# Is Moon really rotating about its axis?

Wikipedia says yes but on Newtonian arguments. From general relativistic point of view Moon is not rotating but moving along geodesic trajectory. And like parallel transport of a vector (pointing to the direction of motion) on a surface of a sphere along equator, from outside it seems like rotation. So, would Moon still be rotating if we remove the Earth? Would Foucault pendulum on Moon detect its rotation?

• "From general relativistic point of view Moon is not rotating but moving along geodesic trajectory." I believe that from general relativistic point of view, Moon is rotating with respect to the stars and stars are rotating with respect to the Moon. Jul 31, 2014 at 18:40
• Feb 22, 2015 at 20:10

## 2 Answers

It is really rotating, with a period of one month, according to a Foucault pendulum. That's the prediction of Newtonian gravity, and GR's prediction can't diverge much from that when the gravitational field is so weak. (Also consider that a Foucault pendulum on Earth empirically measures the length of the sidereal day, not the solar day.)

• Where the flaw in my argument: GR says that parallel transport in curved spacetime causes vector to rotate. This rotation is due to and depends on nonflat spacetime metric and NOT on intrinsic property of vector (angular momentum). So even if vector (Moon) has zero angular momentum it still, according to GR, has to rotate on 360 degrees every ellipse cycle (like parallel transport of a vector along equator). But with zero angular momentum Foucault pendulum will show nothing. And when we remove the Earth (flatten metric) rotation of Moon in GR picture will disappear, unlike Newtonian thinking. Jul 31, 2014 at 15:06
• @Pavel Chernov: The moon is not a vector. More precisely: The position of the moon is not a vector, it is a point on the spacetime manifold. Jul 31, 2014 at 15:32
• I agree on that. But if we associate space-vector pointing originally from center of the Moon to the direction of motion, would it rotate due to moving in curved spacetime even with zero angular momentum of the Moon? Jul 31, 2014 at 15:59

The moon rotates once every 27 days (roughly). In order to keep one side facing the Earth, it needs to rotate. If it didn't rotate, it would look like it was rotating backwards as it orbited the Earth.