I have another update concerning my on-going theoretical research into characteristics of celestial mechanic algorithms.
Last Wednesday I mentioned the fact that another way to graph an elliptical orbit (an orbit that obeys Kepler's 1st, 2nd, and 3rd laws) would be to plot the satellite's distance from the central mass on the "Y" axis, while plotting equal time intervals on the "X" axis. What you end up with is a graph that looks like a bouncing ball. The bouncing part of the plot is where the satellite has made its closest approach to the attractive body, the perihelion point in the orbital ellipse. Most curiously, there appears to be a simple algorithm that simulates this x,y "bouncing ball" graph behavior, by incorporating it into a classic feed-back loop. The mathematical formula involves: Distance = 1/r^2 - 1/r^3. If you feed the current calculated vectors back into the formula you will generate the same bouncing ball plot. Keep in mind the squared (1/r^2) value is the attractive "force" whereas the cubed (1/r^3) value is the repulsive "force". If you employ this simple formula into a simple feedback loop you will end up plotting the exact same bouncing ball plot. The implication is that an orbiting satellite as it enters the perihelion phase of the orbit is effectively experiencing something akin to negative gravity, presumably due to centripetal forces that have temporarily overpowered the 1/r^2 attractive force. * * * As of today, Friday, I appear to have uncovered another suspicion of mine: What appears to be the generation of a perfect sine wave if you replace the "x" axis value (which previously contained a fixed time interval) with the accumulated vector value pertaining to the orbiting satellite. Said differently: As the orbiting satellite enters the perihelion phase of the orbit (closest approach to the body) the current vector will be significantly larger than when the satellite reaches its aphelion (farthest distance to the body). If you accumulate these individual slices of vector values and systematically plot them on the "X" axis proportionally, while simultaneously charting the satellite's distance on the "Y" axis, it seems to cause the charted line, which previously looked like a bouncing ball to transform into a perfect sine wave. Oh, by the way, in order to get this sine wave you need to return back to using just 1/r^2 for calculating the "Y" distance. My theoretical research continues. I have more suspicions. Maybe they will turn out to be right. ...or not. That's my Zen thought for the day! Have a good weekend. ;-) Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
