# Guillaume Matheron

Data scientist, PhD in computer science

# Orbit simulator

Orbit is a small orbital simulator made in BlitzPlus. It originated as a research project on Lagrangian points in the {Earth, Moon} system.

The simulation starts un-paused but at a very slow speed. If you want to see something, hit “,” (QWERTY) or “;” (AZERTY) a few times. The earth is in the center, the moon at the right. Five lightweight objects are placed near each of the five Lagrangian points.

### Controls

• R
By default, the frame of reference is geocentric. Hit R to switch it to the frame in which the Earth and the Moon are immobile. In this frame you can observe the movement of the objects that are initially near the Lagrangian points relative to the moon.
• Q (on QWERTY), A (on AZERTY)
When the simulator is paused, displays the force field (gravity + centrifugal force if in a relative frame). Lagrangian points are visible when this command is called from a relative frame. Note that this force field does not include the Coriolis force, since it does not produce a force field (it depends on the object’s speed).
• W (on QUERTY), Z (on AZERTY)
Same as above, but produces a more detailed image
• E
Same as above, but with an even more detailed image
• P
Hold P to enable trajectory recording : the successive positions of the objects leave a trail on screen
• TAB
Same as P except you don’t have to hold down the key
• C
Obsolete : opened a command prompt in previous versions
• M (on QWERTY), “,” (on AZERTY)
Slow time (/2)
• “,” (on QWERTY), “;” (on AZERTY)
Accelerate time (x2)
• Space bar
Pause/Resume the simulation
Hide one of the objects : hitting 1 deleted the object corresponding to L1, etc…

### Interesting findings

#### Horseshoe orbit

Run the simulator, hit R, then 1 and 2 to hide L1 and L2 objects, hit TAB, then W (on QWERTY) or Z (on AZERTY) and wait for the field to finish drawing, and finally increase the simulation speed until the objects start to move.
The L3 object oscillates around L3, while the L4 and L5 objects are on a so-called horseshoe orbit.

#### Foucault trajectory

Run the simulator, hit R, then 2, 3, 4 and 5 to hide all objects except the L1 object. Hit TAB, then W (on QWERTY) or Z (on AZERTY) and wait for the field to finish drawing, and finally increase the simulation speed until the object starts to move.

The L1 Lagrangian point is unstable, which means that unless the object was places EXACTLY on L1, it would eventually start moving away from its position (it is in an unstable equilibrium)

It starts drawing a weird trajectory around the Earth, that bears a close ressemblance to the trajectory of a Foucault pendulum (see this animation). This is because the two systems are driven by the same force : the Coriolis force, that rules the motion of a moving object in a rotating frame.