It comes as a surprise to many that the orbit of the moon around the sun has no loops in it. Indeed, it is a convex curve not very different from the orbit of Earth around the sun.
How far away from Earth would our moon have to be for the moon's orbit around the sun to have a loop? How far away for it to be nonconvex?
Assume all orbits are circular and all lie in the same plane (so that "loop" and "convex" have clear planar meanings), the Earth-sun distance is 93 million miles, the Earth's orbit requires 365 days, and the moon's orbit around Earth takes 27 days (and that is constant in this problem). Using such approximations has negligible impact on the problem.
Note that the moon's orbit is "prograde": in the same direction as Earth moves around the sun. Both motions are counterclockwise, viewed from our north pole.
Not sure this holds up to scrutiny, but off the top of my head it feels like in order for there to be a loop, the moon must be moving faster around the earth than the earth is moving around the sun.
The earth travels a circle of circumference = 186M * pi in 365 days, so it's traveling at a speed of roughly 1.6 million miles per day.
To match that speed, the moon would need to travel a circumference of roughly 1.6 * 27 = 43.2 million miles in a single orbit, so the radius of the moon's orbit around earth would need to be at least 6.875 million miles.
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Posted by tomarken
on 2021-05-20 09:15:10 |
A guess at a simple solution
