DATA
Units of mass, distance and time
If you have an orbit simulator program, and want to try reproducing some interesting orbits, try the starting parameters below.
The data provided here is valid for any set of units for mass distance and time such that the gravitational constant in those units = 1.
There are many sets of units which satisfy this criterion.
Here is one example .....
unit of mass = the mass of our sun
unit of distance = 1 astronomical unit (the average distance from Earth to our sun)
unit of time = 1 sidereal Earth year divided by (2*pi)
These particular units are especially intuitive to use because they are directly related to the orbit we know best, as shown in the first example below.
Data
Using the above units, the following starting parameters produce a simplified circular version of the Earth's orbit .....
| X position | Y position | X velocity | Y velocity | Mass | |
|---|---|---|---|---|---|
| Sun | 0 | 0 | 0 | 0 | 1 |
| Earth | 1 | 0 | 0 | 1 | 0 |
The following parameters produce a simplified version of a binary star system with circular orbits, having the same total mass, seperation and period, as the Sun-Earth system .....
| X position | Y position | X velocity | Y velocity | Mass | |
|---|---|---|---|---|---|
| Star A | -0.5 | 0 | 0 | 0.5 | 0.5 |
| Star B | 0.5 | 0 | 0 | -0.5 | 0.5 |
Next are the approximate starting parameters for some of the orbits in "Theoretical orbits of planets in binary star systems". You need to include both stars plus one (or more) of the planets .....
| X position | Y position | X velocity | Y velocity | Mass | |
|---|---|---|---|---|---|
| Star A | -0.5 | 0 | 0 | 0.5 | 0.5 |
| Star B | 0.5 | 0 | 0 | -0.5 | 0.5 |
| Planet with ice-cream-spoon orbit | -1.2353 | 0 | 0 | -0.3242 | 0 |
| Planet with rounded-square orbit | -1.08156 | 0 | 0 | -1.1283 | 0 |
| Planet with rounded-triangle orbit | -0.7607 | 0 | 0 | -1.6937 | 0 |
Next are the starting parameters for a triple star system with the exotic figure-eight orbit (parameters by Carles Simó) .....
| X position | Y position | X velocity | Y velocity | Mass | |
|---|---|---|---|---|---|
| Star A | -0.97000436 | 0.24308753 | -0.466203685 | -0.43236573 | 1 |
| Star B | 0.97000436 | -0.24308753 | -0.466203685 | -0.43236573 | 1 |
| Star C | 0 | 0 | 0.93240737 | 0.86473146 | 1 |
Scaleability
All of the orbits above are scalable to different masses distances and velocities in accordance with Kepler's laws.