Question

The earth takes 1 year to revolve around the sun at 1 A.U. distance (an astronomical unit = 93,000,000 miles). If a planet were 4 A.U. from the sun, how many years would it take to make 1 orbit?

Answer 1

Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit. In equation form, P^2 / a^3 = constant. For the earth, (1 y)^2 / (1 AU)^3 = 1, so the constant is 1. For a planet 4 AU from the sun:
P^2 / (4 AU)^3 = 1P^2 = 64P = 8 years