| Preface |
|
ix | |
| Author biography |
|
xi | |
|
1 Introduction: getting started 1-1 |
|
|
|
1.1 List of the simulation programs 1-1 |
|
|
|
1.2 How to operate the simulation programs 1-2 |
|
|
|
1.3 Keplerian motions in celestial mechanics 1-3 |
|
|
|
1.4 Numerical and analytical methods 1-6 |
|
|
| Part I Review of the simulations 2-1 |
|
|
|
|
|
2.1 Kepler's first law 2-3 |
|
|
|
Questions and problems 2-7 |
|
|
|
2.2 Kepler's second law 2-8 |
|
|
|
Questions and problems 2-10 |
|
|
|
2.3 Kepler's third law 2-11 |
|
|
|
Questions and problems 2-14 |
|
|
|
2.4 The approximate nature of Kepler's laws 2-15 |
|
|
|
Questions and problems 2-16 |
|
|
|
3 Hodograph of the velocity vector for Keplerian motion 3-1 |
|
|
|
3.1 Hodograph of the velocity for closed orbits 3-1 |
|
|
|
3.2 Hodograph of the velocity for open orbits 3-3 |
|
|
|
Questions and problems 3-5 |
|
|
|
4 Orbits of satellites and trajectories of missiles 4-1 |
|
|
|
4.1 Families of Keplerian orbits 4-2 |
|
|
|
4.1.1 Orbits with various directions of the initial velocities 4-2 |
|
|
|
4.1.2 Satellites with equal magnitudes of the initial velocities 4-5 |
|
|
|
4.1.3 Orbits of satellites launched in one direction with different magnitudes of the initial velocities 4-7 |
|
|
|
Questions and problems 4-9 |
|
|
|
4.2 Evolution of an orbit in the atmosphere 4-10 |
|
|
|
4.2.1 Evolution of an elongated elliptical orbit 4-11 |
|
|
|
4.2.2 Late stage of the evolution and the aerodynamical paradox 4-12 |
|
|
|
4.2.3 Air density over the Earth 4-14 |
|
|
|
Questions and problems 4-17 |
|
|
|
5 Active maneuvers in space orbits 5-1 |
|
|
|
5.1 How to operate the program 5-1 |
|
|
|
5.2 Space flights and orbital maneuvers 5-4 |
|
|
|
5.2.1 Designing a space flight 5-4 |
|
|
|
5.2.2 The way back from space to the Earth 5-5 |
|
|
|
Questions and problems 5-9 |
|
|
|
5.3 Relative motion of bodies in space orbits 5-9 |
|
|
|
5.3.1 The motion of a small body ejected from the orbital station 5-10 |
|
|
|
5.3.2 Numerical estimates 5-12 |
|
|
|
5.3.3 The secular component of the relative motion 5-13 |
|
|
|
5.4 Space probes and relative motion 5-15 |
|
|
|
5.4.1 Space probes in inner orbits 5-15 |
|
|
|
5.4.2 Space probes in outer orbits 5-17 |
|
|
|
Questions and problems 5-19 |
|
|
|
5.5 Rendezvous in space and interplanetary flights 5-20 |
|
|
|
Questions and problems 5-21 |
|
|
|
6 Precession of an equatorial orbit 6-1 |
|
|
|
Questions and problems 6-5 |
|
|
|
7 Binary starsthe two-body problem 7-1 |
|
|
|
Questions and problems 7-5 |
|
|
|
|
|
|
8.1 The restricted three-body problem 8-1 |
|
|
|
8.2 Managing the program 'Planet with a Satellite' 8-2 |
|
|
|
8.3 Satellites of a planet that orbits a star 8-3 |
|
|
|
8.4 Exact particular solutions to the three-body problem 8-8 |
|
|
|
8.4.1 A system with equal masses of heavy bodies 8-8 |
|
|
|
8.4.2 Satellites at the triangular libration points 8-10 |
|
|
|
8.4.3 The collinear libration points 8-12 |
|
|
|
8.5 A space flight over the back side of the Moon 8-18 |
|
|
|
8.6 Lunar perturbations of a satellite's orbit 8-20 |
|
|
|
8.7 A space voyage to a distant planet and back 8-21 |
|
|
|
8.8 Cometsinterplanetary vagabonds 8-25 |
|
|
|
8.9 A double star with a planet 8-28 |
|
|
|
Questions and problems 8-32 |
|
|
|
9 Many-body systems in celestial mechanics 9-1 |
|
|
|
9.1 Planetary systema many-body problem 9-1 |
|
|
|
9.2 A model of the Solar System 9-4 |
|
|
