Which form of Kepler’s third law can you use to recreate the period, T and the radius r of a planet in our solar system as long as the unit year is used for the period and the astronomical unit is used for the radius?

Question

Responses

T=r2
T=r2 - no response given

T2=r
T2=r - no response given

T2=r3
T2=r3 - no response given

T3=r2

Answer 1

The correct form of Kepler's third law that you can use to relate the period \( T \) (in years) and the radius \( r \) (in astronomical units) of a planet in our solar system is:

\[ T^2 = r^3 \]

This means that the square of the orbital period (in years) is equal to the cube of the semi-major axis of the orbit (in astronomical units).