On the problem of two bodies of variable mass
Abstract
The relative orbital motion of two bodies whose mass varies according to the EddingtonJeans 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 EddingtonJeans 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.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 August 1978
 Bibcode:
 1978AZh....55..873G
 Keywords:

 Equations Of Motion;
 Orbital Mechanics;
 Stellar Motions;
 Two Body Problem;
 Variable Mass Systems;
 Asymptotic Methods;
 Differential Equations;
 Elliptical Orbits;
 Orbit Calculation;
 Astronomy