Astronomy / Earth
Where a satellite flies overhead
Pick a real satellite or build your own: altitude, inclination, eccentricity and perigee. Follow its path over the rotating Earth and on the flat map, and find the orbits that repeat, hang over the north, or keep pace with the Sun.
The model and its limits
A spherical rotating Earth with the secular J2 rates of node and perigee (the perigee's only on an eccentric orbit); Kepler's equation for the position; no drag, no higher harmonics, no station keeping, no mean-motion correction. The map is equirectangular; the globe texture puts longitude 0 on +x.
Equations used in the module
Equations T = 2π√(a³/μ); r_ECEF = Rz(-Ω_E t) r_ECI dΩ/dt = −3/2 J2 n (R/p)² cos i; dω/dt = 3/4 J2 n (R/p)² (5cos²i − 1); p = a(1 − e²); E − e sin E = M
