I pity your science teacher, I really do.If the sun was that small, it wouldn't matter how hot it was, the planet would be a frozen popsicle. That doesn't really matter since the smallest a star can get is still about 80 times the mass of Jupiter (roughly 25,400 earths). Any smaller and it wouldn't have the minimum mass required to produce the heat and pressure needed to fuse hydrogen and sustain itself. So coming that close would still destroy the planet and leave it a molten pile of slag.As for the sun and the moon not being in the sky at the same time... *snerk* BUAHAHAHAHA!! Have you never actually looked at the sky?! Seriously, go outside and look up right now. There's a good chance you'll see the moon right up there next to the sun (depending on the current lunar cycle of course, I haven't checked today, but in case it isn't there, here is a picture As for the moon covering the sun, that is called a solar eclipse. It's a pretty common occurrence and happens naturally about 2.4 times a year. (And if Luna was rotating the earth as I suggest or even the moon itself), it would be a pretty easy thing to accomplish, since the moon orbits the planet, all she would have to do is position them so that the moon was blocking the sun.