Gravitationally interacting balls in an ellipse billiard @animations

Uploaded January 2025 | Updated September 2026, 2 weeks ago

Two gravitationally interacting balls move in an ellipse billiard. The balls are point-like and cannot collide even though their depicted size indicate that the could. The softening of the gravitational potential is quite exaggerated to avoid excessive speeds when the balls pass very close to each other.

Music by @gpcbass. The song, made yesterday, is called Dance Floor.

Visuals in Mathematica.

Gravitationally interacting balls in an ellipse billiard

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$Light ray hitting an elliptic water drop Shown is a white light ray hitting an elliptic water drop at a relatively large incident angle, where refraction generates one or more rainbows. When the light is transmitted such that it passes between a focal point and the boundary the light may be subject to total internal reflection before leaving the water drop. Such a total reflection cannot occur when the light ray enters the drop such that it passes between the focal points. Except for the final part, the Fresnel equations are used to determine the reflection coefficient at the water-air boundary. In the final part all rays have the same intensity, being certainly unrealistic, although visually quite spectacular, and further emphasising some familiar ellipse billiard properties. The music is made by @gpcbass specifically for this video, and a bit too cool for the visuals. Its a reproduction of the song No No No originally made by Tribal Tech from the album Nomad, 1988. The visual part is made using Python and FFmpeg.$

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