how fast is the planet traveling

Question

If a planet was located approximately 28 thousand light-years from the center of a galaxy and orbits that center once every 240 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

The period is 240 million years. There are 60 x 60 x 24 x 365.25 sec in a year = 31557600 seconds. So the period of the orbit is 7.5738 x 10¹⁵ sec or 2.1038 x 10¹² hours. A light year is (31557600 sec)(3 x 10⁸ m/sec) = 9.4673 x 10¹⁵ m. Because there are 1000 m in one km, a light year is 9.4673 x 10¹² km. Therefore the radius of the planet's orbit is (28000 ly)(9.4673 x 10¹² km/ly) = 2.6508 x 10¹⁷ km. Circumference = 2πr so the circumference of the orbit is 2π(2.6508 x 10¹⁷ km) = 1.6655 x 10¹⁸ km. Since the planet travels this circumference in the period, its average speed is

(1.6655 x 10¹⁸ km) / (2.1038 x 10¹² hours) = 7.917 x 10⁵ km/hr