Which form of Kepler’s third law can you use to relate the period T and radius r of a planet in our solar system as long as the unit year is used for the period and astronomical unit is used for the radius?(1 point)

Question

Responses

A) T^2=r
cap t squared is equal to r

B) T^3=r^2
cap t cubed is equal to r squared

C) T^2=r^3
cap t squared is equal to r cubed

D) T=r^2
cap t is equal to r squared

Answer 1

The correct form of Kepler’s third law that relates the period \( T \) of a planet in years and the radius \( r \) in astronomical units (AU) is:

C) \( T^2 = r^3 \)

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).