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Elementary derivation of the perturbation equations of celestial mechanicsThe equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.
Document ID
19770033831
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Burns, J. A.
(NASA Ames Research Center Moffett Field, Calif.; Cornell University, Ithaca, N.Y., United States)
Date Acquired
August 9, 2013
Publication Date
October 1, 1976
Publication Information
Publication: American Journal of Physics
Volume: 44
Subject Category
Astrodynamics
Accession Number
77A16683
Distribution Limits
Public
Copyright
Other

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