This preview shows page 1. Sign up to view the full content.
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 semilatus 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 semimajor axis;
 Note that
Period of orbit: is semiminor 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 semimajor axis; is semiminor axis
is also called the impact parameter
(perpendi...
View
Full
Document
This document was uploaded on 03/05/2014 for the course PHYS 350 at The University of British Columbia.
 Fall '08
 MoChen
 mechanics, Energy, Force

Click to edit the document details