Ground Track & Nodal Precession (2D)

Orbit Parameters

Altitude (circular-mean) 700 km

Eccentricity 0.05

Inclination 98.0°

Time acceleration 2000×

Ground-track trail 8 orbits

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's equatorial bulge (the J2 zonal harmonic) tugs harder on an inclined orbit than a plain point-mass model predicts, steadily rotating the whole orbital plane about Earth's spin axis — nodal precession. Instead of a 3D globe, this view is the way ground controllers actually track a real satellite: a flat world map traced by the sub-satellite point (where a line from Earth's centre through the satellite pierces the surface).

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 still obeys plain two-body gravity along its ellipse (Kepler's second law, angular momentum conservation):

dν/dt = √(μp) / r²,   r = p / (1 + e·cos ν)
lat = asin(z/r), lon = atan2(y,x) − θ_Earth(t)

Ground-track map — each successive orbit's track shifts westward because Earth spins underneath the orbital plane; drag to pan, scroll/pinch to zoom.
Sensitivity curve (bottom-left) — plots dΩ/dt against inclination for the current altitude/eccentricity; the dashed line is Earth's ≈0.9856°/day solar rate, and the two curves cross at the sun-synchronous inclination.
RAAN dial (bottom-right) — a compass needle showing the ascending node's current longitude Ω, drifting at the (time-accelerated) nodal rate.
Snap to Sun-Synchronous — solves cos i = Ω̇_target / [-(3/2)n·J2·(Re/p)²] for the inclination that locks local solar time at every equator crossing — the trick behind every polar weather/Earth-observation satellite.

Satellite (ground track) Ascending node crossing dΩ/dt(i) curve

drag to pan · scroll to zoom