# Question about Orbits of Moon/Earth around Sun

How, exactly, is the moon able to orbit the Earth while at the same time moving with Earth's orbit of the Sun? I understand that the Earth/Moon both have the same accelerations caused by the Sun's gravity, but accelerations are not additive - only forces. At any time, the moon will be pulled by both the Earth's gravitational force and the Sun's gravitational force, making the net force on the moon always slightly off from being purely a centripetal force around the Earth. Shouldn't this cause the moon to go off its orbit? This same thing can be applied at a larger scale - the moon goes around the Earth, which goes around the Sun, which goes around the center of the Milky Way. Why doesn't the net force, since there are more forces than only the Sun's pull, cause the planets and their moons to have their orbits messed up?

Drakkith
Staff Emeritus
At any time, the moon will be pulled by both the Earth's gravitational force and the Sun's gravitational force, making the net force on the moon always slightly off from being purely a centripetal force around the Earth. Shouldn't this cause the moon to go off its orbit?

It does. But as the Moon and the Earth circle around their barycenter, the effect ends up being cancelled out. During half of its orbit around the Earth-Moon barycenter, the Moon is moving faster than necessary to stay in its orbit around the Sun. During the other half it is moving too slow. But like I said, the two cancel each other out.

This same thing can be applied at a larger scale - the moon goes around the Earth, which goes around the Sun, which goes around the center of the Milky Way. Why doesn't the net force, since there are more forces than only the Sun's pull, cause the planets and their moons to have their orbits messed up?

Well, in the case of the planets, the forces from other planets are too small to have a major effect on the Earth's orbit around the Sun. However, it's important to remember that all the planets are already in stable orbits. In the past, when the solar system was young and crowded with young proto-planets and other objects, gravitational interaction between these objects absolutely sent many of them out of their orbits and into new ones. That's the basic reason why planets can form in the first place. Gravitational interactions between many different objects gives them a chaotic orbit and many of them end up colliding with each other, building up larger and larger objects over time.

The Sun's path around the Milky Way is a bit different. You can't model the Milky Way as having a point-like source of gravity in the center like you can when modeling the solar system. Interactions with other stars gives the Sun a semi-random path around the galaxy. And by semi-random I mean that the general path of the Sun is around the center, but it dips above and below the plane, moves in and out a bit, and does other things as other stars pass nearby. Luckily the net effect tends to cancel out in the long run and we don't go flying off out of the plane of the galaxy or towards the center or something.

It does. But as the Moon and the Earth circle around their barycenter, the effect ends up being cancelled out. During half of its orbit around the Earth-Moon barycenter, the Moon is moving faster than necessary to stay in its orbit around the Sun. During the other half it is moving too slow. But like I said, the two cancel each other out.

Well, in the case of the planets, the forces from other planets are too small to have a major effect on the Earth's orbit around the Sun. However, it's important to remember that all the planets are already in stable orbits. In the past, when the solar system was young and crowded with young proto-planets and other objects, gravitational interaction between these objects absolutely sent many of them out of their orbits and into new ones. That's the basic reason why planets can form in the first place. Gravitational interactions between many different objects gives them a chaotic orbit and many of them end up colliding with each other, building up larger and larger objects over time.

The Sun's path around the Milky Way is a bit different. You can't model the Milky Way as having a point-like source of gravity in the center like you can when modeling the solar system. Interactions with other stars gives the Sun a semi-random path around the galaxy. And by semi-random I mean that the general path of the Sun is around the center, but it dips above and below the plane, moves in and out a bit, and does other things as other stars pass nearby. Luckily the net effect tends to cancel out in the long run and we don't go flying off out of the plane of the galaxy or towards the center or something.

This helps, thanks!