Wow okay, thanks! I was totally confounding force and energy. The book example is really helpful.

My understanding of orbits is that if every particle in the universe vanished except the Earth and the Sun, the Earth would continue in its orbit, because it is in free-fall around the Sun.

My understanding of conservation of energy makes me think that this is impossible. I was told in HS physics that the Earth is constantly accelerating--not because it gets faster and faster, but because it's changing directions by going in a circle ellipse instead of a straight line. F=ma, so it takes force to change the direction. That force is provided by gravity... but here I get confused. Can gravity just provide this force forever? Does that not mean that it's generating energy (from nowhere)?

I'm ten years out of high school so I can't just raise my hand and ask the teacher :( I suspect that I knew the answer to my question at some point and have since forgotten it.

My Google searches somehow turn up all sorts of sources debunking flat earth theory, which is not what I'm trying to do here lol.