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

This requires Kepler's Third Law.
T^2 = r^3
When dealing with orbits around the Sun, "T" should be stated in years and "r" should be stated in Earth Sun distances (astronomical units).
2,030 days divided by 365.25 = 5.5578 years
r^3 = 5.5578^2
r^3 = 30.889
r = cube root (30.889)
r = 3.1376 astronomical units
which equals 291,660,000 miles = 469,380,000 kilometers

And to be very sure of that answer here is a Kepler's Third Law Calculator:
http://www.1728.org/kepler3a.htm