Mathematical model of a non-coplanar maneuver of an interorbital tugboat to change the longitude of an ascending node

Аuthors

Stelmakh S. F.^*, Slatov V. L., Mikhailov V. A., Ginzburg T. V.

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

*e-mail: vka@mil.ru

Abstract

The article analyzes the use of interorbital tugs for deploying multi-satellite orbital groups. It is shown that in order for an interorbital tug to perform the task with maximum efficiency, optimal schemes for delivering payloads to the working orbit must be developed. These schemes allow certain transport operations to be carried out with minimal energy expenditure in the required time frame. Various methods of non-planar maneuvers are considered to change the longitude of the ascending node, based on the precession of the orbital plane. The main idea behind the proposed schemes for launching payloads into target orbits is to use interorbital tugs to maneuver into an auxiliary orbit with specific height and inclination parameters. These parameters are chosen so that the tug can "wait" in the auxiliary orbit until its orbit's ascending node lines up with the payload's orbit. This is done by taking advantage of the precession effect to change the payload's longitude of ascending node significantly. Two schemes are presented for transporting payloads using interorbital tugs from a reference orbit to a working orbit using an auxiliary orbit. Mathematical models have been developed to calculate the energy required for these transport operations and options for assessing the payback of using tugs have been proposed. It has been shown that, from the perspective of economic and time costs, there is practical significance in using the precession effect of the nodal line, which allows for changing the inclination of the orbital plane based on the longitude parameter of the ascending node, for launching, building, and servicing multi-satellite constellations of spacecraft using interorbital tug systems. The results of calculations of comparative estimates of costs between using interorbital tugs and upper stages for various interorbital flight schemes are presented. It is noted that, in the near future, these tasks will be addressed by interorbital tugs, which have the advantage of reusability over upper stages, which should lead to reductions in the cost of launching spacecraft to target orbits, their operations, and an increase in active lifetime.

Keywords:

interorbital tugboat, upper stage, interorbital flight scheme, non-planar maneuver, transportation, cost estimation, payback

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