two massive particles m1 and m2 are released from a large distance.find their speeds if distance between them is r

at larger distance , the whole energy of system was in form of gravitational potential energy(since massive bodies),

E(initial) = Gm1m2/r^2;

p(initial)=0;      p->momentum;

when released, whole P.E. -> K.E.

=> E(final)= 1/2 m1(v1)^2 + 1/2 m2(v2)^2;

since E(initial)= E(final);

=> Gm1m2/r^2 = (p1)^2/2m1 +(p2)^2/m2       (1),          since K.E.= p*p/2m

also p(final) =0;    since no external force

hence p1 + p2 =0,   =>p1=-p2;

putting in (1), we get

(p1) =√[(2G(m1m2)*(m1m2))/(r*r(m1+m2))]

hence v1 and v2 can be found out by v1 =p1/m1 ,v2 =-p1/m2