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Astronomy and Cosmology
Astronomy and Astrophysics
What exactly is L, Lz and E in orbital mechanics?
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[QUOTE="D H, post: 5506536, member: 42688"] You have that backwards. Angular momentum is [itex]\mathbf L = \mathbf r \times \mathbf p[/itex], so the [I]z[/I] component of angular momentum is given by [itex]L_z = r_x p_y - r_y p_x[/itex]. Spherical coordinates turn out to be not particularly useful (rather useless, in fact) in orbital mechanics. The solution is simple: Don't do that then! Polar coordinates on the other hand are very useful because of the planar nature of Keplerian orbits. It is handy to have the polar axis pointing to periapsis. The angular momentum vector as expressed in arbitrarily oriented Cartesian coordinates that aren't aligned with the orbital plane provides a mechanism to find the first two elements of a z-x-z Euler rotation sequence that rotate the Cartesian x-y-z axes to those of the orbital plane, the right ascension of the ascending node (itex]\Omega[/itex]) and the the argument of periapsis ([itex]\omega[/itex]). Neither. Special relativity does not pertain to orbital mechanics. Special relativity pertains to regions of space where gravitation is so negligibly small as to be essentially non-existent. Generalizing special relativity to areas where gravitation is present is the subject of general relativity. In classical mechanics, it's the total energy (kinetic energy plus potential energy) that is conserved. [/QUOTE]
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What exactly is L, Lz and E in orbital mechanics?
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