Circular and zero-inclination solutions for optical observations of Earth-orbiting objects

Abstract

Situational awareness of Earth-orbiting particles is important for human extraterrestrial activities. Given an optical observation, an admissible region can be defined over the topocentric range/range-rate space, with each point representing a possible orbit for the object. However, based on our understanding of Earth orbiting objects, we expect that certain orbits in that distribution, such as circular or zero-inclination orbits, would be more likely than others. In this research, we present an analytical approach for describing the existence of such special orbits for a given observation pass, and investigate topological features of the range/range-rate space by means of singularities in orbital elements.

Innovative methods of correlation and orbit determination for space debris

“…Fujimoto et al (2010) show that is always possible to find from one to three circular orbits compatible with an optical attributable. Also this method can be useful if there is no confusion between the concept of virtual debris and the one of an orbit determined by the observations.…”

Correlation of Optical Observations of Earth-Orbiting Objects and Initial Orbit Determination

“…where E is the specific geocentric energy of the particle, MIN and MAX are bounds for the physical range of the particle chosen a priori, and r a and r p are, respectively, the apoapsis and periapsis radii of the orbit in units of Earth radii. In this paper, MIN ; MAX 0:3; 20 Earth radii to include all objects observable by optical sensors but outside of the range of radar sensors, corresponding to an altitude of 2000 km (0.3 Earth radii) to 130,000 km (20 Earth radii) [6]. Note that any criterion C i is flexible and, in some cases, not necessary.…”

“…; Xi ! hx; y; z; _ x; _ y; _ zi (6) then to orbital elements [7] T 2 : hx; y; z; _ x; _ y; _ zi ! ha; e; i; ; !…”

Innovative observing strategy and orbit determination for Low Earth Orbit space debris

“…To find a starting guess we select a value K 0 either using the circular orbits corresponding to each of the two attributables (see [7]) or by assuming K 0 = 0. Among the obtained solutions, we cannot know which one could lead to convergence.…”