The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

Semianalytic estimations of boundaries of a corridor of spacecraft entry into the planetary atmosphere at considerable values of permissible maximum overload

Trajectories of spacecraft entry into the planetary atmosphere with a velocity essentially exceeding the first cosmic velocity are considered. An estimation of the minimum permissible value of the altitude of conditional pericenter (perigee in the case of the Earth), at which extreme permissible value of maximum overload is reached, is of the main interest. Semianalytic formulas including the cases of considerable values of the maximum overload are suggested.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

Study of singular surfaces of systems of unsupported gyrodynes by the parameter continuation method

A system of two-degree-of-freedom force gyroscopes (gyrodynes) is considered to be used for spacecraft attitude control. Possible values of its total angular momentum form some finite region P in the frame of reference rigidly connected with the spacecraft. Near the boundary of this region and singular surfaces located inside it the control of the angular momentum is complicated or impossible. The program angular momentum of the gyrodynes, realizing the law of variation of the spacecraft orientation, should lie inside P and outside some singular surfaces, and due to this fact the boundary and internal singular surfaces should be studied. This work is dedicated to the numerical construction of region P and its internal singular surfaces by the method of parameter continuation. Using the results by E.N. Tokar’ we formalize sufficient conditions which in some cases allow one to determine the type of the singular surface. As an example, a system of six gyrodynes is considered, for which the regions of variations of the intrinsic angular momentum and singular surfaces are constructed. The possibilities of the system are demonstrated for the case when one gyrodyne fails.     

An alternative algorithm for the spacecraft information system with magnetometer and solar sensor

The possibility of identification of motion parameters of a low-orbit spacecraft using readings of a three-axis magnetometer and solar position sensor, without integration of the Euler’s dynamic equations or direct measurement of the object’s angular velocity, is considered.     

Ultraviolet studies of the interplanetary and local interstellar medium

A review of the last results of UV observations in the interplanetary space of neutral hydrogen and neutral helium in resonance lines HI λ1215.7 Å and HeI λ584 Å is presented. The history of discovery of the interstellar wind effect is expounded in the review, and interaction of the solar wind with the interstellar medium is briefly described. Models of the inner-heliospheric distribution of emissivity in the lines HI λ1215.7 Å and HeI λ584 Å are discussed, and possibilities of getting the solar wind parameters from UV observations in the L _α line are considered. Currently accepted parameters of the local interstellar medium are presented. The parameters obtained are compared with those derived from non-optical measurements.     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with cavities partially filled with liquid

This paper is a continuation of [1–3] and a generalization of the results for a rotating spacecraft with cavities partially filled with liquid and equipped with an operational magnetohydrodynamic (MHD) element in the loop of its attitude control. This element makes possible the creation of hingeless systems of stabilization and orientation that do not require rocket propellant consumption. The application of an MHD element is considered for stabilization in the mode of spin-up of a spacecraft not having gyroscopic stability.     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with a spike antenna

The problem of stabilization of a rotating spacecraft with a flexible spike antenna located along the axis of spacecraft rotation is considered. A magnetohydrodynamic element is used as a final-control element in the control loop of spacecraft attitude, and the solar direction sensor serves as a measuring device. At the first stage of investigation, the problem of stability is considered for stationary and non-stationary modes of rotation of the spacecraft with a flexible antenna and with a cavity partially filled with a low-viscosity liquid.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

Experimental and theoretical investigation of encounter of a group of particles with protecting elements of spacecraft

We present the results of comprehensive experimental and theoretical investigations of encounter with a barrier of a group of bodies thrown with a high-velocity. Throwing of a group of particles (from two to twelve bodies) was realized on a ballistic route using powder and light-gas units of different calibers in the range of velocities 500–3500 m/s. The process of particle throwing was controlled by acting aerodynamic forces. In experiments on collisions with barriers of a finite thickness (which imitates the protective shield of spacecraft) the number of particles in a homogeneous stream was varied from 2 to 7 at changing the flux density (distances between particles). Experimental data are obtained on variations of the area and mass of back-surface splinters. Numerical calculations simulated a knock of 2 to 4 particles against a barrier in the cases of normal impact and at an angle. The calculations were performed in three-dimensional formulation and applying criteria of complete destruction of material. The appearance of additional destruction centers in the barrier due to mutual influence of particles is revealed. Simple criteria are obtained for estimating the degree of interference of particles and the character of barrier destruction.     

Ballistics, navigation, and motion control for a spacecraft during its landing on the surface of Phobos

Basic concepts and algorithms laid as foundations of the scheme of landing on the Martian moon Phobos (developed for the Phobos-Grunt project) are presented. The conditions ensuring the landing are discussed. Algorithms of onboard navigation and control are described. The equations of spacecraft motion with respect to Phobos are considered, as well as their use for correction of the spacecraft motion. The algorithm of estimation of the spacecraft’s state vector using measurements with a laser altimeter and Doppler meter of velocity and distance is presented. A system for modeling the landing with a firmware complex including a prototype of the onboard computer is described.     

Optimum conditions of observation of tubular-loop structures of the interplanetary magnetic field and estimation of their lifetime

Basic conditions of observation of IMF tubular-loop structures are considered on the basis of experimental data of studying the fluxes of solar cosmic ray protons in the interplanetary medium. Lifetime of these structures, when their sources disappear on the Sun, is estimated.     

Multi-structural estimation of an integrated navigation system of a reusable spacecraft

An approach to the synthesis of an integrated navigation system is considered for a reusable space-craft that performs an arbitrary spatial maneuver under the conditions of internal and external disturbances. The offered approach provides for a noise-suppressing solution of the navigation problem, both in a regular mode of spacecraft motion, and during its descent along the unplanned trajectory.     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

Application of information criteria to control the structurally uncertain navigation system of a reusable spacecraft

The problem of attitude control of a gyro-stabilized platform with the structurally uncertain drift model is solved. The solution is realized in two stages. At the first stage, on the basis of the obtained stochastic model of the reusable spacecraft navigation system, the drift model of gyro-stabilized platform is identified. At the second stage, the control of its spatial orientation is synthesized with regard to the found drift model. The results of numerical simulation are presented in conclusion.     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

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.