Question

An asteroid that has an orbital period of 3 years will have an orbital with a semi-major axis of about _____ years.

Answer 1

An asteroid that has an orbital period of 3 years will have an orbital with a semi-major axis of about 2 years.

Step-by-step explanation:

Given;

orbital period of 3 years, P = 3 years

To calculate the years of an orbital with a semi-major axis, we apply Kepler's third law.

Kepler's third law;

P² = a³

where;

P is the orbital period

a is the orbital semi-major axis

(3)² = a³

9 = a³

a =
`a = \sqrt[3]{9} \\\\a = 2.08 \ years`

Therefore, An asteroid that has an orbital period of 3 years will have an orbital with a semi-major axis of about 2 years.