Estimates of the maneuvers of active space objects are considered. We propose analytical and numerical-analytical algorithms to estimate short-term and long-term one-impulse maneuvers for the case where the initial and final orbits are determined with errors. Both coplanar and noncoplanar maneuvers are considered. Special attention is given to the velocity and reliability of the solution of the problem. The process to find the solution has a geometrical interpretation. We provide examples of estimates for maneuvers of spacecraft located at geosynchronous orbits. The results obtained by the proposed method are compared with the results obtained by the traditional approach, excluding errors of orbit determination.

The problem of calculating the parameters of maneuvering a spacecraft as it approaches a large object of space debris (LOSD) in close near-circular noncoplanar orbits has been considered. In [1–4], the results of analyzing the problem of the flyby of the separated LOSD groups have been presented. It has been assumed that a collector spacecraft approaches the LOSD and captures it or it is inserted into the nozzle of a small spacecraft that has a proper propulsion system (PS). However, in these papers, the flight from one object to another was only analyzed and the problem of approaching to LOSD with a given accuracy was not considered. This paper is a supplement to the cycle of papers [1–4]. It is assumed that, the final stage of approaching the LOSD is implemented by maneuvering in many orbits (up to several dozens) with low-thrust engines, but the PS operating time is fairly small compared with the orbit period in order to make it possible to use impulse approximation in the calculations.

The analysis of NORAD catalogue of space objects executed with respect to the overall sizes of upper-stages and last stages of carrier rockets allows the classification of 5 groups of large-size space debris (LSSD). These groups are defined according to the proximity of orbital inclinations of the involved objects. The orbits within a group have various values of deviations in the Right Ascension of the Ascending Node (RAAN). It is proposed to use the RAANs deviations' evolution portrait to clarify the orbital planes’ relative spatial distribution in a group so that the RAAN deviations should be calculated with respect to the concrete precessing orbital plane of the concrete object. In case of the first three groups (inclinations i = 71°, i = 74°, i = 81°) the straight lines of the RAAN relative deviations almost do not intersect each other. So the simple, successive flyby of group’s elements is effective, but the significant value of total ΔV is required to form drift orbits. In case of the fifth group (Sun-synchronous orbits) these straight lines chaotically intersect each other for many times due to the noticeable differences in values of semi-major axes and orbital inclinations. The intersections’ existence makes it possible to create such a flyby sequence for LSSD group when the orbit of one LSSD object simultaneously serves as the drift orbit to attain another LSSD object. This flyby scheme requiring less ΔV was called “diagonal.” The RAANs deviations’ evolution portrait built for the fourth group (to be studied in the paper) contains both types of lines, so the simultaneous combination of diagonal and successive flyby schemes is possible. The value of total ΔV and temporal costs were calculated to cover all the elements of the 4th group. The article is also enriched by the results obtained for the flyby problem solution in case of all the five mentioned LSSD groups. The general recommendations are given concerned with the required reserve of total ΔV and with amount of detachable de-orbiting units onboard the maneuvering platform and onboard the refueling vehicle.

Estimates of the maneuvers of active space objects are considered. We propose analytical and numerical-analytical algorithms to estimate short-term and long-term one-impulse maneuvers for the case where the initial and final orbits are determined with errors. Both coplanar and noncoplanar maneuvers are considered. Special attention is given to the velocity and reliability of the solution of the problem. The process to find the solution has a geometrical interpretation. We provide examples of estimates for maneuvers of spacecraft located at geosynchronous orbits. The results obtained by the proposed method are compared with the results obtained by the traditional approach, excluding errors of orbit determination.

