# spheresProblem.frink

``` // This solves for the temperature of a rotating sphere in space receiving // energy from the sun. use systemSolver2.frink symbolicMode[true] ball = new System[[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],                            ["sigma", "pi", "sunpower", "K"]] println[join["\n",ball.solveAll[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]]]] println["\nSolving for glass outside:"] args = [["rSubst", .04], ["aSubst", 0.02], ["dsun", sundist]] results = ball.solveForValues["Tsphere", args, false] println[join["\n",array[results]]] println["\nEvaluated:"] println[join["\n",eval[array[results]]]] println["\nSolving for earth:"] args = [["rSubst", .30], ["eSubst", 0.612], ["dsun", sundist]] results = ball.solveForValues["Tsphere", args, false] println[join["\n",array[results]]] println["\nEvaluated:"] println[join["\n",eval[array[results]]]] ```