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The asteroid Hektor that was discovered in 1907 travels in a nearly circular orbit of radius 5.5 AU about the sun, which has a mass of 1.98*10^30 kg. The period of the asteroid in Earth years has to be determined.
Kepler's third law gives the time period of an object orbiting around the sun as T = (a)^(3/2) where a is the radius of the orbit in astronomical units and T is the time period is Earth years.
As the asteroid is an orbit with a radius of 5.5 AU, the time period is (5.5)^(3/2) = 12.898 years
The period of the asteroid in Earth years is approximately 12.898 years.
T^2 = R^3
T^2 = 5.5^3
T = 12.899 earth years
This makes sense, as Jupiter (at 5.2 AU) has a period of 11.86 earth years.
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