This is a short and readable exploration of the question “What is the shape of the Moon’s orbit around the Sun?”
http://www.math.nus.edu.sg/aslaksen/teaching/convex.html
The Moon makes circles (ellipses, really) around the Earth while the Earth makes circles around the Sun, so what does the path of the Moon look like?
It’s a fun problem to think about, and I encourage you to do just that before you click through and see the discussion.
This simply posed problem touches on polar and parametric curves, 3-dimensional geometry, and of course, astronomy. And naturally there are lots of extensions, like “What if something were orbiting the Moon?”
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