Geometry in the GPSORB series
The Earth is at a focus, not at the centre of the ellipse. The inertial X direction is a fixed equinox reference; Z points north.
- a and e
- Size and shape. The perigee and apogee radii are a(1 − e) and a(1 + e).
- i and Ω
- Inclination tilts the orbital plane. RAAN turns its ascending-node direction around Z.
- ω and ν
- Argument of perigee is measured within the orbit from the ascending node. True anomaly is measured from perigee to the satellite.
r = a(1 − e²) / (1 + e cos ν)
M = E − e sin E
R = Rz(Ω) Rx(i) Rz(ω)
Kepler playback advances mean anomaly uniformly, so the satellite moves faster near perigee. Optional J2 applies first-order secular node and apsidal rates with fixed a, e and i. The displayed velocity is the instantaneous two-body osculating velocity.
This is a bound Earth-orbit geometry model, not an LNAV/CNAV broadcast ephemeris decoder. It omits drag, short-period J2 terms, lunar/solar forces, GPS harmonic corrections and Earth-fixed coordinates. Presets are illustrative, not live satellite states.
Julia source · Reference states
Offline project · Provenance
License · Dependencies
Visual inspiration: Ki-math orbital-elements viewer