Schwarzschild Escape & Recoil Solver

(* yukterez.net - Schwarzschild Escape & Recoil Solver - Syntax: Mathematica *)

r=6;
M1=1;
M2=10;

g00=1/(1-2/r);
vPro=Sqrt[1/r] Sqrt[g00];
"vPro"->N[vPro]

ε=1/(Sqrt[1-vt^2] Sqrt[g00]);
vEsc=Quiet@Reduce[ε==1,vt][[2,2]];
"vEsc"->N[vEsc]
vDif=vd/.Solve[(vPro+vd)/(1+vPro vd)==vEsc,vd][[1]];
"vDif"->N[vDif]

v1=vDif;
sol=Simplify[Reduce[
(M1/Sqrt[1-v1^2]-M1)+(M2/Sqrt[1-v2^2]-M2)==Ek&&
((M1 v1)/Sqrt[1-v1^2])+((M2 v2)/Sqrt[1-v2^2])==0&&
Ek>0&&M1>0&&M2>M1&&v1>0&&v2<0,
{Ek,v2}, Reals]];

"vRec"->N[sol[[2,2]]]
"Ek"->N[sol[[1,2]]]