Since satellite buses can vary
greatly along the east-west direction, however, it is further required that the phase angle of the observations be
nearly identical. This requirement ensures that the body is captured in an identical pose for each observation.
5.1.1 IMPORTANT CONSIDERATIONS FOR BODY POINT PAIRING
Although (5-3) provides a simple expression for the panel’s intrinsic albedo-Area, caution must be taken in this
approach. Consider the three main requirements established so far that are necessary for body point-pairing to be
successful.
1. The body’s contribution to the total projected albedo-Area should be identical for each observation.
2. The panel’s contribution to the total projected albedo-Area should be different for each observation.
3. The observations must be made at identical phase angles so that the body’s poses are equivalent.
11. Recall that the solar panel is assumed to articulate towards the sun’s projection in the equatorial plane during the
course of the RSO’s orbit. Because the panel’s motion is assumed to possess only an east-west degree of freedom,
the panel is specifically assumed to track the projection of the sun in the orbital plane. If this is the case, it can be
shown that the solar panel will, in fact, always have the same orientation with respect to the body at identical phase
angles, provided that there is no other change in the system dynamic. This presents a problem because a different
projection of the panel component is required between two observations of the same phase angle if the body point-pairing
method is to work. An investigation into behavior of the angles of observation, however, provides clarity.
RELATIONSHIP BETWEEN ANGLES OF OBSERVATION FOR THE 5.1.2 GROUND BASED CASE
Recall Fig. 2-1, which illustrates all angles relevant to ground based observations of a geostationary satellite. In this
situation, the satellite is nearly fixed with respect to the observer, with any variation owing to an inclination of the
RSO from the equatorial plane or to the declination of the sun. On the other hand, if the observer is space based, the
position of the RSO is constantly changing in relation to the observer.
To illustrate the relationship between the angles of observations, two data sets were simulated from the published
Two Line Elements (TLE) of a geosynchronous satellite. One data set was constructed for the space based situation,
and another was constructed for the ground based situation. For the space based case, the observer is a satellite in a
sun-synchronous low earth orbit, while, in the ground based case, the observer is based in Albuquerque, New
Mexico. Data points were calculated at 5 minute intervals over 120 days (admittedly a much finer temporal spacing
than would occur in reality).
Consider the following plots of the angles 휔, 휃,휓, 푎푛푑 휂 vs. phase angle. This phase angle is actually the
longitudinal phase angle, which is the projection of the total phase angle onto the equatorial plane. We have defined
it such that it ranges from −180° to 180° where 0° occurs when the projections of the observer, the sun, and the
RSO onto the equatorial plane are collinear. Longitudinal phase angle serves as the independent variable against
which the RSO’s angles of observation (휔, 휃,휓, 휂) are analyzed. Fig. 5-1 is a plot of the first night of ground based
observations. The angles relevant to the panel component are plotted in blue, while the angles relevant to the body
component are plotted in red. Note that the fine temporal spacing of the simulation resulted in the illusion of
continuity.
In Fig. 5-1, the ground based case, 휔, the angle between the RSO-Sun vector and the panel normal, appears to be
nearly constant with respect to phase angle. As 휔 is based on the orientation of the solar panel with respect to the
sun, this is to be expected since the panel’s position relative to the sun’s projection in the equatorial plane remains
fixed. Additionally, 휂, the angle between the RSO-observer vector and the body normal (nadir), appears to be nearly
constant. This too is expected in the case of a fixed ground based observer. The angles 휓 and 휃, on the other hand,
vary with relation to the relative position of the sun and are thus both closely tied to phase angle. Recall that 휓 is
the angle between RSO-sun vector and the body normal (nadir), and 휃 is the angle between the RSO-observer vector
and the solar-pointing panel normal.
12. Fig. 5-1: Ground Based Angles of Observation VS. Phase Angle
Consider now plots of the same angles taken 15 days later. In Fig. 5-2, the second set of observations is overlaid
against the initial observations so that the evolution may be observed. The curves from day one are subscripted as
퐴, while the curves from day fifteen are subscripted as 퐵.
