A New Navigation Force Model for the Earth’s Albedo and Its Effects on the Orbital Motion of an Artificial Satellite

ABSTRACT

In this paper, we developed a new approach of an analytical model to calculate the radial and transversal components of the acceleration due to the effects of Earth’s albedo. Its effects on the orbital motion of an artificial satellite are introduced. It is assumed that the satellite’s horizon is illuminated and the sun lies on the equator. The magnitudes of those components are obtained and their effects on orbital evolution have been tested for different satellites elements. The perturbations in orbital elements due to Earth’s albedo have been obtained using Lagrange Planetary equation in Gaussian form, in particular the case of LAGEOS satellite, have been found using this new analytical formalism.

In this paper, we developed a new approach of an analytical model to calculate the radial and transversal components of the acceleration due to the effects of Earth’s albedo. Its effects on the orbital motion of an artificial satellite are introduced. It is assumed that the satellite’s horizon is illuminated and the sun lies on the equator. The magnitudes of those components are obtained and their effects on orbital evolution have been tested for different satellites elements. The perturbations in orbital elements due to Earth’s albedo have been obtained using Lagrange Planetary equation in Gaussian form, in particular the case of LAGEOS satellite, have been found using this new analytical formalism.

KEYWORDS

Satellite Dynamics, Non-Gravitational Forces, Albedo Effect, Orbital Perturbations, Lagrange Planetary Equations

Satellite Dynamics, Non-Gravitational Forces, Albedo Effect, Orbital Perturbations, Lagrange Planetary Equations

Cite this paper

nullY. Abdel-Aziz, A. Abdel-Hameed and K. Khalil, "A New Navigation Force Model for the Earth’s Albedo and Its Effects on the Orbital Motion of an Artificial Satellite,"*Applied Mathematics*, Vol. 2 No. 7, 2011, pp. 801-807. doi: 10.4236/am.2011.27107.

nullY. Abdel-Aziz, A. Abdel-Hameed and K. Khalil, "A New Navigation Force Model for the Earth’s Albedo and Its Effects on the Orbital Motion of an Artificial Satellite,"

References

[1] A. Jaggi, R. Dach, et al., “Phase Center Modeling for LAGEOS GPS Receiver Antennas and Its Impact on Precise Orbit Determination,” Journal of Geodesy, Vol. 83, 2009, pp. 1145-1162.

[2] M. Harris and R. Lyle, “Spacecraft Radiation Torque,” NASA Space Vechile Design Criteria (Guidance and Control) NASA SP-8027, October 1969, pp. 1-37.

[3] E. M. Rocco, “Evaluation of the Terrestial Albedo Applied to Some Scientific Missions,” Space Science Review, Vol. 151, No. 1-3, 2009, pp. 135-147. doi:10.1007/s11214-009-9622-6

[4] J. S. A. Green, “Reflections on the Earth’s Albedo: A Collection of Scattered Thoughts,” Weather, Vol. 57, No. 12, 2002, pp. 431-439. doi:10.1256/wea.223.01

[5] L. Sehnal, “The Earth Albedo Model in Spherical Harmonics,” Bulletin of the Astronomical Institution of Czechoslovakia, Vol. 30, No. 4, 1979, pp. 199-204.

[6] R. Bowman, “Orbit Perturbation Analysis of West Ford Needles Clusters,” American Institute of Aeronautics and Astronautics, Worldwide, 2000.

[7] I. Pater and J. Lissauer, “Planetary Science,” Cambridge University Press, Cambridge, 2001.

[8] K. H. Nisancioglu, “Modeling the Impact of Atmospheric Moisture Transport on Global Ice Volume,” Ph D. Thesis, Massachusetts Institute of Technology, Cambridge, 2004.

[9] L. Anselmo, P. Farinella, A. Milani and A. M. Nobili, “Effects of the Earth-Reflected Sunlight on the Orbit of the LAGEOS Satellite,” Astronomy and Astrophysics, Vol. 117, No. 1, 1983, pp. 1-3.

