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So before we go ahead, I want to mention something important, so all of our plots and all of our solutions

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were purely two dimensional.

3
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And you see here we used the zero and one component and the three to four and six and a seven, which

4
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we never used two to five, and the eight, which are the z components of Sun, Earth and Moon.

5
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And we could have used them actually, because the way we programmed this is really three dimensional.

6
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So here all of these vectors have also a Z component.

7
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And basically, we assumed that all of the motion of Sun, Earth and Moon happens in the same plane

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in the whole X y plane.

9
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However, in reality, the plane in which the Moon circles around the Earth is not the same as the Earth

10
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oscillates around the sun.

11
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So there is a so-called inclination of approximately, I think, something like five degree.

12
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So it's pretty small angles or approximation is OK, but it's not perfect.

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And if you want to do it more precisely, you could give the Moon, for example, a small z component

14
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for the starting velocity and see what happens then.

15
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But please don't make it too large because if you make it too large, then the Moon will escape the

16
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gravity of the Earth, and then it will just leave the Earth and then start to oscillate by its own

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around the Sun.

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But that's really something you can test, or you can generalize the model.

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I mean, it's already generalized.

20
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You just have to play with the starting conditions.

21
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And then, of course, you have to also change the plots because then also the sea component will be

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important and you have to turn to three dimensional plots.

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So this would be a fun exercise, and you can learn or even more about the motion and the three body

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problem.