Question

Two each satellites A and B, each of mass m are to be launched into circular orbits about earth's centre at altitudes $6400$km and $19200$km, respectively. The radius of earth is $6400$km. Find (i) the ratio of potential energy of B to that of A, (ii) ratio of kinetic energy of B to that of A and (iii) Which one has greater total energy?

Answer 1

A) $P_{E_A}=\frac{GmM}{R_A}=\frac{GmM}{6400+6400}$

B) $P_{E_B}=-\frac{GmM}{R_B}=\frac{GmM}{6400+19200}$

$\frac{P_A}{P_B}=\frac{25600}{2\times 6400}=2$

$v_A=\sqrt{\frac{GMm}{R_A}};v_B=\sqrt{\frac{GMm}{R_B}}\frac{v_A}{v_B}=\frac{\sqrt{25600}}{\sqrt{2\times 6400}}=\sqrt{2}$

$A$ has greater kinetic energy.