Two-body motion under gravity: r'' = -mu r / |r|^3 with mu = GM = 398 600 km^3/s^2 for Earth. The craft is integrated with a symplectic velocity-Verlet scheme, which keeps energy error bounded.

Vis-viva: v^2 = mu (2/r - 1/a). Specific energy E = -mu/(2a). Period T = 2 pi sqrt(a^3/mu) (Kepler's third law).

Hohmann transfer between circular orbits r1 and r2: transfer ellipse a = (r1+r2)/2; dv1 = sqrt(mu/r1)(sqrt(2 r2/(r1+r2)) - 1), dv2 = sqrt(mu/r2)(1 - sqrt(2 r1/(r1+r2))), flight time pi sqrt(a^3/mu).

Simplifications: point-mass Earth, no J2, drag, Moon or Sun; burns are instantaneous and along the velocity vector. This is the 2D companion of the 3D Orbital Spaceflight sandbox, which adds patched-conic travel and more.