We mentioned earlier that astronomers have estimated the number of stars in the Milky Way from measurements of the galaxy's mass. But how do you measure the mass of a galaxy? You obviously can't put it on a scale. Instead, you use its orbital motion. From Newton's version of Kepler's Third Law of Planetary Motion, the orbital speed of an object in circular orbit, and a little algebra, you can derive an equation to calculate the amount of mass (Mr) that lies within any circular orbit with a radius (r).
- Orbital speed of a circular object (v) v=2Πa/p
- Because it's a circular orbit, a becomes radius (r) and M becomes the mass within that radius (Mr). Mr rv2/G
For the Milky Way, the sun lies at a distance of 2.6 x 1020 meters (28,000 light years) and has an orbital speed of 2.2 x 105 meters/second (220 km/s), we get that 2 x 1049 kg lies within the sun’s orbit. Since the sun’s mass is 2 x 1030, then there must be 1011, or about 100 billion, solar masses (sunlike stars) within its orbit. When we add the portion of the Milky Way that lies outside the sun’s orbit, we get approximately 200 billion stars.
To learn more about the Milky Way, look at the links on the next page.