Effective Potential - Definition

Definition

The effective potential is defined in the following way:

L is the angular momentum
r is the distance between the two masses
m is the mass of the orbiting body
U(r) is the general form of the potential

The effective force, then, is the negative gradient of the effective potential:

\begin{align} \mathbf{F}_\text{eff} &= -\nabla U_\text{eff}(\mathbf{r}) \\ &= \frac{L^2}{mr^3}\hat{\mathbf{r}} - \nabla U(\mathbf{r}) \end{align}

Where denotes a unit vector in the radial direction.

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