Physics

Problem

Two satellites, A and B, each of mass

500\,\text{kg}

, revolve in coplanar circular orbits about the Earth with radii

2R_{E}

and

4R_{E}

respectively. a. (i) Determine the ratio of their orbital speeds

v_{A}:v_{B}

. b. (ii) Calculate the ratio of their time periods of revolution

T_{B}:T_{A}

. c. (iii) Find the difference in their orbital kinetic energies. d. Given:

G = 6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}

M_{E} = 6.0\times10^{24}\,\text{kg}

R_{E} = 6.4\times10^{6}\,\text{m}

. Ignore all perturbations.