# Astronomy - Correct solution? Part 2

1. Sep 14, 2011

### tosv

1. The problem statement, all variables and given/known data
I have made a solution to an exercise and I need some to check it and please notify me if I have made any misstakes.

Exercise
A satellite that is a black body, spherical and rotates around its own axis is send towards the Sun. How far will the satellite reach before its surface temperatur will be higher then 100 degrees Celsius?

3. The attempt at a solution
The radiation flux density at the surface of the Sun will be
$$F_{\odot}$$

At the distance d from the Sun the radiation flux density of the satellite will be
$$F_{I}=F_{\odot}\left(\frac{R_{\odot}}{d}\right)^{2}$$
where $$R_{\odot}$$ is the radius of the Sun

According to Stefan-Boltzmann law, we have
$$F=\sigma T^{4}$$

We will then find
$$T_{I} = T_{\odot}\sqrt{\frac{R_{\odot}}{d}}$$

The distance d can now be expressed as
$$d=R_{\odot}\left(\frac{T_{\odot}}{T_{I}}\right)^{2}$$

I use the following numerical values:
$$R_{\odot} = 6.955\cdot10^{8}m$$
$$T_{\odot} = 5800\, K$$
$$T_{I} = 373\, K$$

Then I found the distance to be
$$d\approx1.68\cdot10^{11}m\approx1.1\, A.U.$$

Can this be a reasonable answer?