Steven, I know that in the past you have wondered if the second focus of an ellipse could have any role to play in the determination of orbits, since it plays no role in Kepler laws or in Newton's derivation of Kepler laws. Well a few years ago, I invented a geometrical method in which the second focus of an ellipse is first located prior to determining the shape and size of an orbit. Information about speed and escape velocity is first mapped to positions on the circumference of a circle and this point is used to projectively locate the second focus (Fe) relative to the planet which is located at the first focus (Fp). Once the second focus is located the shape of orbit can be computed. However, my computations consist of geometric constructions and a gif animation which you can view here:
https://docs.google.com/document/d/1_i-KDTRAy7I9q54g6H22shW7M5e-fj36Sva_seHj75Y/edit?usp=sharing This method of drawing conic sections is not new, but I think how I use of this method is new. Harry On Sun, May 22, 2016 at 10:38 PM, OrionWorks - Steven Vincent Johnson < orionwo...@charter.net> wrote: > I've been retired now for almost 18 months. I'm happy to report I'm not > bored. My on-going Kepler research project continues to consume much of my > quality time. But alas, summer is just around the corner, and there seems > to be a spate of honey-do projects that are about to consume a good chunk > of my free energy. > > > > Dear Johannes, > > > > I hope you won't mind it too much if I place our work temporarily on the > bench... perhaps for several months while I go about retouching up the > exterior of the house. I just want you to know that I currently see at > least three additional laws that I would like to document as additions, or > complements, to your original three. I think you'll like the additions. I > see a nice symmetry that enhances the simplicity and beauty of your work. > However, the amount of computer coding and animation that I feel I'll need > to create in order to adequately show all of these additional Keplerian > laws feels a tad overwhelming at the moment. It feels important to me that > I develop my animations in easy-to-understand chewable bites. Creating a > new series of easy to chew cookies is not always an easy recipe to bake. > > > > Yours truly > > > > Steven Vincent Johnson > > orionworks.com > > http://www.zazzle.com/orionworks > > http://stevenvincentjohnson.bandcamp.com/ >