The article focuses on the flyby issue involving large-size space debris (LSSD) objects in low Earth orbits. The data on overall sizes of the known upper-stages and last stages of launch-vehicles make it possible to emphasize five compact groups of such objects from the Satellite catalogue in 600–2000 km altitude interval. The flyby maneuvers are executed by a single space vehicle (SV) that transfers the current captured LSSD object to the specially selected circular or elliptical disposal orbit (DO) and after a period of time returns to capture a new one. The flight is always realized when a value of the Right Ascension of the Ascending Node (RAAN) is approximately the same for the current DO and for an orbit of the following LSSD object. Distinctive features of changes in mutual distribution of orbital planes of LSSD within a group are shown on the RAAN deviations’ evolution portrait. In case of the first three groups (inclinations 71°, 74° and 81°), the lines describing the relative orientation of orbital planes are quasi-parallel. Such configuration allows easy identification of the flyby order within a group, and calculation of the mission duration and the required total ΔV. In case of the 4th and the 5th groups the RAAN deviations’ evolution portrait represents a conjunction of lines chaotically intersecting. The article studies changes in mission duration and in the required ΔV depending on the catalogue number of the first object in the flyby order. The article also contains a comparative efficiency analysis of the two world-wide known schemes applicable to LSSD objects’ de-orbiting; the analysis is carried out for all 5 distinguished LSSD groups.

The paper is devoted to the problem of estimating the parameters of two maneuvers performed by an active space object between two successive sessions of measurements, which is very important for the maintenance of the catalog of space objects. The parameters of coplanar and noncoplanar impulse and long-duration maneuvers are determined. An advantage of the proposed method is the high speed of estimation, unattainable in traditional approaches, and simplicity of program implementation, because the solution of each problem depends upon the solution of the preceding, simpler problems.

The paper considers the flyby problem related to large space debris (LSD) objects at low earth orbits. The data on the overall dimensions of known last and upper stages of launch vehicles makes it possible to single out five compact groups of such objects from the NORAD catalog in the 500–2000 km altitude interval. The orbits of objects of each group have approximately the same inclinations. The features of the mutual distribution of the orbital planes of LSD objects in the group are shown in a portrait of the evolution of deviations of the right ascension of ascending nodes (RAAN). In the case of the first three groups (inclinations of 71°, 74°, and 81°), the straight lines of relative RAAN deviations of object orbits barely intersect each other. The fourth (83°) and fifth (97°–100°) LSD groups include a considerable number of objects whose orbits are described by straight lines (diagonals), which intersect other lines many times. The use of diagonals makes it possible to significantly reduce the temporal and total characteristic velocity expenditures required for object flybys, but it complicates determination of the flyby sequence. Diagonal solutions can be obtained using elements of graph theory. A solution to the flyby problem is presented for the case of group 5, formed of LSD objects at sun-synchronous orbits.

Regarding the large-size space debris (LSSD) objects with a cross-section more than 5 square meters situated at LEO, it is possible to mark out 5 non-structured groups of such objects according to their spatial distribution. The orbits of objects in a group have approximately the same inclinations whereas the deviations in the Right Ascension of the Ascending node (RAAN) may be arbitrary. The features of orbital planes' mutual orientation change in a group are seen from the RAAN deviations' evolution portrait. The flights between the objects are being executed by a single active space vehicle (SV) which captures an LSSD object and takes it away to the specially calculated circular or elliptical low disposal orbit (DO), and then returns back for the next object. The calculation of flyby maneuvers in fact breaks up into two independent tasks. At first, one can determine the parameters of the DO for each LSSD object using special software, so the coplanar maneuvers can be calculated ensuring the object's transition to this orbit. Secondly, the flight to attain a new object is carried out from the DO of the previous object at the moment of time when their orbital planes will become equal. So it is possible to calculate the maneuvers which help to return back for the next object using numerical-analytical algorithm developed for non-coplanar rendez-vous of middle duration. The time interval for an active SV to stay at the DO is defined by the difference of precession velocities of orbital planes of the de-orbited object and of the following object. The usage of a circular DO allows an LSSD object to leave promptly from the region (over 700 km) where active SVs and other debris exist for a long time, whereas the apogee of the elliptical DO remains in the mentioned belt for 10 years. While forming elliptical DO one will need approximately 30% less of required summary characteristic velocity as compared with circular DO. The collision risk for an object staying at the elliptical DO during these ten years would constitute a half of the collision risk which takes place if no removal operations were carried out. The paper is enriched by the examples of flyby maneuvers calculation for all the five LSSD groups using the described removal scheme.