On Fri, Dec 27, 2019 at 11:25 PM Bill Gosper <billgosper@gmail.com> wrote:
Speaking of unit eccentricity, consider the idle question: A sine wave rotated +π/4 <http://gosper.org/tiltedsine.png>
BULL! A tilted sine wave looks like the 2nd plot in tilted sin <http://gosper.org/tiltedbs.pdf> . I have no idea what the upper plot is. —rwg
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