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I want to create an animation regarding the restricted three-body problem for the Earth-Moon system. The code is as follows

Clear["Global`*"]; 
r1 = Sqrt[(x + μ)^2 + y^2 + z^2];
r2 = Sqrt[(x - 1 + μ)^2 + y^2 + z^2];
Ω = (1 - μ)/r1 + μ/r2 + 1/2*(x^2 + y^2) + (μ*(1 - μ))/2;

μ = 0.0121506683;

And here is the animation

P0 = Animate[ContourPlot3D[2*Ω, {x, -1.5, 1.5}, {y, -1.5, 1.5}, 
     {z, -1.5, 1.5}, Contours -> {C0}, ImageSize -> 500, 
     PlotLabel -> Row[{"C = ", C0}]], {C0, 3, 3.21}]

My questions now:

(1). I want to be able to inspect the changes in the interior region of the 3D surface. Any suggestions regarding the optimum ViewPoint. Is there a way to exclude the outermost surrounding surface?

(2). If I increase the PlotPoints to more than 50 the program crashes reporting an issue about the speed of the dynamic evaluation. How can I solve this issue? I need more plot points so as to obtain smoother and more detailed surfaces.

(3). How can I export the output in an .mp4 file?

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marked as duplicate by MarcoB, m_goldberg, Dr. belisarius plotting Aug 25 '15 at 3:25

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