Expert: Philip Stahl - 7/9/2009

Question
QUESTION: I would like to know how many years it takes for other galaxies, large and small, to make one rotation (besides our own, which I know is about 220 million years).
Thank you so much

ANSWER: Hello,

First, there are many other types of galaxies, including elliptic, colliding, spiral etc. so one method that can be applied, say to spirals, may not work for ellipticals. In this sense, Kepler's 3rd law is often useful to obtain a rough estimate of the revolution period of some nearby galaxies (spiral) if a reference point can be measured to the galaxy's center and an estimate of the central mass can be made.

Recall, according to Kepler's 3rd law;

a^3 ~  P^2

the semi-major axis cubed is proportional to the period squared.

For example, we know 1 parsec = 2 x 10^5 AU and let's say a reference point in a member of the Local Group of Galaxies (which includes Andromeda and the Milky Way) is found to be 10^5 pc from the center.

Then a = 10^5 pc (2 x 10^5 AU /pc) = 2 x 10^10 AU

Assume the central mass of the galaxy to be measured is M= 10^11 solar masses

Then one can work out P.

Since most other galaxies are far beyond the Local Group you can see this method will not work for most, and not plausibly for those like ellipticals.

Thus, it is safe to say we know nothing of the revolution periods of most of the galaxies in the universe.



---------- FOLLOW-UP ----------

QUESTION: Great answer. Thank you.
Do we know the revolution periods for galaxies in the local group?

Answer
Hello,

I consulted the text 'The Galaxies of the Local Group' (Cambridge University Press, 2000) by Sidney van den Bergh, and while each chapter on each member featured a table with a wealth of data - none of it referred directly to rotation rate or specified a period of revolution.

However, this is enough data to work out (again, using Kepler's 3rd law) what the revolution period would be.

For example, Table 3.4 (p. 44) gives the estimate of the Andromeda galaxy's diameter as 760 kpc.

Making appropriate conversion to AU (as I showed in the prior reply) and using Kepler's 3rd law, one would find that the estimate of the period works out to about 675 million years. This would be making a number of assumptions, including that the radius (r = 380 kpc) can be equated to the "semi-major" axis, e.g. for a reference point on the extreme rim.


Of course, as Andromeda and the Milky Way are the only two member spirals (cf. Table 2.1, p. 5) and it is not at all clear that the same Keplerian method can be applied to irregulars, spherical galaxies, or dwarfs (like the Fornax) galaxy, it is actually immaterial whether the others' revolutions are given or not.

Clearly, the revolution period of galaxies is a quantity not well defined or easily computed.

Perhaps there is scope here to provide a fertile field for research for someone interested?

One last point, the comparative rotation velocities for the Milky Way and Andromeda *are* given (Table 4.3):

Andromeda:   V(r) =  260 km/s

Milky Way: V(r) = 220 km/s

Obviously, however, these cannot be used to infer the period of the Andromeda galaxy (e.g. from the Milky Way's).

Say, simply taking the ratio (260/220) and multiplying it by 225 million years (Milky Way period of revolution) to get 266 million years.