In our first assignment we developed a model to predict the temperature given the heating rate. In that assignment we made some assumptions and neglected some terms that give unrealistic temperatures. In this homework we will refine our original model to attempt a better estimate of temperature given the heating rate.
1) Starting with the equation for Q: (Q=S_0*cos(Z)/(1-ecc*cos)**2) assume that ecc is small and show that you can approximate the function as (Q=S_0*cos(Z)*(1+2ecc*cos)**2). Use maple to estimate the error that you make in Q by making this approximation.
2) One of the largest sources of error is that the value for the solar constant is not appropriate for the daily averaged heating rate (we are in darkness for much of time). Is there some way to adjust Q to represent the average heating for one day?
3) Modify your model to account for the fact that as the
Earth heats up it starts to radiate heat and so comes to an equilibrium
temperature. You can assume that the equilibrium temperature is constant
over the course of the year if it makes your solution easier.