If a planet was located approximately 24 thousand light-years from the center of a galaxy and orbits that center once every 256 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.
1 - First let us figure out the circumference of the galaxy from the center to the orbit of the planet. The planet is at a distance of 24,000 light years from the center of the galaxy.
2 - Then the diameter of the orbit of the planet is: 24,000 x 2 =48,000 light years.
3 - Circumference of the orbit =48,000 x 3.141592=150,796.416 light years.
4 - 1 light year =3 x 10^5 km/sec x 3,600 seconds x 24 hours x 365 days =9,460,800,000,000 km/year.
5 - 150,796.416 light years x 9,460,800,000,000 km/year =1.427 x 10^18 km -circumference of the orbit.
6 - Will convert the orbital period of the planet from 256,000,000 years to hours x 365 days x 24 hours =2,242,560,000,000 hours - orbital period of the planet in hours.
7 - Will divide the km of the circumference in 5 above by the number of hours in one orbital period, from 6 above.
8 - 1.427 x 10^18 km / 2,242,560,000,000 =636,172.38 km/hour - the orbital speed of the planet