Question

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

Answer 1

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

Answer 2

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]