The Starshade is a space telescope with a large occulter that can fly off and block the light of a star so its telescope can picture the surrounding exoplanets:
I sort of understand the optics behind its shape; the light that bleeds around the edges their waves cancel each other out. But I can't get the math of the distance right. Say it wants to image the Trappist system, which is 4e17m away and its star is 7e7m in diameter and the shade is 10m. So the distance/size ratio would be 5e9, thus the shade would have to be 5e10m (50,000,000km) from the telescope right? Or is my math wrong?
Isn't that way too far?! Why is it so big? The orbital-mechanics behind it are also problematic. Will they orbit the Earth? Getting in an orbit 5e9m from the Earth is rather energetically expensive, not to mention the difference in orbital period they'd have to deal with.
I guess these are a lot of questions, but I can't find a proper explanation of the New Worlds mission (it's real name). So I'm hoping someone can explain the gist of it to me.