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I have started looking at Finite Element Analysis of gradients in space using the GNU for Octave. A program language very similar to MATLAB, but for FREE. I was using Wolfram Mathematica version 10, but ran into errors that I could not resolve nor find support for. Probably because most of the support now is for version 14. I have not had any problems with Octave the high-level programming language and environment, primarly intended for numerical computations. Thanks to John W. Eaton and many others. 

The base equations, just for motion, are as follows just for a simplified Earth – Moon system:

For[i=1, i<=1000,i++,

r=Sqrt[(x^2 + y^2 + z^2)];

vx= vx -((G * M * x * dt)/(r^3));

vy= vy -((G * M * y * dt)/(r^3));

vz= vz -((G * M * z * dt)/(r^3));

x = x + (vx * dt);

y = y + (vy * dt);

z = z + (vz * dt);

axyz[[i]] = {x,y, z};

]

* Note that the mass of the Moon is irrelevant in the simplified model of the interaction between the Earth and the Moon. Whereas, in a more realistic model the Moon would also be affecting the Earth.  And that it is r^3 not r^2 as some people have failed to realize.