Satgen323 In Orbit Pt7 Comets by GM4IHJ 3 June 1995 Orbits come in many shapes and sizes , but those of Comets , the icy visitors from the outer limits of the solar system are particularly difficult to track in that , they usually have high eccentricity, and they rarely repeat the same path one orbit visit to the next. The high eccentricity means that we have to deal with orbits which are near the parabolic eccentricity of 1.0 , ie that orbit which goes out to infinity . The ordinary Ephemeris and Keplerian element calculations mentioned in previous satgens cannot handle high eccentricity , so a new form of calculation is necessary. In 1809 the German mathematician Carl Gauss published what has become one of the standard techniques for solving this type of orbit.His solution was tailored to lists of tables and logarithms, but a computer version was published in 1969 in the Proceedings of the Astronomical Society of the Pacific by Benima et al at p121 in the April issue. For this type of calculation we need the following data which is usually obtained by big telescopes tracking the comet as it approaches the inner Solar system :- Q = perhelion distance ( Comet to Sun at closest approach to Sun ) e = Eccentricity of orbit ( can be anywhere between 0.95 and 1.05 ) T = Days from perihelion ( - before + after ) The solution for True anomaly and distance from the Sun is achieved via a complex set of formulas using coefficients devised by Gauss. The comet distance and bearing from earth , can then be extrapolated using Solar data derived as described in Satgen 321. Very few comets have accurately repeated orbit sequences. Travelling as they must across the orbits of the planets , comets are frequently perturbed by the gravitational attraction of those planets. They can even be trapped by the big planets Jupiter and Saturn and forced to stay forever in orbits which circle the Sun at one end and either Saturn or Jupiter at the other end. In addition , as comets approach the Sun, Solar heating melts their icy outer surface so that they give off gas , Jet propelling themselves and thereby altering and still further complicating their orbit pattern. Two recent comets are good examples of this perturbation. Comet Swift Tuttle Kegler in 1993 had been lost . Then when recovered it was clear that its new orbit would bring it uncomfortably close to the earth. If not that orbit , probably on its next orbit or the one after that. Unless of course further perturbation alters the orbit yet again. By contrast Comet Shoemaker Levy of 1994, had become trapped in a Sun Jupiter circuit, and then got too close to Jupiter and been torn apart by the big planets gravity, eventually producing a spectacular display as its many parts collided with the planet. Hence the general rule that comet orbits are never confirmed until they begin to get into telescope range and are tracked inside Jupiter. From which point the Gaussian method produces useful tracking data.