Solve Radiation Problem: Find Temp as Function of Time

[Physics-101]

Homework Statement

We have a sensor onboard a satellite that is faced towards Earth, from the Sun. The LW absorptivity is 0.8 (a_LW) and SW is 0.2 (a_SW).
I need to find a equation for the temperature as a function of time. Given datas is the Area=0.3 m^2 and Specific Heat of 4 J/K

Homework Equations

See below.

The Attempt at a Solution

I think that I need to calculate the equilibrium temperature, which I did by using T=((a_sw/a_LW)*(Fs/omega))^1/4,
Fs=solar flux=1368 W/m^2 and omega= Stefan-Boltsmann constant.

Later, one equation that I have in mind for the temperature as a function of time is:
m*c*(dT/dt)=A*omega*T^4 , where A= area and m= mass. The sensor might be really small, so the mass m is negligible (?). What should I do now, I'm stuck.

Thanks!

 

[Greg Bernhardt]

Have you thought of anything else to help solve the problem?

 

[mfb]

Later, one equation that I have in mind for the temperature as a function of time is:
m*c*(dT/dt)=A*omega*T^4 , where A= area and m= mass. The sensor might be really small, so the mass m is negligible (?).

A negligible mass is equivalent to a satellite that is always at its equilibrium temperature .

You'll have different areas for absorption of sunlight and emission of infrared light, and those areas depend on the orientation of the satellte.