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