How many times has the Milky Way rotated?

Question

I would think that is a highly naive question, but I still ask it.

Given current experimentally discovered numbers:

• the Milky Way galaxy is ~13-14 billion years old
• At the galactic radius where our sun is, the rotational period is about 240 million years.

So, with nothing changing at all (the galaxy and stars pop fully formed into existence, the rotation period doesn't change), the galaxy has rotated roughly

~14/(1/4) = 50 to 60 times.

Since the assumptions are naive, what is a better approximation for the number of times? How long has the mass that is recognizable now as the Milky Way been rotating (and what has been the speed by radius over time)? Is it a lot more than 50 times and if so, has it been slowing down as a whole or just at the Sun's position, or a less because the coalescence into stars rotating took a few billion years to translate into the faster rotation which it is now mostly set at? Or some other reason which is more articulate?

Note: This question is similar to but distinct from The equation for how many times the Earth has revolved around the galaxy, as the title asks similarly what I'm asking but the content just asks for how to calculate rotational speed.

Answer 1

The question doesn't have a single answer, because the Milky Way's rotation is differential rather than solid-body. This means that stars in the inner part complete their rotation about the center in a shorter period of time than stars at a larger radius. Stars orbiting with a radius of 1 kpc (about 3,000 light years) will take about 30 million years to go once around; stars like the Sun, with orbital radii of about 8 kpc, will take about 220 million years; stars orbiting with a radius of 20 kpc will take about 500 million years.

If you mean "how many times has the narrow region of the Milky Way currently containing the Sun's orbit rotated" -- ELNJ's answer is probably reasonable, given that the last major merger contributing to the Milky Way's growth was probably about 10 billion years ago, so changes in the amount of mass inside the Solar radius (which would change the orbital timescales) were probably fairly small after that.

Answer 2

In general, Milky Way stars that are 13-14 billion old are part of the Galactic halo, and roughly spherical distribution of stars that contains the globular clusters. This part of the Galaxy formed first, and the flattened Galactic disk is more like 10 billion years old.

At that point, the disk had formed, and large-scale movements of mass were probably less likely than they were at earlier epochs, so it's likely a reasonable assumption to say that the mass interior to our current position in the Galaxy (which is what sets the orbital speed) hasn't changed a lot since then.

So probably using the same speed, but an age more like 10 billion years, would be more realistic - that yields 10/0.24 = 42.

So the answer to this question, as to some others, is 42. :-)