Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits

Author(s)
M. H. A. Youssef

ABSTRACT

For certain values of semi-major axis and eccentricity, orbit plane precession caused by Earth oblate is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Many forces cause slow changes in the inclination and ascending node of sun-synchronous orbits. In this work, we investigate the analytical perturbations due to the direct solar radiation pressure and gravitational waves effects. A full analytical solution is obtained using technique of canonical Lie-transformation up to the order three in (the oblateness of the Earth). The solar radiation pressure and gravitational waves perturbations cause second order effects on all the elements of the elliptic orbit (the eccentricity, inclination, ascending node, argument of perigee, and semi-major axis) consequently these perturbations will cause disturbance in the sun-synchronism. Also we found that the perturbation or the behavior of gravitational waves almost the same as the perturbation or the behavior of solar radiation pressure and their coupling will incorporate the sun-synchronism through the secular rate of the ascending node precession.

For certain values of semi-major axis and eccentricity, orbit plane precession caused by Earth oblate is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Many forces cause slow changes in the inclination and ascending node of sun-synchronous orbits. In this work, we investigate the analytical perturbations due to the direct solar radiation pressure and gravitational waves effects. A full analytical solution is obtained using technique of canonical Lie-transformation up to the order three in (the oblateness of the Earth). The solar radiation pressure and gravitational waves perturbations cause second order effects on all the elements of the elliptic orbit (the eccentricity, inclination, ascending node, argument of perigee, and semi-major axis) consequently these perturbations will cause disturbance in the sun-synchronism. Also we found that the perturbation or the behavior of gravitational waves almost the same as the perturbation or the behavior of solar radiation pressure and their coupling will incorporate the sun-synchronism through the secular rate of the ascending node precession.

Cite this paper

Youssef, M. (2018) Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits.*World Journal of Mechanics*, **8**, 11-25. doi: 10.4236/wjm.2018.82002.

Youssef, M. (2018) Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits.

References

[1] Kozai, Y. (1961) Effects of Solar-Radiation Pressure on the Motion of an Aritificial Satellite, Smithsonian Astrophys. Obs. Spec. Rep., 56.

[2] Aksnes, K. (1976) Short-Period and Long-Period Perturbations of a Spherical Satellite Due to Direct solar Radiation. Celestial Mechanics, 89.

[3] Hough, M. (1981) Sun-Synchronous Orbits near Critical Inclination. Celestial Mechanics, 111, 137-157.

https://doi.org/10.1007/BF01230515

[4] Youssef, M.H. (2005) Relativistic Effects on Sun-Synchronous Orbits including the Influence of Direct Solar Radiation Pressure. Bulletin of Faculty of Pharmacy, Cairo University, 73, 53-75.

[5] Youssef, M.H. (2017) Short-Period and Long-Period Effects of Weak Gravitational Waves. IJAA, 7, 230-237.

[6] Youssef, M.H. (2017) Semi-Analytical Theory of the Mean Orbital Motion Due to the Effect of Gravitational Waves. EJSR, 147, 342-350.

[7] Will, C. (1981) Theory and Experiment in Gravitational Physics. Cambridge University Press.

[8] Fitzpatrick, P. (1970) Principles of Celestial Mechanics, Academic Press, New York and London.

[9] Hori, G. (1966) The Effect of Radiation Pressure on the Motion of an Artificial Satellite, Space Mathematics, American Mathematical Society.

[10] Hori, G. (1966) Theory of General Perturbations with Unspecified Canonical Variables. Publications of the Astronomical Society of Japan, 18, 287.

[11] Kamel, A.A. (1969) Expansion Formulae in Canonical Transformations Depending on a Small Parameter. Celestial Mechanics, 1, 19.

https://doi.org/10.1007/BF01228838

[1] Kozai, Y. (1961) Effects of Solar-Radiation Pressure on the Motion of an Aritificial Satellite, Smithsonian Astrophys. Obs. Spec. Rep., 56.

[2] Aksnes, K. (1976) Short-Period and Long-Period Perturbations of a Spherical Satellite Due to Direct solar Radiation. Celestial Mechanics, 89.

[3] Hough, M. (1981) Sun-Synchronous Orbits near Critical Inclination. Celestial Mechanics, 111, 137-157.

https://doi.org/10.1007/BF01230515

[4] Youssef, M.H. (2005) Relativistic Effects on Sun-Synchronous Orbits including the Influence of Direct Solar Radiation Pressure. Bulletin of Faculty of Pharmacy, Cairo University, 73, 53-75.

[5] Youssef, M.H. (2017) Short-Period and Long-Period Effects of Weak Gravitational Waves. IJAA, 7, 230-237.

[6] Youssef, M.H. (2017) Semi-Analytical Theory of the Mean Orbital Motion Due to the Effect of Gravitational Waves. EJSR, 147, 342-350.

[7] Will, C. (1981) Theory and Experiment in Gravitational Physics. Cambridge University Press.

[8] Fitzpatrick, P. (1970) Principles of Celestial Mechanics, Academic Press, New York and London.

[9] Hori, G. (1966) The Effect of Radiation Pressure on the Motion of an Artificial Satellite, Space Mathematics, American Mathematical Society.

[10] Hori, G. (1966) Theory of General Perturbations with Unspecified Canonical Variables. Publications of the Astronomical Society of Japan, 18, 287.

[11] Kamel, A.A. (1969) Expansion Formulae in Canonical Transformations Depending on a Small Parameter. Celestial Mechanics, 1, 19.

https://doi.org/10.1007/BF01228838