Model and notation
The simulation integrates position and velocity with central gravity plus the selected radial, transverse, and normal accelerations. The displayed ellipse is the osculating orbit: the two-body orbit matching that instant’s position and velocity. The dashed starting orbit stays fixed. Gauss rates are calculated independently using the variational equations. This is an educational model, with no atmosphere, oblateness, or third bodies. Time pauses for an Earth intersection, unbound orbit, or a near-singular classical-element state.
p = a(1−e²), h = √(μp), u = ω+f. Specific orbital energy is labeled ε; E denotes eccentric anomaly. The formulas for ω and M are singular for e = 0, and Ω is undefined for i = 0° or 180°. Controls avoid those exact states. Geometry and anomaly modes coast with F = 0; force controls are used only in the force lab.