Saturn Shadow (exaggerated)
Gravitoelectrodynamics has been used to model Saturn's rings.

Gravitoelectrodynamics

See also: Dusty plasmas: dynamics

Gravito-electrodynamics is the physics of the influence of gravity and electromagnetic forces on particle. The motion of solid particles in a plasma follows the momentum equation for ions and electrons:

\(m \frac{d\mathbf{v}}{dt} = m\mathbf{g} + q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) – mv_\mathrm{c} \mathbf{v} + \mathbf{f}\)
where m, q are the mass and charge of the particle, g is the gravitation acceleration, mvcv is due to viscosity, and f respresents all other forces including radiation pressure. q (E + v x B) is the Lorentz force, where E is the electric field, v is the velocity and B is the magnetic field.

Then depending in the size of the particle, there are four categories:

  1. Very small particles, where q (E + v × B) dominates over mg.
  2. Small grains, where q/m ≈ √G, and plasma still plays a major role in the dynamics.
  3. Large grains, where the electromagnetic term is negligible, and the particles are referred to as grains. Their motion is determined by gravity and viscosity, and the equation of motion becomes mvcv = mg.
  4. Large solid bodies. In centimeter and meter-sized bodies, viscosity may cause significant perturbations that can change an orbit. In kilometer-sized (or more) bodies, gravity and inertia dominate the motion.

References

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