Two satellites P and Q are moving in different circular orbits around the Earth(radius R ). The heights of P and Q from the Earth surface are h P and h Q , respectively, where h P = R 3 . The accelerations of P and Q due to Earth’s gravity are g P and g Q , respectively. If g P g Q = 36 25 , what is the value of h Q ?

Step-by-step solution

Acceleration due to gravity at any height from the Earth's surface is given by, g = G M r 2 , where r = distance from the centre of the Earth. Now, we can write g P g Q = G M r P 2 G M r Q 2 ⇒ 36 25 = r Q r P 2 ⇒ r Q r P = 6 5 ⇒ r Q = 6 5 × R + R 3 ⇒ R + h Q = 8 5 R ⇒ h Q = 3 5 R