Re: Does the Moon speeds up and slows down during it's orbit depending on the direction?

Does the Moon accelerates when going towards the Sun (heading to over the day side of Earth) and then decelerates when moving away (going towards over the night side)?

Hello Tiago-

The Moon is unique among satellites in the Solar System, in that the Sun exerts a greater gravitational force on it than does its parent body, the Earth. A consequence of this is that the Moon never moves away from the Sun at all- it always has a positive acceleration towards the Sun. The easiest way to visualize the Moon is as a body that is fundamentally in orbit around the Sun, and which is perturbed by the Earth in such a way that the orbital trajectory wiggles a little (with a period of 29.5 days, the Moon's synodic orbital period around the Earth), but is always concave with respect to the Sun.

That said, it is important to remember that the Earth-Moon-Sun system must be analyzed as a three-body problem. In general, that means viewing the system as two bodies from a given frame of reference, and then treating the third body as a perturber. As you have posed your question, you are setting the center of the Earth as the origin of your frame of reference, and considering the Moon in orbit around this. Viewed this way, the Sun does perturb the orbit of the Moon. The Moon does not merely feel a gravitational force from the Earth, but from the Sun as well, and that force is different at different points in its orbit. When the Moon is at inner syzygy (Sun-Moon-Earth) it feels the minimum pull towards the Sun, because it is offset by the pull from the Earth. When it is at outer syzygy (Sun-Earth-Moon) it feels the maximum pull towards the Sun, because the two bodies act in the same direction.

Here is a nice mathematical treatment of the Moon's orbit around the Sun: www.mathpages.com/home/kmath405/kmath405.htm

Chris Peterson
Research Associate
Denver Museum of Nature and Science>