An orbit is
a permanent fall
The sheet below is the gravitational potential, its depth set by −GM/r. Place the satellite, aim it, release. Too slow and it falls in; too fast and it leaves for good. Between the two lies an ellipse that never quite lands.
whatA central mass and a satellite on the potential sheet. The dashed curve is the predicted path; launch to integrate it for real.
lawNewtonian gravity, −GM/r for the potential and inverse-square for the force. Total energy decides the conic: bound below zero, escaping above it.
tryPress circular speed, then nudge the velocity tip slightly longer.
noticeThe circle opens into an ellipse with the mass at one focus. Push past √2 times circular speed and the orbit never returns.
in lifeMission planners pick launch speeds by this classification: park in orbit, or spend the extra and leave.
found byKepler found the ellipses in 1609; Newton showed in 1687 why an inverse-square force produces them.