Altitude of Midnight Satellite?
I'll venture a guess that the 7000 kilometers (your software's camera position) was with respect to the center of the Earth. Using 6371 km as a value for the Earth's radius, that would make the altitude only 629 km, which it turns out is quite a popular altitude for satellites in LEO.

For the simplifying case of midnight, one can draw a simple diagram. I get

$$h = R_{\textrm{Earth}} \left(\frac{1}{\cos(35°)} - 1\right)$$

which is about 1400 km at midnight, and the height will be lower before and after.

I'll wait to hear about the camera "height" and try to find another tool for you to use. Do you ever use Python programming language?



Red dots are Perth at local noon and midnight.