The nucleus follows a true Keplerian ellipse: r(θ) = p / (1 + e·cos θ), with the sweep rate set by conservation of angular momentum (Kepler's second law), dθ/dt = L / r². Every dust grain is released from the nucleus carrying the comet's own velocity, then integrated under a reduced gravity, g·(1 − β), where β is the ratio of outward radiation-pressure force to inward solar gravity for that grain size:
β ≈ k / s (s = grain radius; smaller grains feel radiation pressure far more strongly)
Small grains (large β) are shoved almost straight outward, producing the broad, curving dust tail (a "syndyne"). Ions are modelled the same way but with β forced close to 1 by the solar-wind slider, so the ion tail stays thin and points radially away from the Sun at all times — exactly the real distinction between a comet's curved dust tail and its straight ion tail.
- Dust grain size — sets β for newly emitted dust particles; smaller grains bend the tail harder.
- Orbit time-scale — speeds up or slows down the nucleus's Keplerian sweep.
- Emission rate — how many dust grains leave the nucleus per second.
- Solar wind strength — how strongly the separate ion stream is pushed outward.