Just to add an interesting point not many know - the lunar month is so long, and the Moon so close to the Earth compared with the Earth's distance from the sun - that the Moon's orbit is never concave towards the sun. It's basically doing a somewhat irregular but always convex orbit around the sun that interweaves with the Earth's orbit. It is a kind of rounded 13 gon orbit around the sun, like this:

see: The Orbit of the Moon around the Sun is Convex!

IN DETAIL: the lunar sidereal month is 27.321661 sidereal days - the time it takes for the Moon to return to the same position relative to the fixed stars.

The lunar synodic month, or the time between successive full Moons is 29.530587981 solar days on average - you have to take account of both the Earth's rotation (which cause it to vary between 29.18 and 29.93 days) and the direction of rotation of the Moon around Earth relative to the motion of Earth around the Sun.

So, the easiest way to find the number of sides is to use the sidereal month. So then the sidereal year is 365.25636 sidereal days, so it has 365.25636/27.321661 sides so a little over 13 sides.

But it is so rounded that if you drew it, it would look more like a circle than anything else

Also - at the same time the Earth is orbiting the centre of the galaxy, about 26,000 light years away. Cosmic Distance Scales - The Milky Way

And actually the sun also simultaneously oscillates above and below the galactic disk, as do all the stars, because they are attracted gravitationally by the plane of the galaxy as well as its centre.

It is currently perhaps 100 light years above the galactic plane, and heading towards it (hard to estimate, astronomers writing papers about this come up with many different estimates, e.g.: The Sun's Distance from the Galactic Plane )

And at the same time the galaxy itself is moving within our cluster of galaxies, and that's the fastest motion of all, about 1.3 million miles per hour, as measured using the 3 degree cosmic radiation dipole (asymmetry in the measurements thought to be caused by the Earth's motion relative to the radiation).

Cosmic Distance Scales - The Milky Way

How Fast Are You Moving When You Are Sitting Still?

That compares with Earth's orbital velocity (so also the Moon's approximately) of 67,108 mph

So if you plotted it in absolute coordinates relative to the 3 degree background radiation, it would be more or less a straight line on the timescale of centuries and millennia.
 
There would be small deviations at an angle of atan(67,108/1,300,000) or about 3 degrees to one side or the other of that line, oscillating back and forth every year.

Then other far more slowly changing deviations in direction due to the motion above and below the galactic plane every 32 million years, and the orbit of the sun around the galaxy every 250 million years.