Celestial mechanics

, Volume 23, Issue 4, pp 307–363 | Cite as

Theory of the motion of an artificial Earth satellite

  • Felix R. Hoots


An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.

Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions.


Differential Equation Density Function Power Density Drag Coefficient Atmospheric Model 
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Copyright information

© D. Reidel Publishing Co. 1981

Authors and Affiliations

  • Felix R. Hoots
    • 1
  1. 1.Aerospace Defense CommandColorado Springs

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