Question

Can anyone give me the mathematic formula for a spiral galaxy?

Answer 1

Special shapes such
as ring galaxies with inward and outward arms are also described by the analytic
continuation of the same formula. The formula is r A ( )φ = / log[B tan(φ / 2N)] . This
function intrinsically generates a bar in a continuous, fixed relationship relative to an arm
of arbitrary winding sweep. A is simply a scale parameter while B, together with N,
determine the spiral pitch. Roughly, greater N results in tighter winding. Greater B results
in greater arm sweep and smaller bar/bulge while smaller B fits larger bar/bulge with a
sharper bar/arm junction. Thus B controls the “bar/bulge-to-arm” size, while N controls
the tightness much like the Hubble scheme. The formula can be recast in a form
dependent only on a unique point of turnover angle of pitch – essentially a 1-parameter
fit, aside from a scale factor. The recast formula is remarkable and unique in that a single
parameter can define a spiral shape with either constant or variable pitch capable of
tightly fitting Hubble types from grand design spirals to late type large-barred galaxies.
We compare the correlation of our pitch parameter to Hubble type with that of the
traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our
formula produces a very tight correlation with ideal Hubble type suggesting it is a good
discriminator compared to logarithmic pitch, which shows poor correlation here similar
to previous works

Answer 2

Here's the source of the above abstract if you want to see the whole paper...

A New Formula Describing the Scaffold Structure of Spiral Galaxies
Authors: Ringermacher, Harry I.; Mead, Lawrence R.
Source: Monthly Notices of the Royal Astronomical Society, Volume 397, Number 1, July 2009 , pp. 164-171(8)

Answer 3

Someone gave me a formula for spiral galaxy once. I tried to create one but it didn't work out. I couldn't compress enough matter. I couldn't make it dense enough to make a moon much less a galaxy. Next time in going to ask for the formula for to root beer.