Orbital Motion

Explore paths created by an inverse-square gravitational force.

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Question

What initial velocity makes a launched object collide with a planet, enter orbit, or escape?

A small change in launch velocity can turn a collision path into an orbit or an escape path.
A small change in launch velocity can turn a collision path into an orbit or an escape path.

Goals

  • Simulate motion under a central inverse-square force.
  • Compare collision, orbit, and escape paths produced by different launches.

Method

Recompute the gravitational acceleration from the object’s current position at every step.

  • Point the acceleration toward the planet and scale its size by the inverse square of the distance.
  • Update velocity and position numerically while recording the trajectory.
  • Repeat with different initial directions and speeds and classify the resulting paths.

Try an example

Rocket!

Source code ↗ Open full screen ↗

Launch an object inside a central gravitational field and compare collision and curved-flight paths.

Controls: Press Enter, then click and drag from the rocket to choose its initial velocity.