exploreYOUR WORLDFIELD NOTE 02 / MOTION
An orbit is a fall that keeps going.
Solid: simulated sampleDashed: expected mean
Violet hollow circles: stable product.
Make a prediction. Change one thing. See what happens.
FOLLOW THE SCIENCE
An orbit is a continuous fall. Gravity bends a moving object’s path inward while its sideways motion carries it around the central body. A circular orbit needs a particular tangential speed at a given radius.
Use the launch presets to compare trajectories, then make your own by dragging in the scene. The arrow sets the initial direction and speed; after release, gravity determines the motion.
A FEW QUESTIONS TO TRY
Launch at the circular speed. Does the probe’s distance change?
Launch more slowly. Where does the probe move fastest?
Give the probe more than the escape speed. Does gravity suddenly stop acting?
| Speed / circular speed | What to look for |
|---|---|
| 1.00× | A circular path: nearly constant distance and speed. |
| 0.72× | An ellipse: the probe speeds up as it falls closer. |
| 1.50× | An escape trajectory: the probe leaves without returning. |
Escape begins at √2 ≈ 1.414 times the circular speed at the same radius. Slower launches can remain bound, but a path that intersects the central body ends in a collision.
A probe moves under inverse-square gravity from one fixed central mass. Launch controls set a tangential speed at a radius of 1.6 model units. Dragging chooses both position and velocity: the arrow points in the initial velocity direction.
A speed equal to the circular speed gives a circle. Other bound launches give ellipses unless they intersect the central body. Escape begins when specific orbital energy, v²/2 − μ/r, reaches zero. The dashed curve previews the next launch; coloured trails show the probes’ actual integrated motion.
μ = GM = 1 in normalized units. A velocity-Verlet integrator advances the test particles with substeps no larger than 0.004 model time units. Simulation time runs at 0.75 model units per visible second. Probes do not attract each other, and there is no atmosphere, thrust, or relativity. The central body has a collision radius of 0.16 model units.
The deep-space backdrop is imagined artwork. Display scale changes with screen size; the physics uses the same normalized coordinates. This is a learning model, not mission-planning software.