Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites

Author(s)
Hadia Hassan Selim

Affiliation(s)

Department of Astronomy, National Research Institute of Astronomy and Geophysics, Cairo, Egypt.

Department of Astronomy, National Research Institute of Astronomy and Geophysics, Cairo, Egypt.

ABSTRACT

Coupling effects of Earth oblateness and direct solar radiation pressure on the motion of an artificial satellite are evaluated. Secular and periodic terms are retained up to order three and two respectively, where the coefficient of the second zonal harmonic of the geopotential is considered of first order. The solution revealed the existence of secular terms at order three that arises from the couplings between terms, of lower orders, resulting from the solar radiation pressure.

Coupling effects of Earth oblateness and direct solar radiation pressure on the motion of an artificial satellite are evaluated. Secular and periodic terms are retained up to order three and two respectively, where the coefficient of the second zonal harmonic of the geopotential is considered of first order. The solution revealed the existence of secular terms at order three that arises from the couplings between terms, of lower orders, resulting from the solar radiation pressure.

Cite this paper

Selim, H. (2014) Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites.*International Journal of Astronomy and Astrophysics*, **4**, 530-543. doi: 10.4236/ijaa.2014.43049.

Selim, H. (2014) Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites.

References

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[2] Giacaglia, G.E.O. (1972) Perturbation Methods in Non-Linear Systems. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-6400-2

[3] Musen, P.J. (1960) The Influence of the Solar Radiation Pressure on the Motion of an Artificial Satellite. Journal of Geophysical Research, 6, 1391-1396.

http://onlinelibrary.wiley.com/doi/10.1029/JZ065i005p01391/abstract

[4] Kozai, Y. (1961) Effects of Solar Radiation Pressure on the Motion of an Artificial Satellite. Smithsonian Astrophys. Obs. Spec. Re, 56, 25-33.

[5] Brouwer, D. (1962) Dynamics of Satellites (Roy, M., Ed.). Springer, Berlin.

[6] Hori, G. (1966) Theory of General Perturbation with Unspecified Canonical Variable. Publications of the Astronomical Society of Japan, 18, 287. http://adsabs.harvard.edu/abs/1966PASJ...18..287H

[7] De Moraes, R.V. (1981) Combined Solar Radiation Pressure and Drag Effects on the Orbits of Artificial Satellites. Celestial Mechanics, 25, 281-292. http://link.springer.com/article/10.1007%2FBF01228965

[8] Kampos, B. (1986) Nasa CR1008-Guidance, Flight Mech. and Trajectory Optimization, Vol. IX.

[9] Sehnal, L. (1970) In Dynamics Satellites (Morando, Ed.). Springer, Berlin.

[10] Sehnal, L. (1975) In Satellite Dynamics (Giacalia, Ed.). Springer, Berlin.

[11] McInnes, C.R. and Browen, J.C. (1990) The Dynamics of Solar Sails with a Non-Point Source of Radiation Pressure Celestial Mechanics and Dynamical Astronomy, 49, 249-264.

http://link.springer.com/article/10.1007%2FBF00049416

[12] Feraz-Mello, S. (1972) Analytical Study of the Earth’s Shadowing Effects on Satellite Orbits. Celestial Mechanics, 5, 80-101. http://link.springer.com/article/10.1007%2FBF01227825

[13] Anselono, L., Bertotti, B., Farinella, P., Milani, A. and Mobili, A.M. (1983) Orbital Perturbation Due to Radiation Pressure for a Spacecraft of Complex Shape. Celestial Mechanics, 29, 27-43.

http://link.springer.com/article/10.1007%2FBF01358596

[14] Geyling, F.T. and Westerman, H.R. (1971) Introduction to Orbital Mech. Addison Wesley.

[15] Lála, P. (1972) Combined Gravitational and Solar Radiation Pressure Effects on The Semimajor Axis of the Earth’s Satellite. Bulletin of the Astronomical Institute of Czechoslovakia, 23, 342.

http://adsabs.harvard.edu/abs/1972BAICz..23..342L

[16] McMahon, J.W. (2011) ProQuest Dissertations and Theses. Ph.D. Thesis, University of Colorado at Boulder, Boulder.

[17] Lücking, C., Colombo, C. and McInnes, C.R. (2012) A Passive Satellite Deorbiting Strategy for Medium Earth Orbit Using Solar Radiation Pressure and the J2 Effect. Acta Astronautica, 77, 197-206. http://adsabs.harvard.edu/abs/2012AcAau..77..197L http://dx.doi.org/10.1016/j.actaastro.2012.03.026

[18] Cook, D.G. (2001) Master’s Thesis, AD-A390187; AFIT/GSP/ENY/01M-01 Graduate School of Engineering and Management.

