on the computation of preliminary orbits for space debris with radar observations
- Paper number
IAC-15,A6,9,8,x29740
- Author
Ms. Helene Ma, University of Pisa, Italy
- Coauthor
Dr. Giovanni Federico Gronchi, University of Pisa, Italy
- Coauthor
Dr. Linda Dimare, Space Dynamics Services s.r.l., Italy
- Coauthor
Mr. Davide Bracali Cioci, SpaceDyS s.r.l., Italy
- Year
2015
- Abstract
\noindent Different methods for obtaining preliminary orbits using optical and/or radar observations already exist in the literature: e.g. Gibbs' method [1], Kepler integrals (KI) method [2,3].\\ \noindent We introduce a new algorithm that we call Infang [4], that computes preliminary orbits for space debris on Low Earth Orbits from radar data collected in short time intervals. This method works with two tracks of radar observations. Each track consists of $n \geq 4$ topocentric position vectors per pass of the satellite: \begin{center} ($t_j$ , $\rho_j$ , $\alpha_j$ , $\delta_j$ ), $j = 1...n$. \end{center} Here ($\rho$, $\alpha$, $\delta$) are the spherical coordinates of the target at time t: $\rho$ is the range, $\alpha$ is the right ascension, and $\delta$ is the declination. We assume $\rho$ is very accurately known but $\alpha$ and $\delta$ are not precise. \noindent The new method forms a linkage of the two tracks using the two-body dynamics, Lambert's theorem, and the equations of motion projected onto the line of sight direction.\\ \noindent We consider some test cases to compare the orbits computed by the Gibbs', KI and Infang methods for one simulated object, assuming errors in the observations and without including the perturbation from the J2 effect. The numerical results illustrate the good performance of Infang in correcting errors in the angular positions assuming exact knowledge of the range.\\ \noindent We are still investigating the case including the $J_2$ effect and we intend to test the new algorithm on a larger scale.\\ References : [1] Herrick, S., "Astrodynamics.", Vol. 1, Chapter 8, Van Nostrand Reinhold, 1976. [2] G.F. Gronchi, L. Dimare, and A. Milani, “Orbit determination with the two-body integrals,” Celest. Mech. Dyn. Astr., Vol. 107/3, pp. 299-318, 2010. [3] L. Dimare, D. Farnocchia, G. F. Gronchi, A. Milani, F. Bernardi, and A. Rossi: "Innovative system of very wide field optical sensors for space surveillance in the LEO region" - project SARA (LEO), AMOS Conference Hawaii, 2011. [4] G.F. Gronchi, L. Dimare, D. Bracali Cioci, H. Ma : "On the computation of preliminary orbits for space debris with radar observations", 2015, submitted.- Abstract document
- Manuscript document
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