Classical Dynamics of Particles and Systems · Problem 8-6

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-gravitational-speeds

Problem

Two gravitating masses

m_1

and

m_2

(

m_1 + m_2 = M

) are separated by a distance

r_0

and released from rest. Show that when the separation is

r (< r_0)

, the speeds are

v_1 = m_2\sqrt{\frac{2G}{M}\left(\frac{1}{r} - \frac{1}{r_0}\right)}, \qquad v_2 = m_1\sqrt{\frac{2G}{M}\left(\frac{1}{r} - \frac{1}{r_0}\right)}