Use of an Energy-Like Integral to Study the Motion of an Axi-Symmetric Satellite under Drag and Radiation Pressure

ABSTRACT

The axi-symmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. An energy-like is given for a general drag force function of the polar angle*θ*, and then it is used to find a relation for the orbit equation of the satellite with initial conditions satisfying the vanishing of arbitrarily choosing higher derivatives of the velocity.

The axi-symmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. An energy-like is given for a general drag force function of the polar angle

Cite this paper

Mostafa, A. (2015) Use of an Energy-Like Integral to Study the Motion of an Axi-Symmetric Satellite under Drag and Radiation Pressure.*International Journal of Astronomy and Astrophysics*, **5**, 148-154. doi: 10.4236/ijaa.2015.53019.

Mostafa, A. (2015) Use of an Energy-Like Integral to Study the Motion of an Axi-Symmetric Satellite under Drag and Radiation Pressure.

References

[1] Brouwer, D. and Hori, G. (1961) Theoretical Evaluation of Atmospheric Drag Effects in the Motion of an Artificial Satellite. The Astronomical Journal, 66, 193-225.

http://dx.doi.org/10.1086/108399

[2] Mittleman, D. and Jezwski, D. (1982) An Analytic Solution to the Classical Two-Body Problem with Drag. Celestial Mechanics and Dynamical Astronomy, 28, 401-413.

http://dx.doi.org/10.1007/BF01372122

[3] Jezwski, D. and Mittleman, D. (1983) Integrals of Motion for the Classical Two-Body Problem with Drag. International Journal of Non-Linear Mechanics, 18, 119-124.

http://dx.doi.org/10.1016/0020-7462(83)90039-2

[4] Danby, G.M.A. (1962) Fundamentals of Celestial Mechanics. MacMillan, New York.

[5] Leach, P.G.L. (1987) The First Integrals and Orbit Equation for the Kepler Problem with Drag. Journal of Physics A: Mathematical and General, 20, 1997-2004.

http://dx.doi.org/10.1088/0305-4470/20/8/019

[6] Gorringe, V.M. and Leach, P.G.L. (1988) Hamiltonlike Vectors for a Class of Kepler Problems with Drag. Celestial Mechanics and Dynamical Astronomy, 41, 125-130.

http://dx.doi.org/10.1007/BF01238757

[7] McMahon, J. and Scheeres, D. (2010) Secular Orbit Variation due to solar Radiation Effects: A Detailed Model for BYORP. Celestial Mechanics and Dynamical Astronomy, 106, 261-300.

http://dx.doi.org/10.1007/s10569-009-9247-9

[8] Mavraganis, A.G. (1991) The Almost Constant-Speed Two-Body Problem with Resistance. Celestial Mechanics and Dynamical Astronomy, 51, 395-405.

http://dx.doi.org/10.1007/BF00052930

[9] Mavraganis, A.G. and Michalakis, D.G. (1994) The Two-Body Problem with Drag and Radiation Pressure. Celestial Mechanics and Dynamical Astronomy, 58, 393-403.

http://dx.doi.org/10.1007/BF00692013

[10] El-Shaboury, S.M. and Mostafa, A. (2014) The Motion of Axisymmetric Satellite with Drag and Radiation Pressure. Astrophysics and Space Science, 352, 515-519.

http://dx.doi.org/10.1007/s10509-014-1975-y

[1] Brouwer, D. and Hori, G. (1961) Theoretical Evaluation of Atmospheric Drag Effects in the Motion of an Artificial Satellite. The Astronomical Journal, 66, 193-225.

http://dx.doi.org/10.1086/108399

[2] Mittleman, D. and Jezwski, D. (1982) An Analytic Solution to the Classical Two-Body Problem with Drag. Celestial Mechanics and Dynamical Astronomy, 28, 401-413.

http://dx.doi.org/10.1007/BF01372122

[3] Jezwski, D. and Mittleman, D. (1983) Integrals of Motion for the Classical Two-Body Problem with Drag. International Journal of Non-Linear Mechanics, 18, 119-124.

http://dx.doi.org/10.1016/0020-7462(83)90039-2

[4] Danby, G.M.A. (1962) Fundamentals of Celestial Mechanics. MacMillan, New York.

[5] Leach, P.G.L. (1987) The First Integrals and Orbit Equation for the Kepler Problem with Drag. Journal of Physics A: Mathematical and General, 20, 1997-2004.

http://dx.doi.org/10.1088/0305-4470/20/8/019

[6] Gorringe, V.M. and Leach, P.G.L. (1988) Hamiltonlike Vectors for a Class of Kepler Problems with Drag. Celestial Mechanics and Dynamical Astronomy, 41, 125-130.

http://dx.doi.org/10.1007/BF01238757

[7] McMahon, J. and Scheeres, D. (2010) Secular Orbit Variation due to solar Radiation Effects: A Detailed Model for BYORP. Celestial Mechanics and Dynamical Astronomy, 106, 261-300.

http://dx.doi.org/10.1007/s10569-009-9247-9

[8] Mavraganis, A.G. (1991) The Almost Constant-Speed Two-Body Problem with Resistance. Celestial Mechanics and Dynamical Astronomy, 51, 395-405.

http://dx.doi.org/10.1007/BF00052930

[9] Mavraganis, A.G. and Michalakis, D.G. (1994) The Two-Body Problem with Drag and Radiation Pressure. Celestial Mechanics and Dynamical Astronomy, 58, 393-403.

http://dx.doi.org/10.1007/BF00692013

[10] El-Shaboury, S.M. and Mostafa, A. (2014) The Motion of Axisymmetric Satellite with Drag and Radiation Pressure. Astrophysics and Space Science, 352, 515-519.

http://dx.doi.org/10.1007/s10509-014-1975-y