Energy is released by the Crab Nebula at a rate of about 5×10^31W, about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every 0.0331 s, and this period is increasing by 4.22×10^−13s for each second of time that elapses.
a) If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, find the moment of inertia of the neutron star.
2. Relevant equations
KE = Iw^2 , w = 2pi/ T , P = dE/dT
3. The attempt at a solution
KE = Iw^2 , w = 2pi/ T , so KE = 1/2 I 4 pi^2 T^-2
take the derivative of that i get P = -4 I pi^2 T^-3
set it equal to -5×10^31
solve for I and i got 4.59*10^25 which is wrong 🙁
help please, thanks