<p>Gravitationally bound dynamical systems evolve towards their equilibrium states on a dynamical timescale of $\sim (G \rho)^{-1/2}$, where $\rho$ is their average density.</p>

<p>If we assume the Galaxy started of with $10^{12}$ solar masses in a sphere of radius $10^5$ pc, then the dynamical timescale is 1 billion years.</p>

<p>If we consider an object at the "edge" of such a system, Newtonian gravity and a bit of rotational mechanics, we find that the fastest possible bound orbital period is also of order $(G\rho)^{-1/2}$. The Sun is not at the edge and the average density inside the solar orbit is much higher and so the orbital period can be a bit shorter than this (a factor of four).</p>

<p>Thus what we see is exactly what is expected for a $&gt;10$ billion years old universe - a relatively settled dynamical system.</p>

<p>You could extend this argument to the timescale for major galaxy mergers. The distance between galaxies is of order ten times their size and thus the mean density of galaxy systems is 1000 times lower than for an individual galaxy. This <em>increases</em> the relevant dynamical timescale to $1 \times 1000^{1/2} \sim 30$ billion years. That the Milky Way and Andromeda will collide some 17-18 billion years post big-bang is also therefore not an unexpected event.</p>

CC BY-SA 3.0
2017-10-22T23:05:38.113Z
Would this mean that in about another 20 billion years we would expect the universe to be a collection of "boring" elliptical galaxies? If so, we are so lucky to be living at this time in the history of the universe.
Jack R. Woods
CC BY-SA 3.0
2017-10-09T06:41:41.353Z
2017-10-09T16:41:48.627Z
2017-10-09T16:41:48.627Z
ProfRob
<p>If the universe is only 40 to 50 galactic revolutions old, how has it acquired its present state so "quickly" relative to this time scale?</p>

<galaxy><cosmology>
Galactic revolutions relative to the age of the universe
martino
# Galactic revolutions relative to the age of the universe

(Asked by: username_0 on 2017-10-09)

If the universe is only 40 to 50 galactic revolutions old, how has it acquired its present state so "quickly" relative to this time scale?

**Tags:** galaxy, cosmology


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## 1 answers

### Answer by username_1 on 2017-10-09. Score: 5

Gravitationally bound dynamical systems evolve towards their equilibrium states on a dynamical timescale of $\sim (G \rho)^{-1/2}$, where $\rho$ is their average density.

If we assume the Galaxy started of with $10^{12}$ solar masses in a sphere of radius $10^5$ pc, then the dynamical timescale is 1 billion years.

If we consider an object at the "edge" of such a system, Newtonian gravity and a bit of rotational mechanics, we find that the fastest possible bound orbital period is also of order $(G\rho)^{-1/2}$. The Sun is not at the edge and the average density inside the solar orbit is much higher and so the orbital period can be a bit shorter than this (a factor of four).

Thus what we see is exactly what is expected for a $>10$ billion years old universe - a relatively settled dynamical system.

You could extend this argument to the timescale for major galaxy mergers. The distance between galaxies is of order ten times their size and thus the mean density of galaxy systems is 1000 times lower than for an individual galaxy. This *increases* the relevant dynamical timescale to $1 \times 1000^{1/2} \sim 30$ billion years. That the Milky Way and Andromeda will collide some 17-18 billion years post big-bang is also therefore not an unexpected event.

> **Comments:**
> **username_2**: Would this mean that in about another 20 billion years we would expect the universe to be a collection of "boring" elliptical galaxies? If so, we are so lucky to be living at this time in the history of the universe.  

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