Question

A satellite is in a circular orbit around Earth with an altitude equal to 2.50 times Earth's radius. What is the magnitude of the centripetal acceleration of this satellite? [Hint: you do not need to look up Earth's mass or radius to solve this one.]

can you solve this?

Answer 1

The velocity of the satellite, v = SQRT[(G * M) / h]
Where G is the universal gravitational constant, M is the mass of the earth and h is the satellite's altitude
Substituting h = 2.5 * R,
v = SQRT[(G * M) / (2.5 *R)]
Squaring,
v² = (G * M) / (2.5 *R)

Centripetal acceleration, a_c = v²/h
= v² / (2.5 * R)
Substituting the value of v²,
a_c = 1 / (2.5 * R) [(G * M) / (2.5 *R)]
= (G * M) / (6.25 *R²)
= 1 / 6.25 * [(G * M) / R²]
= 1/6.25 * g
Where g is the acceleration due to gravity.
a_c = 9.81 / 6.25
= 1.57 m/s²