An Innovative Approach to Initial Orbit Determination Based on the Admissible Region

In this thesis, we propose a new initial orbit method based on three observations of a Near-Earth Object (NEO) or space debris. This method is based on the concept of the admissible region, defined as the area in space where the object may plausibly be located. This region is defined by the dynamical constraints on the position of the celestial body. We first define the admissible region for solar system objects and then study the case of space debris based on TSA, using both optical and radar observations. It has been demonstrated that, in all cases, the admissible region has at most two connected components. By introducing certain constraints, a compact set can be obtained, allowing for the admissible region to be sampled using a finite number of virtual asteroids (VAs) or virtual space debris. The method has been implemented and to test its efficacy, we analysed 100 asteroids with observations from the same night, and 30 asteroids with observations from two different nights. All tests show that the method can compute a preliminary orbit, even in cases where classical methods, such as Gauss’s and Laplace’s, fail.