Question

The Milky Way has a diameter of about 150,000 light years. Our solar system is located 27,000
light years from the center of the Milky Way and orbits the center with a speed of 220 km/s.
(a) How long does it take for the solar system to circle the center of the Milky Way?
(b) The earth has formed about 4.5 billion years ago. How oen has the earth circled the center?

Answer 1

Distance from center of the Milky Way to solar system:

$$27,000 \, \text{light years} = 2.55 \cdot 10^{17} \,\text{km}$$

1) Time for one turn around the center of the Milky Way:

$$t= \frac{2\pi \cdot 2.55 \cdot 10^{17} \,\text{km}}{220 \, \text{km/s}} = 7.29 \cdot 10^{15} \,\text{s} = 231\, \text{million years}$$

2)

Therefore, Earth circled

$$\frac{4.5 \,\text{billion years}}{231 \,\text{million years}} = 19.5$$

times.