Three Body Problem - Earth, Sun, and Moon

[metgt4]

How would you go about solving the three body problem in the case of our sun, earth, and moon? The moon's gravitational effects are enough to rule out using the restricted three body problem solution, right? So if given a set of initial conditions, how would one find equations for the motions of each of these bodies?

 

[Filip Larsen]

If you want a trajectory with any kind of accuracy I would say that you need to turn to numerical solutions, which luckily are fairly easy do to in this case. Numerical solutions using the force model also has the benefit that you can add non-gravitational forces like solar wind and light pressure in the same framework later if you like (well, that of course not that relevant for the moon I guess).

The analytical results you can get from the circular restricted three-body do require the third body to be of insignificant mass and since the earth-moon system has one of the highest mass ratios in the solar system, I would, like you, say that requirement clearly is not satisfied.

Perhaps others here can offer more insight - I'm sure simulation of the Sun-Earth-Moon system must be a well practised exercise for astronomy majors?