# Angles in Moon, Earth and Sun system

Consider the vector positions of the center of mass of Moon, Sun and Earth, $\vec{r}_{\rm M}$, $\vec{r}_{\rm S}$, $\vec{r}_{\rm E}$, respectively, in a given reference frame.

Consider:

• the angle between the vector $\vec{r}_{\rm S} - \vec{r}_{\rm E}$ and $\vec{r}_{\rm M} - \vec{r}_{\rm E}$,
• the angle between the vector $\vec{r}_{\rm E} - \vec{r}_{\rm S}$ and $\vec{r}_{\rm M} - \vec{r}_{\rm S}$,
• the angle between the vector $\vec{r}_{\rm E} - \vec{r}_{\rm M}$ and $\vec{r}_{\rm S} - \vec{r}_{\rm M}$.

Does any of these angles have a name in astronomy, or can be important for some specific reasons? If so, may you please give me some general indications of why this is the case, and point to some references?

• I don't know if they all have names, but you're computing the angular distance of two of these from a third of these. For Earth, the moon/sun angle is called lunar elongation and results in the phases of the moon. – user21 Apr 18 '17 at 16:38
• By the way, is there any good astronomy book focused on lunar theory that you would suggest? – James May 8 '17 at 20:55
• I'm actually not much into books, but naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/index.html has open source subroutines (and discussion) re how to calculate the moon's position, libration, nutation, etc. – user21 May 11 '17 at 20:50