This is surprising, but less surprising when you realise it is rotating about one of the foci, not the centre.
perihelions•5h ago
Hmm, that can't be true; it's of uniform density, and the thing it's rotating about has to be its center of mass.
What's odd about it (to me) is the optimal solution isn't symmetric (cylindrically symmetric). It's an intuition trap that you'd expect symmetric solutions. If the Wikipedia history is to be believed, Lagrange fell for this wrong assumption, and there was a 45-year gap before anyone noticed the subtle wrongness of it.
namibj•1h ago
Remember the spontaneously flipping spinning hammer on the ISS?
...rotation for sufficiently non-spherical(-cow) objects in free fall is kinda weird.
MycroftJones•4h ago
That page didn't have a formula, in either cartesian or polar coordinates, for the shape of the object. Lots of formulas, but I didn't see anything I could use to create a 3d mesh and print one of these things out on my printer.
groos•4h ago
It's the general ellipsoid formula: x*2/a*2 + y*2/b*2 + z*2/c*2 = 1, where a, b and c are all unequal. The interesting part is actually that this shape could be made of a liquid, held by gravitation and maintain this asymmetrical shape. Normally, one would imagine it would be ellipsoid of revolution, where two of the axes are equal.
masfuerte•5h ago
perihelions•5h ago
What's odd about it (to me) is the optimal solution isn't symmetric (cylindrically symmetric). It's an intuition trap that you'd expect symmetric solutions. If the Wikipedia history is to be believed, Lagrange fell for this wrong assumption, and there was a 45-year gap before anyone noticed the subtle wrongness of it.
namibj•1h ago
...rotation for sufficiently non-spherical(-cow) objects in free fall is kinda weird.