Planet a has an orbit with a semi-major axis of 2 astronomical units. planet b has an orbit with a semi-major axis of 8 astronomical units. how does the orbital period compare between the two planets

The options.

A) Planet B has an orbital period 64 times shorter than Planet A.

B) Planet B has an orbital period 4 times shorter than Planet A.

C) Planet B has an orbital period 64 times longer than Planet A.

D) Planet B has an orbital period 4 times longer than Planet A.

E) Planet B has an orbital period 8 times longer than Planet A.

The CORRECT ANSWER IS E)

E) Planet B has an orbital period 8 times longer than Planet A.

Explanation:

Using P2 = a3 to do the estimation.

Let the size of the orbit (a) be represented in astronomical units (1 AU is the average distance between the Earth and Sun) and the period (P) is estimated in years, then Kepler's Third Law says P2 = a3.

It implies that:

A) the period of a planet is independent on its mass.

B) all orbits that possess equal semimajor axis possesses equal period.

C) planets that very distant from the Sun moves slowly than those that are nearer to the sun.

P2 = a3

Given, a =2

P2 = (2)^3

P2 = 8

E) Planet B has an orbital period 8 times longer than Planet A

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