Question

A satellite of mass m is moving in a circular orbit of radius r. Due to atmospheric drag, it loses energy at a constant rate W. The time in which the satellite will fall to the surface of Earth is:

a) Directly proportional to mass (m) and inversely proportional to r.
b) Inversely proportional to both mass (m) and r.
c) Directly proportional to both mass (m) and r.
d) Inversely proportional to mass (m) and directly proportional to r.

Answer 1

Earth is: d) Inversely proportional to mass (m) and directly proportional to r.

Why is it inversely proportional?

Orbital energy and drag: The satellite maintains its circular orbit due to a balance between its centripetal force and the gravitational pull of Earth. Atmospheric drag reduces the satellite's energy, causing its orbit to shrink.

Time to fall: The time taken for the satellite to fall to Earth depends on the rate at which its energy is lost due to drag and its initial orbital energy.

Therefore, option d) is the most accurate description of the relationship between the time to fall and the satellite's mass and orbital radius.