If a planet was located approximately 27 thousand light-years from the center of a galaxy and orbits that center once every 232 million years, how fast is the planet traveling around

Question

If a planet was located approximately 27 thousand light-years from the center of a galaxy and orbits that center once every 232 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.

Answer 1

If you need to know the speed of the planet in km/hr, then you need the distance of the orbit in km and the time it takes to travel that distance in hrs. First, it is given that the speed of light is about 3.0x10^8 m/s, which means that a light year would be 3.0x10^8 m times 60 times 60 times 24 times 365, which is equal to about 9.46x10^15 m. The planet is 27,000 light years from the galaxy’s center. Assuming a circular orbit, we need the circumference of the circle. That will give the distance we need. Circumference equals pi (about 3.14) times 2 radii (also known as the diameter of the circle). 27,000 times 9.46x10^15 m times 2 times 3.14 equals about 1.60x10^21 m. Divide by 1,000 to get 1.60x10^18 km.

We know its orbital period is 232 million years. 232 million times 365 times 60 will convert years into hours, which gives us about 2.03x10^12 hrs.

1.60x10^18 km divided by 2.03x10^12 hrs. equal about 7.89264x10^5 km/hr.



Thus, the speed of the planet is about 789,254 km/hr relative to the galactic center. I hope that this helped you. Thank you.