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.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.