[10] E. Levin, “Reflected Radiation Received by an Earth Satellite,” AES Journal, Vol. 32, No. 9, 1962, pp. 1328-1331.

[11] S. Wyatt and P. Springer, “The Effect of Terrestrial Radiation Pressure on Satellite Orbits,” In: M. Roy, Ed., Dynamics of Satellites, Paris, May 1962, pp. 186-196.

[12] L. Sehnal, “The Perturbations of the Orbital Elements Caused by the Pressure of the Radiation Reflected from the Earth,” Proceeding of Symposium, Paris, 1965.

[13] D. E. Smith, “Earth Reflected Radiation Pressure,” Dynamics of Satellites, Prague, 1969.

[14] R. M. L. Baker, “Radiation on a Satellite in the Presence of Diffuse and Partially Specular Reflecting Body,” Proceeding of Trajectories of Artificial Celestial bode as Determined from Observations, Paris, April 1965, pp. 85-150.

[1] A. Jaggi, R. Dach, et al., “Phase Center Modeling for LAGEOS GPS Receiver Antennas and Its Impact on Precise Orbit Determination,” Journal of Geodesy, Vol. 83, 2009, pp. 1145-1162.

[2] M. Harris and R. Lyle, “Spacecraft Radiation Torque,” NASA Space Vechile Design Criteria (Guidance and Control) NASA SP-8027, October 1969, pp. 1-37.

[3] E. M. Rocco, “Evaluation of the Terrestial Albedo Applied to Some Scientific Missions,” Space Science Review, Vol. 151, No. 1-3, 2009, pp. 135-147. doi:10.1007/s11214-009-9622-6

[4] J. S. A. Green, “Reflections on the Earth’s Albedo: A Collection of Scattered Thoughts,” Weather, Vol. 57, No. 12, 2002, pp. 431-439. doi:10.1256/wea.223.01

[5] L. Sehnal, “The Earth Albedo Model in Spherical Harmonics,” Bulletin of the Astronomical Institution of Czechoslovakia, Vol. 30, No. 4, 1979, pp. 199-204.

[6] R. Bowman, “Orbit Perturbation Analysis of West Ford Needles Clusters,” American Institute of Aeronautics and Astronautics, Worldwide, 2000.

[7] I. Pater and J. Lissauer, “Planetary Science,” Cambridge University Press, Cambridge, 2001.

[8] K. H. Nisancioglu, “Modeling the Impact of Atmospheric Moisture Transport on Global Ice Volume,” Ph D. Thesis, Massachusetts Institute of Technology, Cambridge, 2004.

[9] L. Anselmo, P. Farinella, A. Milani and A. M. Nobili, “Effects of the Earth-Reflected Sunlight on the Orbit of the LAGEOS Satellite,” Astronomy and Astrophysics, Vol. 117, No. 1, 1983, pp. 1-3.

[10] E. Levin, “Reflected Radiation Received by an Earth Satellite,” AES Journal, Vol. 32, No. 9, 1962, pp. 1328-1331.

[11] S. Wyatt and P. Springer, “The Effect of Terrestrial Radiation Pressure on Satellite Orbits,” In: M. Roy, Ed., Dynamics of Satellites, Paris, May 1962, pp. 186-196.

[12] L. Sehnal, “The Perturbations of the Orbital Elements Caused by the Pressure of the Radiation Reflected from the Earth,” Proceeding of Symposium, Paris, 1965.

[13] D. E. Smith, “Earth Reflected Radiation Pressure,” Dynamics of Satellites, Prague, 1969.

[14] R. M. L. Baker, “Radiation on a Satellite in the Presence of Diffuse and Partially Specular Reflecting Body,” Proceeding of Trajectories of Artificial Celestial bode as Determined from Observations, Paris, April 1965, pp. 85-150.