Mathematics of Interplanetary Flight
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Chapter 6 is a discussion of the complex aspects of the design of the trajectory of a spacecraft and the maneuvers that direct it to its target. Applying Newton’s analysis and using the NEAR-Shoemaker, the Voyagers, and Cassini missions as contexts, the chapter studies the essentials of gravitational spheres of influence, transfer orbits, orbit insertion, hyperbolic gravity assist flybys, and the ephemerides of trajectories. The study of hyperbolic trajectories and the motion of spacecraft along them is analogous to their motion along elliptical orbits, except that in terms of the calculus involved, hyperbolic functions and the hyperbolic Kepler equation take the place of trigonometric functions and the elliptical Kepler equation.