I'm trying to make a movie about planets interacting under gravity, but when I try this with Mathematica, the movie show the planets getting chopped in half and then disappearing when they leave the boundaries of a "bounding box". I don't want the planets to suddenly disappear. Is there any way to solve this problem? This is not supposed to be a movie about planets getting chopped in half or disappearing.

Thanks. That looks like what I'm after. I'll study your code.

I'm not exactly sure what is desired, but fixing ViewAngle seems to correspond to its description:

Graphics3D[{Sphere[{-1, 0, 0}], Sphere[{0, 0, 0}], 
  Sphere[{+1, 0, 0}]}, Axes -> True, PlotRange -> All, Boxed -> True, 
 ViewAngle -> 10*Degree]

Sounds like my approach, which is similar to Chris P's, is on the right track, then, yes? As Chris shows, there are other view parameters, and you can use them to set up your shot in just the way you want. The most general one is ViewMatrix. It can take some effort to solve the geometry problem, though. This post on StackExchange has a nice picture showing the principal view parameters: https://mathematica.stackexchange.com/questions/3528/extract-values-for-viewmatrix-from-a-graphics3d/3538#3538

Maybe the option SphericalRegion->True could be of help

Manipulate[
    Graphics3D[
     {
        Sphere[{-Cos[\[Theta] \[Degree]] sep, 0, -Sin[\[Theta] \[Degree]] sep}],
        Sphere[{0, 0, 0}], 
        Sphere[{Cos[\[Theta] \[Degree]] sep, 0, Sin[\[Theta] \[Degree]] sep}]
        },
     Axes -> False, PlotRange -> {{-2, 2}, {-1, 1}, {-1, 1}},
     Boxed -> True, SphericalRegion -> True 
    ],
    {{\[Theta], 0, "Angle around Y"}, -180, 180, Appearance -> "Labeled"},
    {{sep, 1, "Separation"}, 0, 3, Appearance -> "Labeled"}
 ]

You really need to specify an explicit PlotRange setting if you don't want any surprises. That is, you should (or are supposed to) have an idea about the bounds of your objects at any point in your animation, and then set PlotRange to the extreme values of those bounds.

As a concrete example: if the $y$-range of one frame of your animation is {-5, 4}, and another frame has the range {2, 6}, then you need to set {-5, 6} as the range for $y$, and similarly for the other two dimensions.