# Calculate how long it takes for the sun to complete one orbit around the galaxy?

We know the speed that the sun travels around the galaxy is $$220\, {\rm km/s} = 0.00021 \, {\rm parsec/year}$$. I'm unsure of how to find the period?

• Find the distance of the Sun from the Galactic Center and then, assuming a circular orbit, find the circumference... Commented Mar 5, 2020 at 2:17
• or the value is easily found by searching for google.com/… Commented Mar 5, 2020 at 7:14

Now if you know the speed of the Sun in the Galaxy and you know how far the Sun is from the center, you can estimate this period. Let's assume a circular orbit and ignore the (large) error bars, for the sake of simplicity. The Sun is roughly $$8\,200$$ parsecs away from the Galactic center. So the circumference of the Sun's orbit is $$8\,200 \cdot 2 \cdot \pi = 52\,000 {\rm \,parsecs}$$. You mention the speed of the Sun is $$2.1\cdot 10^{-4} {\rm \,parsec/year}$$. So to complete one orbit, it takes circumference/speed = $$52\,000 / 2.1\cdot 10^{-4} = 245 \cdot 10^6 {\rm years}$$, that is 245 million years. Pretty close to the actual value!