Steven, I was puzzled because I took your bouncing ball metaphor literally. Thanks David and Robert. I guess the graph approaches the path described by bouncing ball as the ellipse becomes flatter.
harry On Thu, Mar 1, 2012 at 12:01 PM, David Roberson <dlrober...@aol.com> wrote: > The orbital distance is changing faster when the object is closest to the > earth which would tend to look like a quick bounce. At the far spacing, the > change in orbital distance is slower depending upon the elliptical shape. > The mathematical equation defining the function of orbital distance versus > time should be available and in a closed form. I recall that equal orbital > areas are swept out in equal time, which is one of Kepler's laws as derived > by Newton. Wikipedia has a fairly good article on Kepler's laws. > http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion > > Dave > > > -----Original Message----- > From: Harry Veeder <hveeder...@gmail.com> > To: vortex-l <vortex-l@eskimo.com> > Sent: Thu, Mar 1, 2012 11:25 am > Subject: Re: [Vo]:Nature Editorial: If you want reproducible science, the > software needs to be open source > > On Wed, Feb 29, 2012 at 12:50 PM, OrionWorks - Steven V Johnson > <svj.orionwo...@gmail.com> wrote: >> From Harry: >> >>>> From OrionWorks: >>>> What I can say is that the new system involves an alternative way of > graphing out a periodic orbit - where you plot an "elliptical" orbit on a > TIME-LINE chart. The orbital distance is the "Y" vertical value and the > horizontal "X" value is the time value. >>> >>> That graph should look something like a sine curve....or not? >> >> You're on the right track. However the time-line looks more like a >> bouncing ball. > > I think I understand now. You are mapping a two dimensional distance > vector to the distance axis of your distance-time graph, so that a > perfectly circular orbit corresponds to a straight line. > This differs from a distance time graph in an introductory course in > physics where the distance axis represents the length of a one > dimensional vector so that a straight line in this graph corresponds > with a stationary body (and by implication zero velocity and zero > acceleration.) > > > > >> The "bouncing" part is where the satellite has reached the perihelion >> (closest distance) in the orbital period. > > I am puzzled by this. Why isn't there a "bouncing part" at the aphelion? > >> Ironically, at this moment >> in time I would conjecture that it would not be incorrect to stipulate >> that the orbiting satellite is behaving as if it's being influenced by >> a NEGATIVE gravitational field. That's where the 1/r^3 (cubed) part of >> the algorithm comes into play. It influences the direction the >> satellite is taking by pushing it away. Traditionally speaking, we are >> used to interpreting that aspect of the orbit as the influence of >> centripetal action. It's all a matter of interpretation! The cubed >> (negative forces) influence only comes into play in close proximity to >> the planet for which the satellite is orbiting around. At farther >> distances, the normal 1/r^2 (attractive forces) take over. >> >> It's really kind of a nifty perspective, if not a little wacky! ;-) >> >> Regards >> Steven Vincent Johnson >> www.OrionWorks.com >> www.zazzle.com/orionworks >> >
