There are two planets in orbit around a star. Both planets have circular orbits. Planet has a speed of , and Planet has a speed of . (Give your answers to these questions as a decimal if necessary.)
What is the ratio of the orbital radii of the two planets, ?
What is the ratio of the orbital periods of the two planets, ?
A small satellite is placed in a circular orbit around a nearby asteroid. The orbital period of the satellite is seconds and the orbital radius is km. What is the mass of the asteroid?
The asteroid Vesta has a mass of kg and a radius of 520 km. What would be the orbital period for a space probe in a circular orbit of 10.0 km from Vesta’s surface?
What is the gravitational potential energy between two spheres, each of mass 9.5 kg, separated by a center-to-center distance of 20.0 cm?