Question

3.7.6. A satellite is in a circular orbit around the Earth. If it is at an altitude equal to twice the radius of the Earth, 2RE, how does its speed v relate to the Earth's radius RE, and the magnitude g of the acceleration due to gravity on the Earth's surface?a)b)c)d)e)

Answer 1

Step-by-step explanation:

For acceleration due to gravity

g = GM / R² ---------------------------- ( 1 )

At height 2R , radius of orbit is 3R .

If speed of satellite be v

m v² / 3R = GMm / (3R)² ( centripetal force = gravitational force )

v² = GM / 3R -------------------------------------- ( 2 )

Dividing (1) and (2)

v² / g = R / 3

v² = gR / 3

v = √( gR / 3 )