|
9.2.1 The kinematics of planetary motion 9-4 |
|
|
|
9.2.2 Kinematics of the inferior planets 9-7 |
|
|
|
9.3 Hypothetical planetary systems and heavenly catastrophes 9-7 |
|
|
|
|
|
|
9.5 Exact particular solutions to the many-body problem 9-13 |
|
|
|
9.5.1 A star with two planets of equal mass 9-13 |
|
|
|
9.5.2 A 'round dance' of identical planets 9-15 |
|
|
|
9.5.3 Keplerian motions in equilateral configurations 9-16 |
|
|
|
9.5.4 A remarkable three-body motion along a figure-eight 9-20 |
|
|
|
Questions and problems 9-21 |
|
|
| Part II The simulated phenomena 10-1 |
|
|
10 Phenomena and concepts in celestial mechanicsan introductory approach 10-3 |
|
|
|
10.1 Newton's law of universal gravitation 10-3 |
|
|
|
10.2 Potential energy of a body in the Newtonian gravitational field 10-5 |
|
|
|
10.3 Circular velocity and escape velocity 10-6 |
|
|
|
10.4 Geometric properties of Keplerian orbits 10-8 |
|
|
|
10.5 Initial conditions and parameters of Keplerian orbits 10-10 |
|
|
|
10.6 A satellite in the atmosphere 10-13 |
|
|
|
10.7 Trajectories of a landing module 10-16 |
|
|
|
|
|
|
10.9 Space rendezvous 10-21 |
|
|
|
10.10 Kepler's laws and the solar system 10-24 |
|
|
|
10.11 An approximate approach to the restricted three-body problem 10-25 |
|
|
|
Questions for further thought 10-28 |
|
|
|
11 Theoretical background 11-1 |
|
|
|
11.1 Angular momentum and areal velocity 11-1 |
|
|
|
11.2 Dynamical derivation of Kepler's first law 11-3 |
|
|
|
11.3 Kepler's third law 11-6 |
|
|
|
11.4 A hodograph of the velocity vector for Keplerian motion 11-8 |
|
|
|
11.5 Another derivation of Kepler's first law 11-11 |
|
|
|
11.6 A family of orbits with equal energies and a common initial point 11-14 |
|
|
|
11.6.1 The envelope surface for the family of orbits 11-14 |
|
|
|
11.6.2 Applications of the envelope surface 11-17 |
|
|
|
11.7 Relative orbital motion 11-19 |
|
|
|
11.8 The gravitational field of a distorted planet 11-23 |
|
|
|
11.8.1 A planet with additional masses at the poles 11-24 |
|
|
|
11.8.2 A planet with an equatorial bulge 11-25 |
|
|
|
11.9 The two-body problem 11-26 |
|
|
|
11.9.1 Reduced mass and relative motion 11-27 |
|
|
|
11.9.2 An alternative approach to the two-body problem 11-29 |
|
|
|
11.10 Exact particular solutions to the three-body problem 11-30 |
|
|
|
11.11 The non-restricted three-body problem 11-35 |
|
|
|
11.11.1 A star with two identical planets 11-36 |
|
|
|
11.11.2 The regular Keplerian motions of three different bodies in the equilateral configuration 11-37 |
|
|
|
11.12 The sphere of gravitational action 11-40 |
|
|
|
11.13 The oceanic tides 11-42 |
|
|
|
11.13.1 The origin of tidal forces: an elementary approach 11-44 |
|
|
|
11.13.2 Tidal forces at an arbitrary point near the Earth 11-47 |
|
|
|
11.13.3 The horizontal and vertical components of the tidal force 11-48 |
|
|
|
11.13.4 The static distortion of the water surface 11-50 |
|
|
|
11.13.5 Tidal forces on the rotating Earth 11-51 |
|
|
|
11.13.6 The potential function for tidal forces 11-53 |
|
|
|
11.13.7 The natural wave and the driving tidal forces 11-54 |
|
|
|
11.13.8 The tides as forced oscillations of the ocean 11-56 |
|
|
|
11.13.9 A mathematical description of the forced oscillations 11-57 |
|
|
|
11.13.10 Real-world complications 11-59 |
|
|
|
11.13.11 The evolution of orbital motions and spins of celestial bodies induced by tidal forces 11-60 |
|
|
|
|
|
