Essays on the Motion of Celestial Bodies

First Essay. On the unperturbed and perturbed motion of a satellite, with a digression on asymptotic methods of nonlinear mechanics.- 1. Lucky us!.- 2. Keplerian motion.- 3. Perturbed motion. Osculating elements.- 4. Osculating orbit of an equatorial satellite.- 5. The equations in osculating elements. Delaunay elements.- 6. Digression on asymptotic methods of nonlinear mechanics. Oscillations of a satellite about its center of mass. Averaging of canonical equations.- 7. Satellite in the gravitational field of Earth.- Second Essay. On the rebirth of an old problem, or what happens if two masses are placed at a purely imaginary distance from one another.- 1. From Euler to our days.- 2. The connection between the two problems.- 3. Integration. Coordinate system.- 4. The Hamilton-Jacobi method.- 5. Integration.- 6. The region of motion of a satellite.- 7. Jacobi's elliptic functions.- 8. The motion of a polar Earth satellite.- Third Essay. Yet another reincarnation of an old problem.- 1. And what sort of problem is that?.- 2. Briefly on the equations of motion and their integration.- 3. Plane motion.- 4. Description of the trajectories of plane motion.- 5. A few words about the influence of radiation pressure on the motion of Earth satellites.- Fourth Essay. Motion of the worlds.- 1. One more time about the "Laplace Theorem" and other [Serious] "Things".- 2. Wouldn't you like to see the Moon fall on Earth?.- 3. The region of weakly-perturbed motion.- 4. Stability of the Solar System.- 5. Is the Solar System resonant?.- Fifth Essay. The restricted three-body problem, flight to the Moon, and galactic evolution.- 1. The Hill surfaces.- 2. Digression on libration points.- 3. Moon intercept trajectories and a method for their investigation.- 4. Galactic evolution.-Sixth Essay. They are waltzing in orbits.- 1. Gravitational potential.- 2. Rotation of the Moon. Background material on stability theory.- 3. Stability of relative equilibrium in a gravitational field.- 4. Rhinogradentia in orbit 151.- 5. Passive stabilization of artificial satellites.- 6. Nonlinear oscillations.- 7. Fast rotations.- 8. Where the author slightly frightens the reader.- 9. Explicit form of the perturbed motion.- 10. Pegasus.- 11. Moon, Mercury, resonances.- 12. Schiaparelli and others.- 13. Resonant rotations of celestial bodies and the generalized Cassini laws.- 14. Tendency toward synchronization of rotational motion in complex gravitational fields. Lunar-solar precession and nutation of the Earth's axis.- 15. A model of tidal phenomena and capture into resonant rotation.- 16. Magnetic and magneto-gravitational stabilization.- Seventh Essay. In a spiral to space.- 1. Low thrust.- 2. Escape parameters and paradoxes.- 3. A monotone escape spiral.- 4. Arbitrary trajectories with small eccentricities.- Eighth Essay. The full force of the sun blows in the sails.- Ninth Essay. The gravity flyer.- 1. Force of attraction on a body of non-negligible dimensions.- 2. A pulsating spaceship.- 3. Left behind by your spaceship? Swim breaststroke!.- 4. The gravity flyer and the reader.- 5. The gravity flyer as a resonance phenomenon.- 6. The gravity flyer and writers.- Tenth Essay. Interplanetary flights: low trusts for high goals.- 1. Prelude.- 2. Larger payloads, less fuel.- 3. The Pontryagin maximum principle.- 4. The equation of optimal flight.- 5. No constraints.- 6. The method of carrier trajectories.- 7. The scheme for solving the boundary value problem.- 8. Integration.- 9. Some problems of relative motion.- 10. Computational results for optimalinterplanetary trajectories.- 11. Presentation of results of the computation of series of trajectories.- 12. Correction of interplanetary trajectories.- Eleventh Essay. Relative motion of orbiting bodies.- 1. In orbit - two satellites.- 2. The equations of relative motion.- 3. Free motion of an astronaut relative to his spaceship.- 4. Leonov and the lens cap.- 5. Space probe.- 6. Boleadoras in space.- 7. The evolution of mixed motion.- 8. System of linked bodies in space.- 9. Cloud of particles in orbit and the Poincaré recurrence theorem.- Twelfth Essay. Cosmic pinwheel.- 1. The Proton satellites.- 2. Here is how all this was discovered.- 3. What was discovered.- 4. Here is how all this is explained.- References.- Author index.