Speaking of unit eccentricity, consider the idle question: A sine wave rotated +π/4 <http://gosper.org/tiltedsine.png> is the graph of what function? Evidently, the pacefudging function that describes Kepler motion along radial trajectories. The idle question leads to impacting comets. But notice my sinewaves are slightly asymmetrical. I don't know why. I wish I could blame Einstein. —rwg On Thu, Dec 26, 2019 at 11:20 AM Bill Gosper <billgosper@gmail.com> wrote:
Here are 9 co-periodic planets <http://gosper.org/9planets.gif>. Shades of Shoemaker Levy 9. The string appears to periodically develop an inflection. —rwg I always thought that orbits with unit eccentricity were unbounded parabolas. Counterexample(?): Radial trajectories.
On Thu, Dec 26, 2019 at 3:03 AM Bill Gosper <billgosper@gmail.com> wrote:
The orbital period of a planet depends only on its major axis. gosper.org/4planets.gif . Does anybody feel like proving that with this phasing, these planets are collinear only twice per period? —rwg