Central Force Integrator (CFI) Help File
HELP. Displays this help screen. To exit, click one of the "Exit
Help" buttons located at the top and bottom of this screen.
Radial Force Equation:
This program solves the
differential equation d2r/dt2 =
-f(r) (r/r) where f(r) = (Arm +
Brn) is an inwardly directed force. You can control the
force law by choosing the four constants A, m, B, and n. Here are some
examples to try:
Choose A=1,m=-2,B=0,n=0 for gravity.
Choose A=1,m=1,B=0,n=0 for a spring (Hooke's Law).
Choose A=1,m=-2,B=0.001,n=-4 to simulate the effects of General Relativity
(in reality, B would be much much smaller).
Choose A=1,m=-3,B=0,n=0 for Cotes' Spirals. See what happens for
the purely azimuthal velocities
Vtheta = 0.99 and Vtheta = 1.01. Try
Vtheta = 0.999.
The RADIUS, r, is the initial distance between the origin and
the particle's position.
The RADIAL VELOCITY, Vr, is the rate at which the
radius, r, is changing its length. Velocities are given in units
of the circular speed.
The AZIMUTHAL VELOCITY, Vtheta, is
the rate at which the radius, r, is changing direction. Velocities are
given in units of the circular speed (so Vr = 0 and
Vtheta = 1 results in an initially circular orbit.
Approximate Number of Orbits: This entry determines the
length of the orbital integration; more precisely, it is the number of
orbits that the particle would complete if it were following a
circular path. Try small numbers first to cut down your wait time.
SUBMIT FORM. Send the parameters that you have chosen to the
orbital integration program!
LOAD DEFAULTS. Set all parameters back to their default values.