Orbit Simulator

Two-body gravitation: launch a satellite and see elliptical, circular, or hyperbolic orbits depending on speed and direction. Connects to Kepler’s laws and energy in the central field.

Who it's for: Mechanics and astronomy; orbital energy and escape speed.

Key terms

  • orbit
  • Kepler
  • eccentricity
  • escape velocity
  • two-body problem

How it works

A test mass in the central gravity field obeys a = −GM/r² toward the center. If the initial velocity is perpendicular to the radius with magnitude √(GM/r), the orbit is circular; lower speeds fall inward, higher speeds yield elliptical orbits or escape. Motion is integrated with velocity Verlet for better energy conservation than a basic Euler step.

Key equations

a = −GM/r² · r̂
v_circ = √(GM/r)

Frequently asked questions

What makes an orbit circular?
For a given radius, there is a specific tangential speed where centripetal requirement matches gravitational attraction; too slow you fall in, too fast the orbit opens.