Optimization of Low-Thrust Interplanetary Transfers

A method for approximate analytical optimization of low-thrust transfers, described in [1] and based on linearization of the equations of motion, is considered. A more precise method of reducing the errors due to linearization is suggested. The method of optimization is generalized for the case of a mission to several celestial bodies.     

Optimization of transfers under constraints on the thrust direction: II

This paper completes the study of optimal transfers with constraints imposed on the thrust vector direction that was opened by paper [1]. The linear inhomogeneous and homogeneous constraints on the thrust direction are considered (specified either by equalities or inequalities), as well as mixed constraints. Some examples of the constraints are presented. A modified method of the transporting trajectory is applied in order to find the optimal transfer under the linear constraints on the thrust direction. This method also gives the necessary condition for a transfer possibility at a given constraint on the thrust direction. A numerical example is considered, in which the propellant consumption is analyzed for the cases of transfers with and without constraints.     

Estimation of the determination accuracy of orbit parameters of the apophis asteroid from measurement results

An analysis of the existing astrometric and radar observations of the Apophis asteroid is performed. On the basis of this analysis, characteristics of future measurements of the asteroid orbit and limitation on their conduction are accepted. A proposed launching of a spacecraft to the asteroid in order to obtain high-accuracy measurements of its distance and radial velocity is also considered. Trajectories of the flight to the asteroid in 2012–2022 are studied. Estimates of the accuracy of the Apophis position determination at various sets of both available and planned measurements at various numbers of determined parameters are obtained. The method of estimating accuracy is similar to that used in [1] for the Vega project.     

Optimization of transfers under constraints on the thrust direction: I

Transfers with a low thrust are considered under constraints imposed on the thrust vector direction. These constraints can be caused by peculiarities of the attitude control system and the mode of stabilization of a spacecraft, and, in the general case, they are functions of the time and state vector. The constraints specified by equalities and inequalities are investigated. It is shown that the optimal thrust is directed along the projection of the Lawden’s primer vector onto the restricting set.     

Charged particles on the Earth–Jupiter–Europa spacecraft trajectory

Charged particle fluxes on the trajectory of future Russian space research mission to Jupiter and its satellite Europa are investigated. The existing experimental data and models of Jupiter’s main magnetic field and radiation belts are summarized. Preliminary results of computations of energetic particle fluxes and radiation doses for each stage of the flight are given. Special attention is paid to estimation of radiation conditions in Europa’s orbit and on its surface; influence of the satellite on spatial distribution of the fluxes of charged particles of various energies is studied.     

A Modification of the Method of Transporting Trajectory

Further development of an approximate method for optimizing a flight with an ideally controlled small thrust is proposed. The method is based on the employment of the transporting trajectory and considered in [1–3]. A detailed analysis of the means of improving the accuracy of this method suggested in [2, 3] is carried out, and the solution is presented in finite form. The proposed approach is applied to the flights making flybys of many celestial bodies. In the case of small bodies the solution is also obtained in finite form. A numerical example is considered confirming the high efficiency of this method.     

Optimization of low-thrust transfers in the three body problem

We consider transfers with low thrust in an arbitrary field of forces. The modified method of transporting trajectory [1–4] is used for optimization of the transfers. The complexity of finding the transporting trajectory of a preset type can be the main obstacle to application of this method. This challenge is solved for the three-body problem in the Hill motion model. Numerical analysis of the method is performed using an example of the transfers to halo-orbits around the solar-terrestrial libration points.     

The Aster project: Flight to a near-Earth asteroid

The information on the project being developed in Brazil for a flight to binary or triple near-Earth asteroid is presented. The project plans to launch a spacecraft into an orbit around the asteroid and to study the asteroid and its satellite within six months. Main attention is concentrated on the analysis of trajectories of flight to asteroids with both impulsive and low thrust in the period 2013-2020. For comparison, the characteristics of flights to the (45) Eugenia triple asteroid of the Main Belt are also given.     

On one approach to the optimization of low-thrust station keeping manoeuvres

A simple and effective mathematical method to calculate optimal station-keeping manoeuvres by means of electric propulsion is suggested. The method is based on a linearization of the satellite motion near a reference orbit. Two versions of the method allow station keeping both in an assigned position and in any position of the orbit. The method is fully analytical for the two-body problem and takes a simpler form for the circular assigned orbit. The suggested method may also be used in the case when constraints are imposed on the thrust direction due to specific features of the satellite stabilization mode. An application of the method to any force field is shown. Illustrative examples of satellite station keeping in a circular orbit are given. Both cases of the station keeping, i.e., in an assigned position and in an assigned orbit, are considered without and with a constraint on the thrust direction.