If a planet was located approximately 31 thousand light-years from the center of a galaxy and orbits that center once every 286 million years, how fast is the planet traveling around the galaxy in km/hr? If needed, use 3.0 × 108 m/s for the speed of light.
+128474 radius of circle = 31000 light years
Number of m in one light year = 3 * 10^8 / s * (3600 * 24 * 365)s = 9.4608 * 10^15 m
Converting this to km (divide by 10^3) = 9.4608 * 10^12 km in one light year
So .....radius of this circle = 31,000 * 9.4608 * 10^12 km = 2.932848 * 10^17 km
Total distance traveled by planet in one orbit = 2pi * r = 2 pi * 293.2848 * 10^17km
Convert 286,000,000 years to hrs = 286,000,000 * 24 * 365 = 2.50536 * 10^12 hrs
So....the speed is
D / T = [ 2pi * 293.2848*10^17] km / [ 2.50536 * 10^12 ]hr ≈ 7.36 * 10^7 km/hr
