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Analytic theory of orbit contraction
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Culp, R. D. Longuski, J. M. Vinh, N. X. Busemann, A. |
| Copyright Year | 1977 |
| Description | The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory. |
| File Size | 3028093 |
| Page Count | 42 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19780022079 |
| Archival Resource Key | ark:/13960/t6935mz7j |
| Language | English |
| Publisher Date | 1977-01-01 |
| Access Restriction | Open |
| Subject Keyword | Astrophysics Orbital Mechanics Numerical Analysis Gravitational Effects Satellite Orbits Lagrange Multipliers Differential Equations Orbit Calculation Poincare Problem Aerodynamic Forces Equations of Motion Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
