<p>I'm not 100% sure what equation you would like, but I'll try at an answer to see how it goes.</p>

<p>The <em>observed speed</em> of the Sun orbiting around the center of the Milky way is about 220 km/sec. The distance to the center is about 8.1 kiloparsec, which is 2.5E+17 kilometers.</p>

<p>The time it takes to travel around a circle is the circumference divided by the speed, </p>

<p><span class="math-container">$$\frac{2 \pi R}{v} \approx \frac{6.28 \times 2.5\times 10^{17}}{220} \approx 7.17 \times 10^{15} \text{seconds} \approx 227 \text{ million years}$$</span></p>

<p>The speed is a measured quantity. There isn't a simple way to calculate the speed with an equation, because the mass distribution in the galaxy is complicated and dominated by dark matter, whose presence we can only infer from the orbital motion of our own star as well as a large number of other stars in our galaxy.</p>

<hr>

<p><a href="https://i.sstatic.net/R1MKr.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/R1MKr.jpg" alt="enter image description here"></a> <a href="https://en.wikipedia.org/wiki/File:Rotation_curve_(Milky_Way).JPG" rel="nofollow noreferrer">Source</a></p>

<p>From Wikipedia's <a href="https://en.wikipedia.org/wiki/Milky_Way" rel="nofollow noreferrer">Milky Way</a>:</p>

<blockquote>
  <p>Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the Galactic Center. Horizontal axis is distance from the Galactic Center in kpcs. The Sun is marked with a yellow ball. The observed curve of speed of rotation is blue. The predicted curve based upon stellar mass and gas in the Milky Way is red. Scatter in observations roughly indicated by gray bars. The difference is due to dark matter</p>
</blockquote>

CC BY-SA 4.0
2019-04-10T04:28:11.537Z
2019-04-10T04:28:11.537Z
uhoh
<p>I have seen it said on <a href="https://www.quora.com/How-many-times-has-the-Earth-gone-around-the-Milky-Way-Galaxy" rel="nofollow noreferrer">Quora</a> and <a href="https://www.reddit.com/r/askscience/comments/2xt7rd/how_many_rotations_has_our_solar_system_made/" rel="nofollow noreferrer">Reddit</a> that it's about every 220-250 million years to go around the Milky Way from Earth. Wondering what the rough equation is for calculating it. That is, I guess, the angular momentum and distance from the center, so I could visualize it on a sped up animation and otherwise derive something like those numbers 220 to 250.</p>

<earth><milky-way><rotation>
The equation for calculating how many times Earth (or our solar system) has revolved around the Milky Way
Lance Pollard
# The equation for calculating how many times Earth (or our solar system) has revolved around the Milky Way

(Asked by: username_0 on 2019-04-10)

I have seen it said on [Quora](https://www.quora.com/How-many-times-has-the-Earth-gone-around-the-Milky-Way-Galaxy) and [Reddit](https://www.reddit.com/r/askscience/comments/2xt7rd/how_many_rotations_has_our_solar_system_made/) that it's about every 220-250 million years to go around the Milky Way from Earth. Wondering what the rough equation is for calculating it. That is, I guess, the angular momentum and distance from the center, so I could visualize it on a sped up animation and otherwise derive something like those numbers 220 to 250.

**Tags:** earth, milky-way, rotation

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## 1 answers

### Answer by username_1 on 2019-04-10. Score: 3

I'm not 100% sure what equation you would like, but I'll try at an answer to see how it goes.

The *observed speed* of the Sun orbiting around the center of the Milky way is about 220 km/sec. The distance to the center is about 8.1 kiloparsec, which is 2.5E+17 kilometers.

The time it takes to travel around a circle is the circumference divided by the speed,

$$\frac{2 \pi R}{v} \approx \frac{6.28 \times 2.5\times 10^{17}}{220} \approx 7.17 \times 10^{15} \text{seconds} \approx 227 \text{ million years}$$

The speed is a measured quantity. There isn't a simple way to calculate the speed with an equation, because the mass distribution in the galaxy is complicated and dominated by dark matter, whose presence we can only infer from the orbital motion of our own star as well as a large number of other stars in our galaxy.

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[![enter image description here](https://i.sstatic.net/R1MKr.jpg)](https://i.sstatic.net/R1MKr.jpg) [Source](https://en.wikipedia.org/wiki/File:Rotation_curve_(Milky_Way).JPG)

From Wikipedia's [Milky Way](https://en.wikipedia.org/wiki/Milky_Way):

> Galaxy rotation curve for the Milky Way. Vertical axis is speed of rotation about the Galactic Center. Horizontal axis is distance from the Galactic Center in kpcs. The Sun is marked with a yellow ball. The observed curve of speed of rotation is blue. The predicted curve based upon stellar mass and gas in the Milky Way is red. Scatter in observations roughly indicated by gray bars. The difference is due to dark matter


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