Question

Binary stars of comparable masses m₁ and m₂ rotate under the influence of each other gravity with a time period T. If they are stopped suddenly in their motions. find their relative velocity when they collide with each other . The radii of the stars are R₁ and R₂ respectively. G is the universal constant of gravitation.

Answer 1

Both the stars rotate about their centre of mass(COM)

For the position of COM

Applying conservation of mechanical energy we have

v_r = relative velocity between the two stars.

Substitution the value of r from Eq. (i), we get