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Space sciences --- Astronautics --- Space stations --- Congresses. --- 629.78 <063> --- -Space sciences --- -#TWER:WTCM --- Manned orbital laboratories --- Manned space stations --- Orbiting vehicles --- Satellite vehicles --- Space cars --- Space laboratories --- Artificial satellites --- Space flight --- Space ships --- Space vehicles --- Large space structures (Astronautics) --- Space colonies --- Science and space --- Space research --- Cosmology --- Science --- Astronomy --- Aeronautics --- Astrodynamics --- Ruimteschip--Congressen --- Congresses --- #TWER:WTCM --- Space sciences - Congresses.

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Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

Astrodynamics. --- Apollo program. --- Bate, R. --- Brahe, Tycho. --- Delaunay elements. --- Earth-Moon system. --- Greenwich Meridian. --- Hamiltonian Mechanics. --- Julian date. --- Kepler's equation. --- Kepler's laws. --- Kepler, Johannes. --- LVLH plane. --- Legendre polynomials. --- Lyapunov stability. --- Mathematica. --- abort problem. --- absolute origin. --- angular velocity, Earth. --- center of mass. --- column vector. --- computer arithmetic. --- conic section equation. --- conservative potential. --- contact acceleration. --- direct orbit. --- direction cosines. --- dissipative acceleration. --- dot product. --- embedding. --- entry interface. --- escape velocity. --- first-order system. --- fixed origin. --- fundamental plane. --- geocentric coordinate system. --- geopotential. --- harmonic oscillator. --- hyperbolic functions. --- hyperbolic motion. --- inertial frame. --- infinite series. --- integrable system. --- irregular planet. --- linearization. --- moments of inertia. --- near-circular orbit. --- nonhomogeneous mass. --- numerical solution. --- oblateness term. --- orthogonal system. --- perturbed system. --- perturbed two-body motion.