"you discover a planet orbiting a distant star that has about the same mass as the sun, with an orbital period of 63 days. what is the planet’s orbital distance? "

0.31 AU Since the mass of the new star is roughly equal to the mass of the sun, you can assume the same orbital characteristics apply. So using Kepler's Third law, the period of the orbit is proportional to the square root of the cube of the orbit distance. First, determine how much faster the orbit period is compared to Earth. 63 / 365 = 0.172603 Since the period is proportional to the square root of the cube (3/2 power), you can invert that and raise the relative period to the 2/3 power. So 0.172603^(2/3) = 0.31 Since the Earth's semi-major axis is 1 AU, that would mean that the new planet's semi-major axis is 0.31 AU.