[19] Selim, H.H. (1991) The Effect of Solar Radiation Pressure on The Motion of Artificial Satellite. M.Sc. Thesis, Cairo University, Giza.

[20] Deprit, A. (1969) Canonical Transformations Depending on a Small Parameter. Celestial Mechanics, 1, 12-30. http://adsabs.harvard.edu/abs/1969CeMec...1...12D

[1] Kamel, A.A. (1971) Lie Transformation and the Hamiltonian of Non-Hamiltonian Systems. Celestial Mechanics, 4, 397-405. http://link.springer.com/article/10.1007%2FBF01231400

[2] Giacaglia, G.E.O. (1972) Perturbation Methods in Non-Linear Systems. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-6400-2

[3] Musen, P.J. (1960) The Influence of the Solar Radiation Pressure on the Motion of an Artificial Satellite. Journal of Geophysical Research, 6, 1391-1396.

http://onlinelibrary.wiley.com/doi/10.1029/JZ065i005p01391/abstract

[4] Kozai, Y. (1961) Effects of Solar Radiation Pressure on the Motion of an Artificial Satellite. Smithsonian Astrophys. Obs. Spec. Re, 56, 25-33.

[5] Brouwer, D. (1962) Dynamics of Satellites (Roy, M., Ed.). Springer, Berlin.

[6] Hori, G. (1966) Theory of General Perturbation with Unspecified Canonical Variable. Publications of the Astronomical Society of Japan, 18, 287. http://adsabs.harvard.edu/abs/1966PASJ...18..287H

[7] De Moraes, R.V. (1981) Combined Solar Radiation Pressure and Drag Effects on the Orbits of Artificial Satellites. Celestial Mechanics, 25, 281-292. http://link.springer.com/article/10.1007%2FBF01228965

[8] Kampos, B. (1986) Nasa CR1008-Guidance, Flight Mech. and Trajectory Optimization, Vol. IX.

[9] Sehnal, L. (1970) In Dynamics Satellites (Morando, Ed.). Springer, Berlin.

[10] Sehnal, L. (1975) In Satellite Dynamics (Giacalia, Ed.). Springer, Berlin.

[11] McInnes, C.R. and Browen, J.C. (1990) The Dynamics of Solar Sails with a Non-Point Source of Radiation Pressure Celestial Mechanics and Dynamical Astronomy, 49, 249-264.

http://link.springer.com/article/10.1007%2FBF00049416

[12] Feraz-Mello, S. (1972) Analytical Study of the Earth’s Shadowing Effects on Satellite Orbits. Celestial Mechanics, 5, 80-101. http://link.springer.com/article/10.1007%2FBF01227825

[13] Anselono, L., Bertotti, B., Farinella, P., Milani, A. and Mobili, A.M. (1983) Orbital Perturbation Due to Radiation Pressure for a Spacecraft of Complex Shape. Celestial Mechanics, 29, 27-43.

http://link.springer.com/article/10.1007%2FBF01358596

[14] Geyling, F.T. and Westerman, H.R. (1971) Introduction to Orbital Mech. Addison Wesley.

[15] Lála, P. (1972) Combined Gravitational and Solar Radiation Pressure Effects on The Semimajor Axis of the Earth’s Satellite. Bulletin of the Astronomical Institute of Czechoslovakia, 23, 342.

http://adsabs.harvard.edu/abs/1972BAICz..23..342L

[16] McMahon, J.W. (2011) ProQuest Dissertations and Theses. Ph.D. Thesis, University of Colorado at Boulder, Boulder.

[17] Lücking, C., Colombo, C. and McInnes, C.R. (2012) A Passive Satellite Deorbiting Strategy for Medium Earth Orbit Using Solar Radiation Pressure and the J2 Effect. Acta Astronautica, 77, 197-206. http://adsabs.harvard.edu/abs/2012AcAau..77..197L http://dx.doi.org/10.1016/j.actaastro.2012.03.026

[18] Cook, D.G. (2001) Master’s Thesis, AD-A390187; AFIT/GSP/ENY/01M-01 Graduate School of Engineering and Management.

[19] Selim, H.H. (1991) The Effect of Solar Radiation Pressure on The Motion of Artificial Satellite. M.Sc. Thesis, Cairo University, Giza.

[20] Deprit, A. (1969) Canonical Transformations Depending on a Small Parameter. Celestial Mechanics, 1, 12-30. http://adsabs.harvard.edu/abs/1969CeMec...1...12D