Asri-unix.735 net.space utcsrgv!utzoo!decvax!ucbvax!ARPAVAX:C70:sri-unix!Lynn.ES@PARC-MAXC Tue Feb 9 11:16:48 1982 Re: Re: sri-unix.707: Horseshoe Orbits Nice try on the orbital explanation, but it's unfortunately not right (even ignoring the ground speed business). Both linear velocity and angular velocity increase for satellites closer to the body they are orbiting. Take the moon (radius 238,000 miles, period 27+ days => 2200 mph, 0.04 rev/day) versus a low earth orbit satellite (radius 4000 miles, period 1.5 hrs => 17,000 mph, 16 rev/day). The angular velocity decreases with the 1.5 power of distance, the linear velocity decreases with the 0.5 power (square root) of distance. The actual explanation of why adding speed moves a satellite away from the body is this: With additional speed, the satellite tends to go in more of a straight line (has less time to fall toward the parent body), and increases its orbital distance. While increasing its distance, it is slowed by gravitation. It reaches equilibrium at a greater distance and a slower orbital speed than it originally had. This can be viewed another (equivalent) way: an orbiting body, given extra speed, has too much kinetic energy for that orbit, so it exchanges some of its kinetic energy for potential energy. The equilibrium is reached when the extra speed we gave it and some of its original speed are exchanged, ending up quite a bit higher and moving a little slower than originally. Point of view is important in understanding the name "horseshoe". Imagine two horseshoes, of slightly different size, mouth to mouth, on a plate. The plate spins quickly. As seen by a viewer on the plate, the satellite on the inner orbit is moving slowly counterclockwise along the smaller horseshoe, while the outer one is moving slowly clockwise on the larger horseshoe. The spinning of the plate represents the average rate of revolution of the two satellites, and so the viewer on the plate sees only the DIFFERENCE between a satellite's orbital speed and the average (plate's) speed. At encounter, we switch the sizes of the horseshoes, and the satellites (still seen from our spinning point of reference) seem to each reverse direction and traverse their (now slightly larger or smaller) respective horseshoes in the opposite directions. /Don Lynn ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.