The expression for gravitational potential energy is given as, PE=‌
−Gm1m2
r2
The negative sign shows the decrease in potential energy, which gives rise to increase in kinetic energy. By applying energy conservation law, we get ‌
1
2
m1v12‌‌=‌
Gm1m2
r
v1‌‌=√‌
2Gm2
r
And ‌
1
2
m2v22‌‌=‌
Gm1m2
r
v1‌‌=√‌
2Gm1
r
The relative velocity of approach is, v1+v2‌‌=√‌