Comet Tail Lab

Orbit and activity

The comet moves on a Kepler ellipse of perihelion distance q and eccentricity e, integrated with a leapfrog scheme and adaptive sub-steps (units: AU, years, GM = 4 pi^2). Its speed at perihelion obeys vis-viva, v^2 = GM (1 + e) / q. Water-ice sublimation scales with the sunlight received, Q ~ 1/r^2, and switches on inside roughly 3 AU, so a comet is most active near the Sun.

The dust tail: radiation pressure and beta

A grain of radius s and density rho feels solar gravity GM m / r^2 and radiation pressure L Q_pr A / (4 pi r^2 c), both falling as 1/r^2. Their ratio is constant, beta = 0.57 Q_pr / (rho s) with s in micrometres and rho in g/cm^3, so the grain simply orbits in a weaker gravity GM (1 - beta). Large grains (beta near 0) follow the comet’s orbit and trail along it; fine grains (beta near 1) are blown almost straight away from the Sun; for beta = 1 the force cancels and the grain moves in a straight line (a check below). Grains released at different times and with different beta fan out into the curved dust tail.

The ion tail: apparent solar wind

Ionised gas is carried by the solar wind (about 400 km/s, radially outward) and magnetic field. In the comet’s own frame the wind arrives with velocity u = v_sw r_hat - v_comet, and the ion tail is straight and points along u, so it is nearly anti-solar but tilted by the aberration angle tan(alpha) ~ v_t / v_sw, where v_t is the comet’s tangential speed. Faster wind straightens the tail; a fast comet near perihelion shows a larger angle.

Honest simplifications

Point-mass Sun, no planetary perturbations, no non-gravitational forces on the nucleus, Q_pr = 1 for every grain size, a fixed density, no grain fragmentation or sublimation, no collisions or electrostatic charging of grains, no interplanetary magnetic-field structure for the ion tail (a straight line, not a time-varying plasma). Ejection is isotropic with a small speed. The 3D nucleus and probe are drawn much larger than their true size. The sublimation law is a rough 1/r^2 with a smooth cut-off between 2.5 and 3.6 AU, not a thermal model of ice.

• Choose the sungrazer preset: grains with high beta are expelled in a brief burst at perihelion while big grains hardly move.
• Raise the smallest grain radius: the dust tail becomes short and orbit-hugging (beta falls below 0.01).
• Raise the solar-wind speed to 700 km/s and watch the ion tail swing closer to the Sun line.
• Pause near perihelion and compare the aberration angle with the tangential speed.
• Look at the beta graph: where is the beta = 1 line crossed? That grain size feels no net force.