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Orbital Mechanics for Engineering Students is an aerospace engineering textbook by Howard D. Curtis, in its fourth edition as of 2019. [1] The book provides an introduction to orbital mechanics, while assuming an undergraduate-level background in physics, rigid body dynamics, differential equations, and linear algebra.
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation .
Final v s, θ s and r must match the requirements of the target orbit as determined by orbital mechanics (see Orbital flight, above), where final v s is usually the required periapsis (or circular) velocity, and final θ s is 90 degrees. A powered descent analysis would use the same procedure, with reverse boundary conditions.
Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity , including both spacecraft and natural astronomical bodies such as star systems , planets , moons , and comets .
Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press. ISBN 9780521876223. Müller-Kirsten, Harald J.W. (2024). Classical Mechanics and Relativity (2nd ed.). World Scientific. ISBN 9789811287114. Taylor, John (2005). Classical Mechanics. University Science Books. ISBN 978-981-12-8711-4.
In orbital mechanics, the universal variable formulation is a method used to solve the two-body Kepler problem. It is a generalized form of Kepler's Equation , extending it to apply not only to elliptic orbits , but also parabolic and hyperbolic orbits common for spacecraft departing from a planetary orbit.
An orbiting body's mean longitude is calculated L = Ω + ω + M, where Ω is the longitude of the ascending node, ω is the argument of the pericenter and M is the mean anomaly, the body's angular distance from the pericenter as if it moved with constant speed rather than with the variable speed of an elliptical orbit.
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