The satellite follows a Keplerian ellipse with Earth fixed at one focus. Mean anomaly advances linearly with time (Kepler's second law: equal areas in equal times), then Kepler's equation is solved by Newton–Raphson each frame to recover position and speed:
M(t) = M0 + n·t, n = sqrt(mu / a^3)
E - e·sin(E) = M (solved for E, Newton-Raphson)
r = a(1 - e·cos E)
x = a(cos E - e), y = a·sqrt(1-e^2)·sin E
v = sqrt(mu·(2/r - 1/a)) (vis-viva equation)
Perigee altitude and eccentricity set the ellipse's size and shape; semi-major axis a = (Earth radius + perigee altitude) / (1 − e). Plane inclination is shown as a vertical squash of the ellipse, matching how an inclined orbit foreshortens when viewed from outside the plane. mu = GM_Earth = 398,600.4 km³/s².