Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a...101..134h&link_type=abstract
Astronomy and Astrophysics, vol. 101, no. 1, Aug. 1981, p. 134-137.
Astronomy and Astrophysics
Astrophysics
4
Asymptotic Methods, Binary Stars, Orbit Perturbation, Stellar Mass Ejection, Supernovae, Two Body Problem, Boundary Layers, Harmonic Oscillators, Orbit Calculation, Power Series
Scientific paper
The two time-scale method for obtaining approximate solutions to singular perturbation problems is applied to the two-body problem with quick mass loss, as happens in supernova explosions. Asymptotic expansions by the two time-scale method are introduced and illustrated for the example of a harmonic oscillator. The method is then used to obtain approximate solutions for the motion of two point masses following the isotropic ejection of mass from the system at high velocities in a very short period of time, corresponding to a boundary layer in time. An expression for the critical remaining mass fraction below which the initially circular orbit is disrupted is derived as an expansion of a power series in a small parameter characterizing the ratio of the time scales of the duration of the explosion and the orbital period, and the first four terms of the expansion are presented in detail.
Hut Piet
Verhulst Ferdinand
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