
Orbit of the Moon around the Sun - anvay
http://www.math.nus.edu.sg/aslaksen/teaching/convex.html
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DrScump

      It is locally convex in the sense that it has no loops
    

Of _course_ it has loops. But _in the scale of the drawing_ , the loops are
lost due to the vast distance from Earth/Moon system to Sun.

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anvay
It doesn't have any "lost" loops.

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DrScump
Dude. You _downvoted_ me for pointing that out? Seriously?

A more thorough explanation was posted by somebody else here:
[https://news.ycombinator.com/item?id=10611002](https://news.ycombinator.com/item?id=10611002)

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ColinWright
anvay could not have downvoted you, as your comment was a reply to them, so
no, they didn't downvote you for that.

And then in reply to what you said:

    
    
      >> It is locally convex in the sense
      >> that it has no loops
    
      > Of course it has loops. But in the
      > scale of the drawing, the loops are
      > lost due to the vast distance from
      > Earth/Moon system to Sun.
    

By my way of thinking, this is wrong. Looking at this from the Sun-centric
point of view, thinking of the Moon's path in space in the Sun's frame of
reference, the path is convex. Take any finite straight line (no, I'm not
going to go into General Relativity) whose endpoints are both, at some point,
between the Moon and the Sun, then _every_ point on that line is such that it
is at some point between the Moon and the Sun.

In other words, the path of the Moon is convex. By any common usage of the
language, that means it has no loops.

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DrScump
Are you saying that retrograde motion would not be observed from the Sun's
perspective?

~~~
ColinWright
Speed of Earth in orbit ~ 150 * 10^9 * 2 * pi / 365.25 / 86400 ~ 30 km/sec

Speed of Moon in orbit ~ 400 * 10^6 * 2 * pi / 27.32 / 86400 ~ 1 km/sec.

Yes, I'm saying that retrograde motion would not be observed from the Sun's
perspective.

