Two-body problem with slowly decreasing mass |
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| Authors: | Ferdinand Verhulst |
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| Institution: | (1) Department of Mathematics, Technological University, Delft, The Netherlands;(2) Present address: Mathematical Institute, University of Utrecht, Utrecht, The Netherlands |
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| Abstract: | Summary Evolution of the orbital elements of a two-body system with slowly decreasing mass according to Jeans' mode is described by a non-linear, non-autonomous system of differential equations.In general the system contains one stationary solution (e=1,f= ), for which an instability criterion is derived. For example the stationary solution is unstable for all Jeans-Eddington functionsm
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(t) with 1 n3 which characterize the loss of mass. Furthermore, it is possible to describe the quantitative behaviour ofE+ ,e anda for arbitrarym(t) in a large number of cases. In the case of the Jeans-Eddington functions we find that the amplitude of the oscillations ine is monotone decreasing with time ifn>3 and it is monotone increasing with time ifn<3.By comparing these analytical results with the numerical calculations of Hadjidemetriou we explain the rapid rotation of the line of apsides which occurs if the initial value ofe is nearly-circular.
                       ,      ,   .   (e=1,f=),  .  ,  -m
n
(t), , 1n 3.  , E+,e a m(t) . - , , n>3, , n<3.   ,  , - e.
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