[William Tell]

Doctor Stochastic said: "It's not really an approximation."

Yes, I agree. The calculus yields an exact answer.

I was open to the possibility that some problems in General Relativity might yield a slightly different answer, since GR predicts some things that Newton would not have predicted. But Newton's assumptions were exactly accounted for in his calculations.

Do you know whether GR invalidates Newton's conclusion or can a spherical mass always be represented by a point source?

[Doctor Stochastic]

I don't think GR messes up the point source with sphere, but I haven't checked carefully. With two point sources moving relative to each other, GR does predict gravitational waves but I don't think Newton does.