Hosted by The Math Forum

Problem of the Week 1250

The Loopy Lunatic

_____________________________________________
MacPoW Home ||  Forum PoWs ||  Teachers' Place ||  Student Center ||  Search MacPoW
_____________________________________________

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.

Imagine a moon orbiting a planet orbiting a star where:

  • distance planet to star = 93,000,000 miles
  • planet's orbital period = 365 days
  • moon's orbital period = 27 days
  • moon's distance to planet = L miles
  • the moon's orbit is "prograde," i.e., in the same direction as
    the planet moves around the star

What is the smallest value of L so that the orbit of the moon around the start has a loop? Is nonconvex?

Assume all orbits are circular and all lie in the same plane (so that "loop" and "convex" have clear planar meanings).

Sources:

Helmer Aslaksen's The Orbit of the Moon around the Sun is Convex!

Noah Samuel Brannen, "The sun, the moon, and convexity," College Mathematics Journal 32 (2001) 268-272.

Laurent Hodges, "Why the moon's orbit is convex," College Mathematics Journal 33 (2002) 169-170.

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/


13 October 2017