As of May 31, 2023, we have updated our Code of Conduct.

Orbital mechanics (also called astrodynamics) is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft on an orbital or escape trajectory. For the movements of celestial bodies, use [celestial-mechanics], not this.

In the frictionless vacuum of space, rockets move with mathematical precision along a trajectory.

Around a single point mass, or even any spherically symmetric body due to the shell theorem, these orbits are simple conic sections and can thus be modelled with simple geometry. Circles and ellipses form cyclic orbits bound by the gravitational field of the parent body, while parabolas and hyperbolas lead to an eventual escape.

Commonly used properties for these orbits are:

  • r_P: The periapsis distance, the closest approach to the parent.
  • r_A: The apoapsis distance, the furthest away
  • a: The semi-major axis, half the distance between the periapsis and apoapsis.
  • e: The eccentricity, how stretched the conic section is. 0 for a circle and 1 for a parabola
  • μ: The gravitational parameter, an object's mass times the gravitational constant.
  • v_e: Escape velocity, the necessary speed (in any direction) to escape a parent body from a given distance.

Velocity in these orbits are governed by Kepler's laws, easily applied through the Vis-viva equation

When three or more bodies are involved (three body problem), systems typically behave chaotically and can't be solved analytically. A notable exception is the circularly restricted three body problem (CR3BP), which has solutions such as the Lagrange points

For spacecraft, the patched conics approximation is often used to model interplanetary flight. Here the trajectory is broken up into multiple conic sections with different parent bodies, the assumption being that the gravity of one object usually dominates.