Comet at Perihelion: Closest Approach — 3D Orbital Mechanics

Orbit

Eccentricity e 0.85

Perihelion distance q (AU) 0.6

Time speed 1.0×

Sublimation-rate constant (tail intensity) 1.0×

Live Readouts (Kepler's laws)

Distance to Sun r

— AU

Orbital speed

—

Areal velocity (now)

—

Areal velocity (constant)

—

Tail length (ion)

—

Phase

—

How it works

The comet's position is not a cosmetic ellipse animation — it is computed by solving Kepler's equation M = E − e·sin(E) for the eccentric anomaly E at every frame (Newton–Raphson), which is exactly what makes the motion obey Kepler's second law: the line from Sun to comet sweeps equal areas in equal times. The two "Areal velocity" readouts should always match — one is measured directly from the instantaneous radius and angular rate, the other is the theoretical constant ½nab derived from the orbit's shape — confirming the law numerically rather than just visually.

Orbital speed follows the vis-viva equation v² = GM(2/r − 1/a), so the comet is fastest at perihelion (minimum r) and slowest at aphelion (maximum r). The ion tail always points directly away from the Sun (radial, driven by the solar wind) regardless of the comet's direction of travel, while the dust tail lags behind the orbital path (radiation pressure on heavier grains). Tail length is driven by a sublimation-rate model where activity grows sharply as r shrinks, then decays again past perihelion.

M = E - e sin(E)          (Kepler's equation)
r = a(1 - e cos E)         (radius)
v² = GM(2/r - 1/a)         (vis-viva speed)
dA/dt = ½ n a b = const    (equal-area law)

Click anywhere near the orbit path to jump the comet there and inspect its instantaneous speed and tail state.

Click near the orbit to jump the comet · drag to orbit camera · scroll to zoom

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