Question

4. A space probe is orbiting Planet A. It is then moved into an orbit around Planet B. Planet B has three times the mass of Planet A, and the probe’s orbit around Planet B is twice the radius of the orbit it had around Planet A. What is the ratio of the orbital period around Planet B to that around Planet A?

A. 2.0

B. 0.62

C. 1.6

D. 0.82

E. There is not enough information to answer.

Answer 1

Gravitational constant = G

Mass of planet A = M₁

Mass of planet B = M₂ = 3M₁

Mass of the probe = m

Radius of the orbit around planet A = R₁

Radius of the orbit around planet B = R₂ = 2R₁

Orbital speed of the space probe around planet A = V₁

Orbital speed of the space probe around planet B = V₂

Period of orbit around planet A = T₁

Period of orbit around planet B = T₂

For planet A,

V₁T₁ = 2R₁

The gravitational force between planet A and the space probe provides the required centripetal force for the circular motion of the probe.

Similarly for planet B,

Ratio of the orbital period around planet B to that around planet A = 1.6