exupero's blog

Spirals from ellipses

In the previous post I showed a teardrop shape made from elliptical orbits, which reminded me of another kind of shape you can make from ellipses. I seem to recall that someone had a pseudo-scientific theory that the spirals seen in galaxies are the product of ellipses. They didn't elaborate, so I've occasionally tinkered with how ellipses can create spirals.

If we draw a set of ellipses that share a focus and whose major axes are aligned, there are no spirals:

If we rotate each ellipse based on the size of its major axis, we can create something like a spiral that gets wider the further it gets from the central focus:

As far as I know, spiral galaxies tend to be more symmetric, and I've often seen pictures with two dominant spirals. We can create something similar by placing the ellipses on a common center, rather a common focus:

That looks reasonably galaxy-like to me, though I don't know any astrophysical processes it could be modeling.

It turns out to be quite easy to produce spirals by rotating ellipses. The above spirals are made by rotating ellipses as a log of the major axis's size. Here's a double spiral made by rotating linearly with the major axis:

Maybe that resembles galactic spirals more than a double logarithmic spiral?

We can rotate ellipses with other formulas to generate different styles of double spirals, though these look increasingly geometric rather than galaxy-like:

If you've heard any interesting theories about the spirals in galaxies, feel free to email me.