Some mechanical invariants of elliptical orbits

Details Some mechanical invariants of elliptical orbits Some mechanical invariants of elliptical orbits

Apr 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983avest..16..247g&link_type=abstract

(Astronomicheskii Vestnik, vol. 16, Oct.-Dec. 1982, p. 247-251) Solar System Research (ISSN 0038-0946), vol. 16, no. 4, April 19

Astronomy and Astrophysics

Astronomy

Elliptical Orbits, Orbital Mechanics, Kepler Laws, Proving, Two Body Problem, Virial Theorem

Scientific paper

The energy integral of the two-body problem is used to obtain some mechanical invariants of transformations of elliptical orbits which reveal some properties of the motion about an attracting center. It is found that the product of the speeds at centrally symmetric points of an elliptical orbit is a constant for the entire family of equal-energy orbits, equaling the square of the speed along the circular orbit of this family, which corresponds to the magnitude of twice the specific total energy of the orbital motion. It is proved that the products of the velocity and the corresponding distance from the attracting focus at an arbitrary pair of centrally symmetric points of any elliptical orbit are always equal.

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