Two stars, with masses m1 and m2 that are initially very far apart and at rest (

Question

Two stars, with masses m1 and m2 that are initially very far apart and at rest (and even farther from
any other stars) are pulled together by their gravitational attraction. Find their relative speed when they
are a distance d apart from one another. Put your answer in terms of given quantities (m1, m2, d) and
any relevant physical quantities.

Explanation / Answer

m1*v1 = m2*v2 1/2* (m1*v1^2 + m2*v2^2 ) = G*m1*m2/d => v2 = m1*v1/m2 => v1^2 = 2*G*m2/[ (1 + m1/m2)*d ] => v1 = sqrt( 2G*m2^2/[ (m1+m2)d] ) => v2 = sqrt ( 2G*m1^2/[ (m1+m2)d] ) => the relative velocity is v1 - v2.

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