Comet Dust Tail (2D)

Radiation pressure on dust

Sunlight pushes on a dust grain with a force that falls off as 1/r^2, exactly like gravity, so their ratio β = F_rad / F_grav does not depend on distance: β = 0.574 Q_pr / (ρ s) with the grain radius s in micrometres and its density ρ in g/cm3 (Q_pr is the radiation-pressure efficiency, near 1 for grains larger than the wavelength). The grain therefore moves as if the Sun's mass were reduced: r'' = -G M (1 - β) r / r^3. Small grains (large β) are pushed far from the comet, large ones (small β) stay near its orbit.

Syndynes and synchrones

A syndyne is the curve occupied now by grains of one β released at different times; a synchrone is the curve occupied by grains of all β released at one instant (Finson and Probstein, 1968). The dust tail is the area these curves sweep out. The curves in the picture are computed by integrating the reduced-gravity orbit from the comet's position at each release time.

Ion tail

The straight blue ion tail is not caused by radiation pressure: ionised gas is carried along the solar-wind magnetic field and points almost exactly away from the Sun. Its direction here is drawn as exactly anti-solar.

Escape

A grain released with specific energy E = v^2/2 - G M (1 - β) / r becomes unbound once E > 0; the critical value β_crit at release is plotted against the comet's orbit.

Simplifications

Planar two-body problem (no planetary perturbations, no Poynting-Robertson drag, no fragmentation), constant Q_pr, spherical grains, Kepler orbit for the nucleus, small random ejection speed independent of grain size.

• Choose a comet near perihelion and widen the view: the dust tail curves behind the ion tail.
• Move the size range to very small grains (0.3 um): beta exceeds 1 and the grains are blown out almost radially.
• Show syndynes only, then synchrones only, and see how the two families cross.
• Set beta to 0.5 in the energy graph and see which orbits release unbound grains.