and R is the position vector of B* relative to P. In other words, V is a force function suitable for dealing with the gravitational interaction of a body and a remote particle when F is used to approximate F.

Derivations Replacing p in Eq. (2.11.5) with [(R + r)2]"2 gives

V = Gm J (R2 + 2R • r + r2)'"2 p dr + C (14)

Introducing q as q = r/R, noting that R/R = a,, and applying the binomial series, convergent for |2R • r + r2! < 1, leads to

V = gfl(1+2ai -9 + q2)-mpdr + C = J [l " a, • q - \ q2 + | (a, • q)2 + • • • jp dr + C

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