Question

Two satellites revolve around the Earth. Satellite A has mass mmm and has an orbit of radius rrr. Satellite B has mass 6m6m and an orbit of unknown radius rbrbr b. The forces of gravitational attraction between each satellite and the Earth is the same. Find rbrbr b.

Answer 1

r(b) = 2.45r

Step-by-step explanation:

Parameters given:

Satellite A

Mass = m

Orbit radius = r

Satellite B

Mass = 6m

Orbit radius = r(b)

Gravitational force between Earth and Satellite A, F(A) is:

F(A) = (G*M*m)/r²

F(A) = GMm/r²

Gravitational force between Earth and Satellite B, F(B) is:

F(B) = (G*M*6m)/r(b)²

F(B) = 6GMm/r(b)²

Since F(A) = F(B),

GMm/r² = 6GMm/r(b)²

=> r(b)² = 6r²

r(b) = 2.45r