Three Bodies This is a rough simulation of 3 bodies under gravity done with Flash 5.

You can now create your own arrangements and see what happens.

You can now change the mass of each body.

Click on a body to display its velocity vector and mass. Drag the vector arrowhead to change the velocity and edit the mass to change mass.

Drag a body to change its position.

The Buttons

Start

Start and pause the animation. When starting or resuming this also adjusts the total momentum of the system to zero so the centre of mass is tracked.

Reset

Reset to the current default arrangement. Also does a tracking adjustment.

Default

Make the current arrangement the default. This lets you try an initial arrangement and then come back to it (with the RESET button) to make adjustments.

open

Open a menu of arrangements saved from this page.

save

Save the current default arrangement.

fig 8

Each body orbits the other 2 in turn tracing out a figure 8. Seems quite stable.

roll

A pair orbit each other closely and "roll" around the other. Like the earth and moon around the sun. Orbits in same direction.

skid

A pair orbit each other closely and "skid" around the other. I think this is called retrograde motion. Orbits in opposite direction.

poise

One body in the middle poised between 2 orbiting opposite each other. This is definitely not in stable equilibrium. Extremely unlikely to occur.

circle

Three bodies orbiting their combined centre of mass. This one breaks down in this simulation. Mustn't be stable.

+

Zoom in.

x1

Zoom to original size.

-

Zoom out.

+

Increase body size.

x1

Set to original body size.

-

Decrease body size.

The simulation uses the instantaneous acceleration and applies it for a fixed interval and then displays the next frame. I think this approach is called Euler's method. It's least accurate when direction or size of the acceleraton is changing rapidly as two bodies approach closely. This can lead to collisions where the bodies shoot off in opposite directions. Collisions can also happen just because of the arrangement. Despite this 4 of the 5 "solutions" are stable and 3 are in stable equilibrium - can be changed a little and still remain stable.

The velocities you set may appear to change. This is because the velocities are adjusted to track the centre of mass by making the total momentum zero. The relative velocities you set don't change.

You can now save the current default arrangement and load a menu of arrangements saved from the page.

Email Bill Stern bill email with questions or suggestions.

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