The asteroid Hektor, discovered in 1907, is in a nearly circular orbit of radius 5.5 AU about the sun, which has a mass of 1.98 X 10^30 kg. Determine the period of this asteroid in Earth years.
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.