An Introduction to Modern Astrophysics · Problem 18.9

Physical Processes in the Solar System — Carroll & Ostlie

Physics — Astrophysics · orbital-period-change-mass-transfer

Problem

(a) Show that in a close binary system where angular momentum is conserved, the change in orbital period produced by mass transfer is given by 1PdPdt=3M˙1M1−M2M1M2.\frac{1}{P}\frac{dP}{dt} = 3\dot{M}_1 \frac{M_1 - M_2}{M_1 M_2}. (b) U Cephei (an Algol system) has an orbital period of 2.49 days that has increased by about 20 s in the past 100 years. The masses of the two stars are M1=2.9 M⊙M_1 = 2.9\,\mathrm{M}_\odot and M2=1.4 M⊙M_2 = 1.4\,\mathrm{M}_\odot. Assuming that this change is due to the transfer of mass between the two stars in this Algol system, estimate the mass transfer rate. Which of these stars is gaining mass?

Related theory

Browse the problem library