Modern Astrodynamics (eBook)

Fundamentals and Perturbation Methods

Mark C. Allman, Victor R. Bond (Autoren)

eBook Download: PDF

2021
263 Seiten
Princeton University Press (Verlag)
978-0-691-22390-2 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 12.1.2021
• Zusatzinfo: 10 tables, 50 halftones
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Luft- / Raumfahrttechnik
• Schlagworte: abort problem • absolute origin • acceleration • algorithm • Angular momentum • angular velocity, Earth • Apollo Program • Apsis • Astronomy • Atmospheric entry • Bate, R. • Big O notation • Brahe, Tycho • Calculation • Cartesian coordinate system • Celestial mechanics • center of mass • Center of mass (relativistic) • Circular Orbit • Closed-form expression • coefficient • column vector • Computation • Computer arithmetic • conic section • conic section equation • conservation law • conservative potential • Constant of integration • contact acceleration • coordinate system • Cross product • Delaunay elements • Delta-V • differential equation • direction cosines • direct orbit • dissipative acceleration • dot product • Earth-Moon system • Elliptic orbit • Embedding • Energy • entry interface • ephemeris • Equation • Equations of motion • escape velocity • Figure of the Earth • First-Order System • fixed origin • fundamental plane • Fundamental plane (elliptical galaxies) • geocentric coordinate system • Geopotential • Gravitational constant • gravitational potential • Gravity turn • greenwich meridian • hamiltonian mechanics • Harmonic oscillator • Hyperbola • Hyperbolic functions • hyperbolic motion • Hyperbolic trajectory • inertial frame • infinite series • Initial Condition • Instant • integrable system • irregular planet • Jacobi integral • Johannes Kepler • Julian date • Kepler, Johannes • Kepler's equation • Kepler's laws • Kepler's laws of planetary motion • Lagrangian point • Lambert's problem • Legendre Polynomials • linear differential equation • Linearization • logarithm • LVLH plane • Lyapunov stability • mass distribution • Mass ratio • Mathematica • Mean anomaly • Mean motion • moments of inertia • near-circular orbit • Newton's law of universal gravitation • Newton's laws of motion • nonhomogeneous mass • Notation • Numerical analysis • Numerical Integration • numerical solution • oblateness term • Orbit • Orbital elements • Orbital mechanics • Orbital period • Orbital plane (astronomy) • Orbit Determination • ordinary differential equation • orthogonal matrix • orthogonal system • Parabola • perturbation function • Perturbation theory (quantum mechanics) • perturbed system • perturbed two-body motion • Phase space • Planet • Planet V • Regularization (mathematics) • relative velocity • Requirement • Right-hand rule • Rocket engine • Rotation Matrix • round-off error • Runge–Kutta methods • scientific notation • Semi-major and semi-minor axes • Solar mass • spacecraft • space shuttle • Special case • Spherical Coordinate System • Standard gravitational parameter • Taylor series • Three-body problem • Total derivative • Trajectory • True anomaly • truncation error • Truncation error (numerical integration) • two-body problem • Unit vector • Variable (mathematics) • variation of parameters • Velocity
• ISBN-10: 0-691-22390-4 / 0691223904
• ISBN-13: 978-0-691-22390-2 / 9780691223902