Physics – Mathematical Physics
Scientific paper
2009-11-18
Physics
Mathematical Physics
23 pages, 1 figure
Scientific paper
10.1007/s10569-010-9271-9
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.
Dimare Linda
Gronchi Giovanni Federico
Milani Andrea
No associations
LandOfFree
Orbit Determination with the two-body Integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Orbit Determination with the two-body Integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbit Determination with the two-body Integrals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-241304