Motion energy conservati on in general equation of

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Unformatted text preview: eneral: Equation of orbit: Usually, need to find E and J from initial conditions and then plug into radial energy - The conditions in different types of orbits can help translate English into math direction - If initial radial velocity is inward, particle changes directions after reaching a minimum attractive case decreases to below 0, then approaches 0 from below (see page 81) Circular orbit: In polar coordinates: Radial energy equation (eliminate above): from Elliptical orbit: Range of motion: Parabolic orbit: Isotropic harmonic oscillator: Hyperbolic orbit: Shapes of orbit: Circular motion occurs at For equating minimum and maximum . - gives This is just an example; know how to derive this Repulsive case: Attractive case: - These are the shapes or orbits in polar coordinate form is eccentricity and determines the orbit; is semi-latus rectum - - - Since , in the repulsive case In the attractive case, can be anything as we have seen the orbits can be any of the four types Condition on can be used to determine energy requirement too Elliptical orbit in Cartesian form: (see page 87 for geometry) is semi-major axis; - Note that Period of orbit: is semi-minor axis Centre of mass: Linear moment um: Angular moment um: “Lab” coordinates: Centre of mass coordinates: Hyperbolic orbit in Cartesian form: (see page 88 for geometry) - - is semi-major axis; is semi-minor axis is also called the impact parameter (perpendi...
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This document was uploaded on 03/05/2014 for the course PHYS 350 at The University of British Columbia.

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