How accurate are Newton's formulas concerning Gravity, and other questions

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seasnake
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Binary System

Fg = G M1M2 / r2 M1d1 = M1d2

I don't have non-binary gravity formulas, so if you know any post them here (or any other algebraic gravity formulas you may be aware of)

I am interested in algebriac formulas that define gravity and energy, but I am a bit skeptical and not always sure which formulas I can trust.

Other than being for a binary system, does Fg = G M1M2 / r2 have any constraints, assumptions, limitations, or contradictions (problems)?
 
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thanks A.T. ... from your link, and following the links on tied link pages I found the equations:

g = - GM / [D^2 (1 - 2 GM / (rC^2))]; and

g = - MG hat r / r^2


these are the types of gravity equations I'm looking for, and any others are greatly appreciated, should anyone know any that are also in algebraic form