Asri-unix.734 net.space utcsrgv!utzoo!decvax!ucbvax!ARPAVAX:C70:sri-unix!Ciccarelli@PARC-MAXC Tue Feb 9 10:42:18 1982 Re: Horseshoe (and other) orbits About "horseshoe" orbits, actually about orbits in general... The higher orbit is not faster (higher *velocity*) but of higher *energy*. As the trailing moon (lower, faster, less energy) catches the leading moon (higher, slower, more energy) it takes some of the leading moon's energy, swapping orbits. It's counterintuitive -- higher energy does NOT imply higher orbital velocity. I dug up the formulas for your reference... --------------- The formula for orbital velocity (circular orbit approximation) is: V = V0 * SQRT( Earth radius / Orbit radius), where V0 = 7.86 KM/SEC ("Circular velocity at Earth's surface), Earth radius = 6400 KM (approx.), and SQRT is the Square-root operation (of course) You can check the formula for the three familiar orbit radii; calculate the velocity using the formula, then see that this velocity gives the right orbital period [distance = 2 * PI * Orbit radius; divide by velocity to get the period]. 1) near-earth: Orbit radius = Earth radius ==> V = V0 [gives 90 min. period] 2) geosynchronous: Orbit radius = 40,000 KM (approx.) [gives 24-hr period] 3) lunar: Orbit radius = 400,000 KM (approx.) [gives 28-day period] This also gives the expected result of V=0 at very great distances. --------------- The formula for orbit energy is: Total Energy = - (G * M1 * M2 / 2 * Orbit Radius), where G = Newton's gravitational constant, and M1, M2 = masses (i.e. Earth and satellite) Note that: 1) the total energy is negative (the physical interpretation is that the orbit is "bound", i.e. the satellite has less energy than that required to escape). 2) Orbit radius appears in the denominator again, thus the total energy will become greater (still negative, but closer to zero) as orbit radius increases. At very great distance, the energy goes to zero (as expected). [ Source: "Introductory Astronomy and Astrophysics", by Smith and Jacobs ] /John ----------------------------------------------------------------- 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.