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Butterworth-Heinemann, Oxford, 3rd ed., Chap., Prob. 3, Eq. 1. The L&L precession result, in our notation, is Δθp(L&L)= 2m∂∂h{1h∫0πdφr2V(r)} where r=L1+ecos φ. Here G, M, m, and E are kept fixed while taking the h derivative so that h∂L∂h=2L, h∂e∂h=-1-e2e, and h∂r∂h=2r+1-e2er2cos φL. The L&L precession result can be rewritten as Δθp(L&L)= 2GMmL∫0πdφ{-r2V(r)+∂(r2V(r))∂r(2r+1-e2er2cos φL)}. From the L&L expression we subtract zero in the form 2GMmL∫0πdφ∂ ∂φ{r2+rLeV(r)sin φ}=2GMmL∫0πdφ{∂∂r(r2+rLeV(r)) ∂r∂φsin φ+r2+rLeV(r)cos φ}. After the subtraction we are left with Δθp(L&L)=2GMme∫0πdφcos φr2∂V(r) ∂r, which is identical (with z=cos φ) to our 29.
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