Least-square Fit to the Edge of Jupiter and Saturn for its Precise Position

Astrometric observations of major planets and their satellites are very important. These observations can be directly used for the improvement of the orbit theories of planets and their satellites, and also for the space exploration in our solar system.At present, some new techniques (such as radar ranging and interferometer)are available to observe the inner planets (Mercury, Venus and Mars)with high precision.Unfortunately, due to the principle limitations of these new techniques, the outer planets can be almost observed only using traditional optical methods, such as meridian circles.Since their "phase effects" on positional measurement, their positional accuracies, usually ±0."20～0."50 are poor.Recent observations adopt mainly an indirectly method, i.e.first observing a satellite of a planet and then deriving the planet'sposition by using the satellite'sephemeris.The accuracy of this method is usually in the range of ±0."10 ～ 0."20. It must be paid attention to the flaw of this method, i.e.with an assumption that the orbit theory of the satellite is precise enough.Obviously, the observed planet'sposition will be subject to the theoretical error of the satellite. Recently, Peng et al ¹.have found a new method based on the edge-detection of Jupiter and obtained very good results with a standard deviation as small as ±0."03.A similar method has already applied to Saturn and its satellites ².The results show that the geometric center of Saturnian ring has good precision better than ±0."05.In this paper, all used formulae of the image processing and related notions are given.We expect it, together with the papers ^1,2 to be useful if some researchers are interested in this new method.