 Central force

A central force on a particle points along the line from a fixed centre to the particle, with magnitude depending only on its distance $r$: $\mathbf{F}=f(r)\hat{\mathbf{r}}$. Its torque about that centre vanishes, since $\mathbf{r}\times \mathbf{F}=0$, so angular momentum is conserved. For nonzero angular momentum, the position vector remains in the plane perpendicular to that fixed vector.

A central potential $U(r)$ gives $f(r)=-dU/dr$. Attractive Newtonian gravity has $U=-GMm/r$; the same inverse-distance form describes the attraction of opposite electric charges through a Coulomb potential. Their radial effective potential separates the physical attraction from the contribution of fixed angular momentum, making turning points and circular orbits accessible without solving every coordinate at once.^[ref]

A central force is a type of force that acts on an object directed towards a fixed point, known as the center. The key characteristics of a central force include: 1. **Direction**: The force always points either directly toward or directly away from the center. 2. **Magnitude**: The strength or magnitude of the force can vary with the distance from the center, but it is always a function of that distance.