%A Sukhanov, Alexander Alexandrovich,
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%T Lectures on astrodynamics
%I Instituto Nacional de Pesquisas Espaciais
%C São José dos Campos
%K engenharia e tecnologia espaciais, astrodynamics, two-body problem, Keplerian motion, perturbed theory, impulse maneuvers, orbital maneuvers, Lambert theory, autonomous navigation, least square method.
%X ABSTRACT: These class notes contain an essence of the author's lectures giving basic knowledge in different areas of Astrodynamics. The notes begin with necessary mathematical information (chapter 1). Then a detailed analysis of the two-body problem is given (chapters 24). The Kepler's laws, the Newton's law of gravity, and first integrals of the two-body problem are given in chapter 2. Then the Keplerian motion is analyzed using both the classical approach (chapter 3) and a universal approach (chapter 4). The classical approach means an individual consideration of the motion for different orbit types. The universal approach gives an effective method of the motion calculation unified for all orbit types. The perturbed motion is considered in chapter 5. This chapter gives a brief introduction into the theory of the perturbed motion and describes influence of the main natural perturbations, both gravitational and non-gravitational ones, on the motion. Chapters 25 are applicable to the both natural and artificial celestial bodies. The spacecraft impulsive maneuvers changing different orbital parameters and performing inter-orbital transfers are analyzed in chapter 6. A simplified approach to the maneuver optimization and analysis is considered in the chapter. Interplanetary transfers including the gravity assist maneuvers are analyzed in chapter 8. This analysis uses the patched-conic approach, which is described in the chapter. The Lambert problem solution (i.e. determination of the transfer orbit between two given positions in a given time) also is necessary for the interplanetary transfer calculation. This problem is analyzed in details and solved in the notes (chapter 7). An advanced approach is used giving a universal solution to the problem, i.e. solution unified with respect to the orbit types and number of complete revolutions. Maneuvering of a spacecraft in the sphere of influence of a planet is considered in chapter 9. The goal of this maneuvering is transfer of the spacecraft approaching the planet from the incoming hyperbola to an operational orbit. An introduction into the space navigation, i.e. orbit tracking and determination and orbital correction maneuvers, is given in chapter 10. Autonomous navigation also is briefly considered there. The optimization of the orbital maneuvers based on the Pontryagins maximum principle and Lawdens primer vector is considered in chapter 12. The basic elements of the optimization theory and its application to the spacecraft maneuvering are given in the chapter. The electric propulsion (low thrust) and some aspects of optimization of the electrically propelled transfers are considered in chapter 13. Chapter 14 gives an approach to the optimization of both impulsive and low thrust if the thrust direction is under a constraint. A method of the optimization of low-thrust transfer between two given positions is given in chapter 15. This method is based on a linearization of the transfer near a close Keplerian orbit. A way of providing any desired accuracy of the optimization is suggested. The optimization method is also applicable to the case of constrained thrust direction considered in chapter 14. Chapter 16 considers a spiral low-thrust transfer between given orbits; this type of transfer takes place near a planet. Planar transfers with transversal thrust between two circular orbits or between circular and parabolic orbits are considered. For this case simple formulas for the calculation of the transfer parameters are obtained in this chapter. A general case of the spiral low thrust transfer between given orbits in an arbitrary gravity field is considered in chapter 17. A simple and effective method of the transfer optimization based on the linearization of motion near reference orbits is described. The method is applicable to different transfer types and also in the cases of partly given final orbit or constrained thrust direction. It is shown that the method gives a locally optimal solution. The state transition matrix, which is widely used in different areas of the Astrodynamics, is considered in chapter 11. In particular, calculation of this matrix is necessary for the spacecraft navigation and correction maneuvers and for the transfer optimization considered in chapters 10, 12, 13, 15, 17. An effective method of the state transition matrix calculation and inversion is described in chapter 11. This method is based on the matrix decomposition simplifying the matrix calculation and unifying the matrix for different orbit types. Chapters 6, 7, 9, 11, 14 17 are based on the methods developed by the author.