It seems that f[rp]
is negative for your values of T
, and rs
is complex:
M = 60; g = 0.3; P = 0.002418/0.09;Clear[T];
solR = Simplify[
Solve[T ==
1/6 r (8 P + (3 M (-2 g^3 + r^3))/(\[Pi] (g^3 + r^3)^2)) &&
0 <= T <= 0.21 && r > 0, r, Reals],
0 < T < 0.21]
Plot[Evaluate[f[rp] /. solR],
{T, 0, .22}]