A friend and I were reading some of the more catastrophic predictions for climate change, and were wondering if it would be possible to recover from complete permanent loss of polar ice (which cools the planet by reflection).
One idea we kicked around was building a giant occulter in space. Technological considerations aside, how big a shadow could we cast?
I can't figure out how to handle the umbra and penumbra. If you have
- Earth of radius $r_e$
- orbiting the Sun of radius $r_s$
- at a distance $d_{se}$
- and an occulter of radius $r_o$ in between the two
- at a distance $d_{so}=d_{se}-d_{oe}$
how much light would be blocked?