# Q & A: effect of Moon's orbit on the Earth

Q:
I have been reading your fascinating articles on orbits, and looking at wikipedia. I am curious about a characteristic of our moon's orbit around the earth relative to the sun. Viewed from a planar perspective, at 2 points in it's orbit, the moon is moving exactly parallel to the earth's motion around the sun. Once the velocity of the moon is equal to it's orbital velocity plus the orbital velocity of the earth, and once it is equal to it's orbital velocity minus the earth's orbital velocity, meaning that the velocity of the moon relative to the sun varies dramatically as it orbits the earth. I guess that relative velocity is given by the moon's angular momentum around the earth (and sun). Does that lunar orbital motion have any effect on the orbital motion of the earth? Am I 'off in the weeds'?
- Chuck Crisler (age 58)
Windham, NH, USA
A:

The Moon does have an effect on the Earth's orbit, just as you suspect. The main effect would be there even if there were just the Earth and Moon, without a Sun. The combined Earth-Moon system rotates around its center of mass. Since the Earth is more massive than the Moon, by about a factor of 80, that's not too far from orbiting around the Earth's center, but it's far enough to be a major effect. The center of mass is still inside the Earth, but closer to the surface than to the center.

That's the first big effect. It leads to additional small effects. Since the Earth is making a monthly orbit around that center of mass point, it's also moving closer to and farther from the Sun. Since the Sun's gravitational field gets weaker farther from the Sun, that makes an additional small effect on the orbits. You have to add up all the little effects like that to get very accurate predictions of the orbits.

Mike W.

(published on 11/14/2014)