Warpriest

Drafting office · Sheet 02

Orbit lab: four bodies around one sun

This is a model drawn in model units. Each body moves along its own ellipse with the sun at one focus, and its position comes from Kepler's equation. The bodies do not pull on one another, so each drawing shows one rule at a time.

The simulator

1 unit
Fig. 02. Four bodies on elliptical orbits, each with the sun at a focus. The scale bar marks one model unit of semi-major axis. The starting frame shows the bodies before any time has passed.

Model time 0.00 years

Reading the controls

  • Play and Pause start or stop the clock. The clock runs at the speed you set, and the model time appears beneath the figure.
  • Step forward moves every body by a quarter of a model year, whether or not the clock is running. It stays available when reduced motion is on and Play is hidden.
  • Speed runs from one tenth to four times. At 1×, Body I completes an orbit in four seconds and Body IV takes about twenty-five. The status line reads the new times aloud when you finish a change.
  • Orbit paths draw each ellipse. Trails draw the recent stretch of each body's path.
  • Reset stops the clock, returns it to zero and places every body at its starting position.

Body parameters

The parameters are in model units. The period follows Kepler's third law: the period equals the semi-major axis raised to the power 3/2. Eccentricity runs from zero, a circle, toward one, a line. The last column gives the same period at 1× speed, in seconds.

Parameters for the four bodies in the orbit lab
Body Semi-major axis a Eccentricity e Period T, model years Period at 1×, seconds
Body I 1.00 0.05 1.00 4.0
Body II 1.60 0.18 2.02 8.1
Body III 2.40 0.32 3.72 14.9
Body IV 3.40 0.12 6.27 25.1

What this model leaves out

  • The bodies do not pull on one another, so the simulator cannot show disturbance between orbits.
  • There is no drag, no tilt between orbital planes and no spin.
  • The clock is a clock for this drawing. Model years are units of the drawing, not calendar years.
  • Eccentricities stay between 0.05 and 0.32, so the ellipses remain easy to compare by eye.