Main Question or Discussion Point
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?