INSTRUMENT 04 / ORBITAL DESK
Gravity, energy,
and orbital motion.
A gravitational mechanics bench. Follow energy and angular momentum while one inverse-square force draws circles, ellipses, and flybys.
INERTIAL FRAME / VELOCITY VERLETt = 0.0
TRAIL = POSITION HISTORY0.00 ms/frame · 2 BODIES
KINETIC22.50
POTENTIAL-44.99
Energy changes form continuously. Numerical drift stays small because velocity Verlet evaluates gravity on both sides of every position update.
Why does falling sideways become an orbit?
REPRESENTATIVE EQUATIONv_c = √(GM / r)
Gravity continually bends the velocity vector. The planet misses the star by exactly enough to keep circling. Gravity always pulls inward and weakens with the square of distance, F = GMm/r². An orbit appears when sideways motion carries a body past the place it was falling toward, over and over again.
The simulation advances with velocity Verlet: half a velocity step, a position step, a fresh gravity calculation, then the remaining velocity step. That symmetry is why the energy ledger stays steady enough to make circles, ellipses, and escape trajectories meaningful.