The Sun orbits the Milky Way galaxy once each 2.60 * 10^8 years, with a roughly circular orbit averaging 3 * 10^4 light years in radius. Calculate the average speed of the sun in m/s.

Whew! Should I convert the 3*10^4 light years to meters, and then divide that by 2.60*10^8 years converted to seconds? I tried to do that and was wrong.

circumference in light years

= 2 pi *3 * 10^4
I think you left the 2 pi out. You need circumference not radius.

Yes, that is it


Did you do the 2PIxr for distance?

https://www.google.com/search?q=+converting+light+years+to+distance&ie=utf-8&oe=utf-8&client=firefox-b-1

Thank you! That was it!

Your approach is correct, but let's make sure we convert the values properly.

To calculate the average speed of the Sun, we need to divide the distance traveled by the time taken. In this case, the distance traveled is the circumference of the Sun's orbit, and the time taken is the period of its orbit.

First, let's convert the radius of the Sun's orbit from light years to meters. Since 1 light year is approximately equal to 9.46 * 10^15 meters, we can calculate:

Radius in meters = 3 * 10^4 light years * (9.46 * 10^15 meters / 1 light year)

This gives us the radius of the Sun's orbit in meters. Now, let's convert the orbital period from years to seconds. Since 1 year has 365.25 days on average, 1 day has 24 hours, and 1 hour has 60 minutes, and 1 minute has 60 seconds, we can calculate:

Orbital period in seconds = 2.60 * 10^8 years * 365.25 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute

Now that we have the radius and orbital period both in meters and seconds, we can calculate the average speed of the Sun:

Average speed = Circumference of orbit / Orbital period

Circumference of orbit = 2 * π * Radius

Average speed = (2 * π * Radius) / Orbital period

Now we can substitute the values into the formula to find the average speed of the Sun.