G m σ(∫_0^a)(∫_(-π)^π)((x )/(((((x^2)+(d^2)-2 x d Cos[θ]))^(1/2)) ))\[DifferentialD]θ\[DifferentialD]x

f[d_,a_]:=G m σ(∫_0^a)(∫_(-π)^π)((x )/(((((x^2)+(d^2)-2 x d Cos[θ]))^(1/2)) ))\[DifferentialD]θ\[DifferentialD]x

f[d,a]

g[d_]:=NIntegrate[((4 x EllipticK[((4 d x)/(((d+x))^2))])/(π (Sqrt[(((d+x))^2)]))),{x,0,d,1},Method->{"GlobalAdaptive","SingularityDepth"->10},WorkingPrecision->20]

g[0.2`25]

hh = Table[{x,g[x]},{x,0.`25,2.`25,0.02`25}]

((hh[[51,2]]-hh[[50,2]])/(hh[[51,1]] - hh[[50,1]]))

slope = Table[{i*.02-0.01,-(((hh[[i+1,2]]-hh[[i,2]])/(hh[[i+1,1]] - hh[[i,1]])))},{i,1,99,1}]

ListPlot[slope]

fslope=Interpolation[slope]

fslope[1.0]

Plot[fslope[x],{x,0,2}]

fslope[1]

f[0.72,1]/π//N

Plot[Evaluate[((f[d,1])/(G m σ))],{d,0,5}]