A satellite is orbiting very close to the surface of a spherical planet of uniform density . The time period of revolution of this satellite is proportional to:

Step-by-step solution

For a satellite orbiting very close to the surface of a planet, the orbital radius is approximately equal to the radius of the planet R . The time period T of the satellite is given by: T = 2 R^3 GM The mass M of the spherical planet of uniform density is: M = Volume Density = 4 3 R^3 Substituting the expression for M into the time period formula: T = 2 R^3 G ( 4 3 R^3 ) T = 2 3 4 G = 3 G Since G and are constants, the time period T depends only on the density as: T 1 T ^ -1/2 Answer: ^ -1/2