Control-Theoretic Analysis of Low-Thrust Orbital Transfer Using Orbital Elements

2003 ◽  
Vol 26 (5) ◽  
Author(s):  
Pini Gurfil
Keyword(s):  
Low Thrust ◽  
Orbital Elements ◽  
Theoretic Analysis ◽  
Orbital Transfer

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

The Dynamics of Low-Thrust Spacecraft Manoeuvres

1968 ◽  
Vol 72 (695) ◽  
pp. 925-940 ◽  
Author(s):  
E. G. C. Burt
Keyword(s):  
Power Supplies ◽  
Relativity Theory ◽  
Time Varying ◽  
Low Thrust ◽  
Orbital Elements ◽  
Propulsion Systems ◽  
Optimum Time ◽  
Orbital Transfers ◽  
Electrical Propulsion ◽  
Increasing Function

Summary Orbital manoeuvres by means of impulsive thrusts, such as those available with chemical rockets, are well known, but a different treatment is needed for the small, continuous thrusts that are typical of electrical propulsion systems. It is shown that with the aid of these small forces it is possible to change independently all the orbital elements of a spacecraft, and thus to proceed slowly from a given orbit to any other. For each manoeuvre there exists an equivalent velocity which depends only on the initial and final orbital states, and which can be related directly to the spacecraft propulsion parameters. For any form of propulsion where the propellent acquires some or all of its energy from a separate energy source, as in electrical propulsion, it is found that optimum time-varying relations exist between the flow of mass and of energy, which may also be expressed in terms of the exhaust velocity and the thrust. In particular, the optimum exhaust velocity is shown to be an increasing function of time, related to the way in which the energy is released. The practical realisation of electrical propulsion depends on the development of efficient propulsion units and of lightweight power supplies; these and other spacecraft components are discussed, and a number of examples of orbital manoeuvres are given, including close-Earth, far-Earth and lunar orbits. The paper concludes with a discussion of these orbital transfers in relation to their possible uses, including communication satellites and a test of relativity theory

scholarly journals On the choice of a parking orbit for a service spacecraft

2020 ◽  
Vol 2020 (3) ◽  
pp. 30-38
Author(s):  
Yu.M. Holdshtein ◽  
Keyword(s):  
Mathematical Model ◽  
Operational Reliability ◽  
Analytical Determination ◽  
Transfer Program ◽  
Low Thrust ◽  
Transfer Energy ◽  
Orbital Transfer ◽  
Energy Expenditures ◽  
Parking Orbit ◽  
Orbital Transfers

At present, the requirements for increasing spacecraft active life and operational reliability and reducing spacecraft operation costs become more and more stringent. Because of this, on-orbit servicing becomes more and more attractive. One of the most promising ways to increase the efficiency of transport operations in space is to carry out on-orbit servicing using reusable spacecraft with low-thrust solar electrojet engines. The aim of this paper is to develop a mathematical model for the choice of an optimal low near-Earth parking orbit for a reusable service spacecraft. The case of noncoplanar near-circular orbits of spacecraft and a shuttle scenario of their servicing is considered. The solution of the problem of choosing an optimal parking orbit for a reusable service spacecraft involves repeated solutions of the problem of determining the delta-velocity of the service spacecraft’s orbital transfers between its parking orbit and the orbits of the serviced spacecraft. In this connection, using the averaging method, a mathematical model is developed for the analytical determination of orbital transfer program controls and trajectories and assessing orbital transfer energy expenditures. With its use, a mathematical model is developed for the choice of a service spacecraft’s optimal parking orbit. The objective function is the total delta-velocity of the service spacecraft’s orbital transfers from its parking orbit to the orbits of the serviced spacecraft and vice versa with the inclusion of the orbital transfer frequency. The optimizable parameters are the service spacecraft parking orbit parameters. The use of the proposed models is illustrated by an example of service spacecraft parking orbit optimization. What is new is the mathematical models developed. The results obtained may be used in the preliminary planning of on-orbit servicing operations.

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