Question

Two planets P and Q of the same mass.The radius of P is twice the radius of Q.v_P and v_Q are escape velocities from planet P and Q respectively.Find their escape velocities?

Answer 1

According to the law of conservation of energy

$\frac{mv_Q^2}{2}-G\frac{Mm}{R}=0\to v_Q=\sqrt{2G\frac{M}{R}}$

$\frac{mv_P^2}{2}-G\frac{Mm}{2R}=0\to v_P=\sqrt{G\frac{M}{R}}$

$v_Q=\sqrt{2}\cdot v_P$