Newtonian orbits and the equivalent one-dimensional
problem
This simulation solves Kepler's problem for the Newtonian potential V(r)
= -k/r, mechanical energy E and angular momentum L
> 0, in dimensionless variables:
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Unit mass is 2-body system's reduced mass m.
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Unit length is the position of the minimum of the effective potential
energy in the attractive case (i.e., the radius of the circular
orbit): r0 = L2/m|k|.
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Time unit is L3/mk2.
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In these unit we have m = L = |k| = 1, the orbit
equation is 1/r = ε cos(φ-φ0)
+ η with η = |k|/k. The
eccentricity is ε = (1+2E)1/2, the
effective potential energy -η/r+1/2r2
and its minimum is at point (1,-1/2) for attractive forces.
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If Orbit is selected, along with the orbit one can see the
conserved Laplace-Runge-Lenz vector, which goes through the
pericentron.
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To get information on one element, put over it the mouse pointer to
see the corresponding tooltip.