The asteroid Hygiea orbits the Sun like the other planets. Its period is about 2030 days. What is its mean distance from the Sun?

Question

unklerhaukus · Answer

Kepler's Law of Periods (K3)

$$T^2=a^3$$

where $T$ is the period in earth years

and $a$ is a the mean distance in astronomical units

unklerhaukus · Answer

Solving for the distance

$$a=T^{2/3}$$



So convert 2030 days into years,    T = 2030/365

and you result for  a  will be in astronomical units ,

if you want kilometres, 1 [AU] =  150 * 10^6 [km]