So before we go ahead, I want to mention something important, so all of our plots and all of our solutions
were purely two dimensional.
And you see here we used the zero and one component and the three to four and six and a seven, which
we never used two to five, and the eight, which are the z components of Sun, Earth and Moon.
And we could have used them actually, because the way we programmed this is really three dimensional.
So here all of these vectors have also a Z component.
And basically, we assumed that all of the motion of Sun, Earth and Moon happens in the same plane
in the whole X y plane.
However, in reality, the plane in which the Moon circles around the Earth is not the same as the Earth
oscillates around the sun.
So there is a so-called inclination of approximately, I think, something like five degree.
So it's pretty small angles or approximation is OK, but it's not perfect.
And if you want to do it more precisely, you could give the Moon, for example, a small z component
for the starting velocity and see what happens then.
But please don't make it too large because if you make it too large, then the Moon will escape the
gravity of the Earth, and then it will just leave the Earth and then start to oscillate by its own
around the Sun.
But that's really something you can test, or you can generalize the model.
I mean, it's already generalized.
You just have to play with the starting conditions.
And then, of course, you have to also change the plots because then also the sea component will be
important and you have to turn to three dimensional plots.
So this would be a fun exercise, and you can learn or even more about the motion and the three body
problem.