Altitude optimality boundary of two variants of large space debris removal to disposal orbits

Abstract

The article considers the mission design problem for removal of large space debris objects from near-Earth orbits. It is assumed that a single active spacecraft-collector (SC) should de/re-orbit several objects. The upper planning level calls for a scenario that specifies the type of repeating operations of an SC. Despite the apparent diversity of these scenarios, they can be reduced to two variants of objects removal to disposal orbits (DOs). In variant I, transfers between objects are effected by an SC with detachable propulsion modules (PMs) onboard. Once the next-in-line object is captured, one module is accommodated on its surface, and, after demating, this PM ensures the relocation of the object to a DO. In variant II, the SC operates as a tug vehicle and transfers the object to DO on its own, and then returns to the next object.A reasonable choice of the removal variant depends on the SC launch mass which should be compared for the same number of de/re-orbited derelict targets. To this end, one should estimate the SC dry mass, the payload mass, and the SC propellant mass. Each of these three terms is nonlinear and depends explicitly on each other, the mass of the captured object, and on the SC maneuvers. Analytical models are proposed for estimation of the SC launch mass for each of the two removal variants. It is also shown that there exists an altitude optimality boundary (the radius of a spherical layer) above which the removal variant II is more advantageous than variant I. Such models are constructed based on several assumptions capable of breaking the iterative search of the SC launch mass.The position of the altitude optimality boundary depends on seven input parameters of the mission: the SC dry mass; the PM dry mass; the mass of the object, the required variation of the semi-major axis Δa to reach the DO, the number of objects removed by a single SC, the average ΔV for a transfer between two objects, and the effective exhaust velocity of SC main engine. In the present paper, four types of objects are considered: heavy and light LV stages in low orbits, upper stages in GEO and GNSS regions. By choosing concrete objects of study one can substantially reduce the solution space by excluding the impossible combinations of input data. By using the developed SC launch mass models, it is possible to formulate removal recommendations for concrete groups of space debris objects. These models were shown as being adequate on the examples of Elsa-M and MRV projects which are due to be implemented in the next one-two years.