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- (* 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]]]
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