# spheresProblem2.frink

``` use Solver.frink symbolicMode[true] showApproximations[false] ball = new Solver[[Pout === area eSubst sigma Tsphere^4,                             Puniv === area eUniverse sigma Tuniv^4,                             Tuniv === 2.725 K,                             eUniverse === 1,                             collectingArea === pi r^2,                             Pfromsun === (Psun / (4 pi dsun^2)) collectingArea,                             Psun === sunpower,                             Pout === Puniv + Pfromsun,                             1 === eSubst + rSubst + aSubst,                             area === 4 pi r^2,                             dsun === sundist],                            ["sigma", "pi", "sunpower", "K", "sundist"]] ball.draw[] //ball.pushSimpler[] solutions = ball.solveFor["Tsphere"] ball.draw[] println[join["\n",solutions]] println[] args = [["rSubst", 0.04], ["aSubst", 0.04]] solutions = ball.solveFor["Tsphere",args] println[join["\n",solutions]] println[] //for s = solutions //   println[eval[child[s,1], false, true]] //println["\nSolving for silver outside:"] //args = [["rSubst", 9/10], ["aSubst", 0], ["dsun", sundist]] //results = ball.solveForValues["Tsphere", args, false] //println[join["\n",array[results]]] //println["\nEvaluated:"] //println[join["\n",eval[array[results]]]] ```