# Neptune’s satellite Triton has an orbital radius equal to the radius of the Moon’s orbit around the Earth

**Neptune’s satellite Triton has an orbital radius equal to the radius of the Moon’s orbit around the Earth, but makes one revolution around Neptune in 6 days. How many times are the masses of Neptune and the mass of the Earth different? Which one is bigger.**

It follows from the law of universal gravitation and Newton’s Second Law that the centripetal acceleration when moving in a circular orbit of radius R around a body of mass M is equal to a = GM / R ^ 2. On the other hand, it is equal to a = v ^ 2 / R, where v is the orbital velocity. Hence it follows that if the radii of the orbits are the same, the mass M is proportional to v ^ 2. The moon makes a revolution in its orbit in about a month. Since the lengths of the orbits are the same, the orbital speed of Triton is about 5 times greater than the orbital speed of the Moon. Therefore, the mass of Neptune is 5 ^ 2 = 25 times the mass of the Earth.