Essays on the Motion of Celestial Bodies [Hardcover]

Interesting and often unexpected achievements of the mechanics of space flight throw a new light onto several classical problems. The books emphasis is on analysis carried out on the level of graphs and drawings, and sometimes numbers, revealing the beauty of the research process leading to the results.

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. Jacobis 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. Wouldnt 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 ll³i