1. The problem statement, all variables and given/known data Trying to answer the question of "what would happen if Sirius take the place of the Sun", I've begin to try to calculate the average temperature of Earth in function of time for any incident flux (and therefore, the average temperature today), knowing the real average temperature of Earth and that 4'6Gy later it has reached it from zero, considering the star like a black body. 2. Relevant equations Luminosity is given by: L=a·4·pi·sigma·R^2·T^4 W Where "R" is radius of the body, "T" its temperature, "sigma" the Stephan-Boltzmann constant and "a" is the absortivity of the body. Flux is given by: F=L/(4·pi·d^2) W/m^2 With "d" the distance where you want to calculate the flux. Temperature in a body is: T=c·Q/M K Where "c" is the calorific capability of the body, "Q" is the total energy of the body, excluding mechanic ("heat" I think is how you call in english), and M is the mass of the body. 3. The attempt at a solution In this problem, we have that Q is the absorbed energy minus the emited energy: Q=Qabs-Qem If Sun (or the star) is a black body, we have that (subindex s and e means "star" and "Earth"): Qabs=Fs·pi·Re^2·a·t ; t=time Fs=Ls/4·pi·d^2 ; Ls=4·pi·sigma·Rs^2·Ts^4 Qem=Le·t ; Le=4·pi·sigma·Re^2·Te^4 We will consider flux of the star and product with the effective section of the Earth and with absortibity like a constant, having: Qabs=Fabs·t Because of there are constants too in Qem, we will write it like: Qem=A·Te^4·t where A=4·pi·sigma·Re^2 Now, with the hipotesis of calorific capability constant throught time, we have: Te=c·(Qabs-Qem)/Me So then: dTe/dt=c·(Fabs-4·A·Te^3·(dTe/dt)·t-A·Te^4)/M Making some algebra: dTe/dt=c·(Fa-ATe^4)/(Me+c·4·A·Te^3·t) Leads to a differential equation that I'm unable to solve. In adition I don't know if my logic is correct. ¿Can you help me? Thanks.