Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978azh....55..873g&link_type=abstract
(Astronomicheskii Zhurnal, vol. 55, July-Aug. 1978, p. 873-880.) Soviet Astronomy, vol. 22, July-Aug. 1978, p. 498-502. Translat
Astronomy and Astrophysics
Astronomy
2
Equations Of Motion, Orbital Mechanics, Stellar Motions, Two Body Problem, Variable Mass Systems, Asymptotic Methods, Differential Equations, Elliptical Orbits, Orbit Calculation
Scientific paper
The relative orbital motion of two bodies whose mass varies according to the Eddington-Jeans law - i.e., the mass decreases in proportion to some exponent greater than unity of the mass - is analyzed. Upper and lower estimates for the coordinates of the relative orbit are obtained. It is shown that the distance between the two bodies increases without limit as the mass approaches zero. If the exponent in the Eddington-Jeans law is between 1 and 3, then the angular distance traveled by the bodies along the relative orbits is bounded from above as the mass approaches zero. The relative orbit of the two bodies asymptotically approaches a straight line as time goes to infinity. For any value of the exponent above 1 one can indicate the initial conditions sufficient for the breakup of a system of two bodies initially moving along relative orbits of the elliptical types to occur at some time when the mass is decreasing.
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