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On Tue, 23 Oct 2001, Carl E. Mungan wrote:...
I could perhaps imagine making gravity turn on and off periodically
in short bursts. (A bunch of equally spaced gravity shields
surrounding the sun with only small open slits between them?) Then
earth would go around the sun in a nearly equilateral figure. (With a
smaller average radius, assuming we start with the same total
mechanical energy, owing to the decreased duty cycle.) Yet its KE
would still be constant.
It is amusing to push this idea to its limits and consider earth
moving around the sun in an equilateral triangle (with very slightly
rounded corners).
To take this topic fully off on the tangent suggested by Carl, I
wonder how many of us have ever considered the shape of orbits
under the influence of a central force of the form
F(r) = F_o(r/R_o)^N
where F_o and R_o are constants and N is a large positive number
like, say, 100. Such a force yields orbits for virtually any
initial condition that all have apoapses near R_o.
John Mallinckrodt