13. Fig. 5-2: Ground Based Angles of Observation 15 Day Overlay
In Fig. 5-2, the angle 휃 has nearly the same phase angle plot in both observations. In fact, since 휃’s azimuthal
component is dependent on phase angle while its elevation component is dependent on solar declination, its phase
angle plot will only change with solar declination. Furthermore, since the solar declination’s range is much smaller
than the phase angle’s range and since it changes much more slowly, its overall effect on 휃 is relatively small.3
Think of 휃 as the contributor to the east-west component of the panel’s projected albedo-Area. A limitation of
ground based point-pairing is now clearly illustrated: the difference required in the panel’s projection cannot be
provided by 휃. On the other hand, consider the vertical translation of 휔. Since 휔 is the angle between the RSO-Sun
vector and the panel normal, it will remain fixed in the short term (in fact, its azimuthal component remains exactly
constant barring operator intervention). However, since the sun changes declination throughout the year and the
panel tracks the projection of the sun in the equatorial plane rather than the actual sun, 휔 will vary significantly
throughout the year with declination. Think of 휔 as the north-south component of the panel’s projection. It is 휔,
then, that provides the necessary diversity in the panel’s projection for successful body point-pairing in the ground
based case.
The black vertical line in Fig. 5-2 at approximately 40° phase angle illustrates a specific example of a body point-pair.
From the plot, it can be seen that there exists a pair of observations at the same phase angle (ensuring an
equivalent body pose) with nearly the same angles of observation for the body (ensuring algebraic equivalence of
the body terms in the two-facet model within a certain tolerance), and a significantly different value for at least one
3 Note that the inclination of the RSO to the equatorial plane also contributes to variation in 휃, but this is usually
small for geosynchronous satellites.
14. of the panel angles of observation, i.e. 휔 (ensuring linear independence). The albedo-Area of the panel component
can now be computed by equation (5-3).4
PANEL POINT 5.2 PAIRING METHODOLOGY
Panel point-pairing is similar to body point-pairing in that one component is cancelled out so that the other may be
isolated. Specifically, two observations are found such that the panel’s contribution to the total projected albedo-
Area is the same. At the same time, the body’s contribution to projected albedo-Area is different, while its pose is
nearly the same from one observation to the next. Because the body’s pose is required to be nearly identical, the
phase angles of the observations must be close. The difference between the two observations will yield a
measurement of the body’s albedo-Area at the particular phase angle of the observations. Consider two such
observations of the same RSO, defined mathematically next in (5-4).
푎퐴!"#! = 푎퐴! cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! [풎ퟐ]
푎퐴!"#! = 푎퐴! cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! [풎ퟐ]
푠푢푐ℎ 푡ℎ푎푡
휔! ≈ 휔! 푎푛푑 휃! ≈ 휃!
휓! ≠ 휓! 표푟 휂! ≠ 휂!
(5-4)
The observations are subtracted (as in the body point-pairing case), shown next in (5-5).
푎퐴!"#! − 푎퐴!"#!
=
푎퐴! cos 휔! cos 휃! − cos 휔! cos 휃! + 푎퐴! cos 휓! cos 휂! − cos 휓! cos 휂! [풎ퟐ]
(5-5)
Since cos 휔! cos 휃! ≈ cos 휔! cos 휃! by equation (5-4), the difference between the trigonometric products for
the panel is very close to zero. This allows the panel’s component to drop out nearly completely when the
difference is computed. Equation (5-3) may now be re-written in terms of just the body’s component, allowing the
body’s intrinsic albedo-Area for the particular phase angle to be computed directly in equation (5-6).
푎퐴!"#! − 푎퐴!"#! ≈ 푎퐴! cos 휓! cos 휂! − cos 휓! cos 휂! [풎ퟐ]
⇓
푎퐴! ≈
푎퐴!"#! − 푎퐴!"#!
cos 휓! cos 휂! − cos 휓! cos 휂!
[풎ퟐ]
(5-6)
5.2.1 RELATIONSHIP BETWEEN ANGLES OF OBSERVATION FOR THE SPACE BASED CASE
Recall Fig. 2-1, in which the angles of observation for a terrestrial observer are illustrated. The angles of
observation for the space based case are the same, and so the figure illustrates them correctly as well. The only
difference is that the relative position between the observer and the RSO is not fixed. The effect this variation has
on the angles’ phase angle plots is explained presently.
In Fig. 5-3, the space based case, 휔 also appears nearly constant with respect to phase angle, as in the ground based
case. As 휔 is not defined with respect to the observer, this continues to be in line with expectations. Similarly,
angle 휓 is not defined with respect to the observer either, so it shows nearly identical behavior to its ground based
counterpart. Angles 휃 and 휂, however, are defined with respect to the observer, so the period of the observer’s orbit
contributes to their variation.5
4 It is assumed that the changes to the material due to long term exposure to space are minimal over such a short
period of time. Although this example uses 15 days, it is possible to find body point-pairs even closer that still
possess an adequate change in the panel’s projected albedo-Area.
