Discussion:
Here's an amusing problem...
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Peter Percival
2017-02-18 23:03:38 UTC
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... or two problems actually.

What shapes could a planetary orbit be if gravity obeyed an inverse cube
law?

What shapes could a planetary orbit be if gravity obeyed an inverse
fourth-power law?

For inverse nth-power law with n an integer > 4 it gets messy with
elliptic functions appearing, but the cases above are easy enough to
deal with.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Dick
2017-02-21 14:11:54 UTC
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Post by Peter Percival
... or two problems actually.
What shapes could a planetary orbit be if gravity obeyed an inverse cube
law?
What shapes could a planetary orbit be if gravity obeyed an inverse
fourth-power law?
For inverse nth-power law with n an integer > 4 it gets messy with
elliptic functions appearing, but the cases above are easy enough to
deal with.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
I (vaguely) remember this coming up in a college class.
Inverse first power law. Ellipse with sun at the center.
Inverse third power. (Logarithmic?) spiral.
Aren't we lucky it's an inverse square law!
Dick

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