Nodal Precession & Sun-Synchronous Orbits

Orbit Parameters

Altitude (circular-mean) 700 km

Eccentricity 0.05

Inclination 98.0°

Time acceleration 2000×

Live Readouts

Not sun-synchronous

Orbital period

— min

Nodal rate dΩ/dt

— °/day

Mission elapsed

0.0 days

RAAN (Ω)

0.0°

How it works

Earth is not a perfect sphere — its equatorial bulge (oblateness, described by the J2 zonal harmonic) adds a small extra pull that, for an inclined orbit, steadily rotates the whole orbital plane about Earth's axis. This is nodal precession: the ascending node — where the orbit crosses the equator heading north — drifts in longitude every revolution.

dΩ/dt = -(3/2)·n·J2·(Re/p)²·cos i
n = √(μ/a³)         (mean motion)
p = a(1 - e²)        (semi-latus rectum)
μ = 398600 km³/s²,  Re = 6378 km,  J2 = 1.08263×10⁻³

The satellite itself still obeys plain two-body gravity along the ellipse (angular momentum conservation, i.e. Kepler's second law):

dν/dt = √(μp) / r²,   r = p / (1 + e·cos ν)

Altitude / eccentricity / inclination — set the orbit's shape and tilt; the disc and dashed ellipse update live.
Time acceleration — real dΩ/dt is only a fraction of a degree per day, far too slow to watch directly, so simulated time runs thousands of times faster than the animation's real seconds.
Snap to Sun-Synchronous — solves cos i = Ω̇_target / [-(3/2)n·J2·(Re/p)²] for the inclination that makes dΩ/dt match Earth's ≈0.9856°/day revolution around the Sun, so the orbit's local solar time at each crossing stays fixed year-round — the trick behind every polar-orbiting weather and Earth-observation satellite.
The polar flattening drawn on the globe is exaggerated roughly 15× (real Earth flattening is only 1/298) so the bulge that causes the whole effect is visible at all.

Satellite Orbit ellipse Ascending node

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