Comet dual tail - 2D orbit plane view

Why a comet has two tails

Sunlight pushes on dust grains with a force F_rad = Q_pr L A / (4πr²c) that falls off as 1/r² exactly like gravity, so the ratio β = F_rad/F_grav is a constant for a grain: roughly β ≈ 0.57 Q_pr / (ρ a) with density ρ in g/cm³ and radius a in micrometres. Each grain therefore orbits the Sun with an effective gravitational parameter (1 − β)GM, released with the comet's velocity. Small grains (large β) are swept far back along a curved path, big grains stay near the orbit, and together they form the broad curved dust tail (a fan of syndynes).

The ion tail

Gas that is ionised by ultraviolet light is picked up by the magnetised solar wind (about 400 km/s) and accelerated almost radially away from the Sun, a billion times more strongly than gravity can hold it. The ion tail is thus thin, straight and points almost exactly anti-sunward, with only a few degrees of aberration from the comet's own motion. It glows blue from CO⁺ fluorescence.

Orbit

The nucleus follows a Kepler ellipse with perihelion q and eccentricity e: a = q/(1 − e), period T = 2π√(a³/GM) (365.25 a^3/2 days with a in AU) and speed v² = GM(2/r − 1/a). Activity (dust and gas release) is scaled as 1/r², as for water-ice sublimation near the Sun.

Honest simplifications: two dimensions in the orbital plane, point grains released with the nucleus velocity and no ejection speed, no gravity of the comet, Q_pr constant, no sublimation or fragmentation of grains, and ions modelled as straight radial streaks of fixed lifetime. Particle counts are small so the picture is qualitative; the orbital mechanics and the β scaling are quantitative.

• Choose the Sungrazer preset: near perihelion the tails are enormous and strongly curved.
• Raise the largest β: the dust fan widens and bends back toward the orbit's trailing side.
• Set the solar-wind speed to a low value and see the ion tail shorten while its direction stays anti-sunward.
• Compare Halley-like (e = 0.97) and a low-eccentricity comet: the dust tail points almost exactly away from the Sun when the comet moves slowly.