5 An observation satellite in sun-synchronous low earth orbit completes a revolution roughly every 90 minutes,
which is about 16 full orbits for each 24 hour geosynchronous orbit.
15. Fig. 5-3: Space Based Angles of Observation VS. Phase Angle
Consider Fig. 5-4, a scale magnification of the plot in Fig. 5-3 at 30° phase angle.
Fig. 5-4: Magnification of Space Based Angles of Observation Plot at 30° Phase Angle
Fig. 5-4 shows a pair of observations (indicated by the vertical black lines) which meet the panel point-pairing
requirements. First, the two observations have a relatively close phase angle. The body’s observed pose is therefore
very similar. Secondly, the panel angles are equal for each observation: 휃! = 휃! 푎푛푑 휔! = 휔!. At the same time,
the body’s projected albedo-Area is different between observations, since 휓! ≠ 휓!. The albedo-Area of the body at
approximately 30° may now be computed by equation (5-6).
16. POINT 5.3 PAIRING FINAL THOUGHTS
An example of body point-pairing was provided in the case of a single ground based observer that results in the
projected albedo-Area of the panel. Although this method requires that there be several days between observations
in the point-pair (note that the time between observations should be minimized), it adds a significant ability to gain
insight into the decomposition of the RSO’s total albedo-Area. Furthermore, note that geographic diversity provided
by observation stations at different locations on the planet would enhance this methodology.
An example of panel point-pairing (resulting in the projected albedo-Area of the body) was provided in the case of a
space based observer. In contrast to the case of the single ground based observer, a space based observer has the
advantage of both longitudinal and latitudinal geographic diversity over a single diurnal cycle. This allows the
point-pairing methodology to be performed on a much smaller time scale than in the case of the single ground based
observer (a single diurnal cycle as opposed to 15 days). The ground based case, however, has the advantage of
being more accessible and more easily tasked for specific observations that meet the point-pairing geometric
requirements. Also, while it was not shown in this paper, body point-pairing is also possible for the case of a space
based observer, and the observations can also be gathered in a single diurnal cycle.
6. CONCLUSIONS
This paper presents the procedure for the determination and use of point pair photometry data with respect to a
ground-based sensor. Similar point pairing conditions can be determined for a space-based sensor. Although the
point pairs are more prevalent in the space-based case due to the motion of the observer, sufficient conditions do
exist in the case of a single ground based sensor by virtue of the change in solar declination.
The determination of body point pair data with respect to a ground-based sensor requires that either the solar panel
offset angle or the RSO’s inclination off the equatorial plane is nonzero. Another pathological condition is reached
where the point pair for the body also corresponds to a point pair for the solar panel. The need for a non-zero solar
panel offset angle is absent for space-based data due to its built-in geographic diversity.
Point pairing is performed independent of the waveband of observation. Thus if the data is collected in n-wavebands,
the separation of the solar panel and body albedo areas is feasible in all n-wavebands. Indeed, in a
notional case where point pairing data is collected by a hyperspectral sensor, the procedure described in this paper
will render the material reflectance spectra for the solar panel and the body.
7. REFERENCES
1. Malvern, L.E., “Introduction to the mechanics of continuous medium”, Library of congress catalog card
number: 69-13712, Prentice-Hall, 1969, page 7.
2. Wikipedia, “Earth-centered inertial”, URL: http://en.wikipedia.org/wiki/Earth-centered_inertial
3. Payne, T. E, Lucas, K., Chaudhary, A., Mutschler, S., Dao, P., Murray-Krezan, J., “A Derivation of the
Analytical Relationship between the Projected Albedo-Area Product of a Space Object and its Aggregate
Photometric Measurements”, AMOS 2013 Technical Conference, Maui, HI.
4. Wikipedia, “Position of the Sun”, URL: http://en.wikipedia.org/wiki/Position_of_the_Sun
5. Chaudhary, A.B., Payne, T.E., Gregory, S., Dao, P., “Fingerprinting of non-resolved three-axis stabilized space
objects using a two-facet analytical model”, AMOS 2011 Technical Conference, Maui, HI.
6. Tatum, Jeremy, “Stellar Atmospheres,” http://orca.phys.uvic.ca/~tatum/stellatm.html, University of Victoria,
2011.