# The Sun-Centered Galaxy

In Milky Way by Brian Koberlein1 Comment

The stars in the Milky Way have generally circular orbits, and move through the galaxy at a speed of about 200 km/s. This is also true for our Sun. But how do we know this, given that our Sun is in the disk of the Milky Way, and we can only see our galaxy from our Sun’s vantage point? It all has to do with relative motion.

Measuring the motion of a star. Credit: Wikipedia

For stars near the Sun, we can determine their motion through the galaxy by measuring two types of motion relative to the Sun. Proper motion, which is the apparent drift of the star relative to more distant stars, and radial motion, which we measure by looking at the Doppler shift of a star’s spectral lines. This gives us the motion of a star through space, but only relative to the Sun. The Sun itself is moving through the galaxy, and we can only measure the Sun’s speed relative to other stars.

So how do we know the Sun and other stars are orbiting the center of our galaxy? One way is to look at the statistics of stars moving around us. If the stars were stationary, or if the stars in our galaxy rotated as a solid disk, then generally the stars in our galaxy would stay together. An individual star could have some velocity relative to the Sun, but on average all the stars around us would have no net velocity. Statistically the velocities of nearby stars should add up to zero.

On the other hand, if the stars orbit galactic center, we would expect stars closer to the galactic center to speed past the Sun, since they trace a smaller orbit than the Sun. Stars farther away from galactic center would be left behind by the Sun, since they would have a larger orbit. You can imagine this as a group of runners on a circular track. If they had to stay in their own lane, the runners on the inside track would finish the race before those on the outer track, because they would have a shorter distance to run. This is why on actual races the starting positions are staggered to make the distances equal.

The relative motion of stars in our galaxy.

For the galaxy this means that stars in the direction of galactic center have (on average) a speed relative to the Sun in the direction of galactic rotation. Stars in the opposite direction have a net speed opposite to galactic rotation. This is exactly what we observe. Not only that, by comparing the relative speeds of stars with their distance from the Sun, we can determine how stellar speed varies with distance. This is one of the ways we know that stars in our galaxy have roughly the same speed, regardless of their distance from galactic center.

Of course this only works for stars where we know their distance from the Sun, and that’s only for stars out to about 500 parsecs, or 1600 light years. The whole galaxy has a diameter of about 100,000 light years, so stellar motion covers only a small portion of the galaxy. To look at the motion of more distant parts of the galaxy we have to use another set of observations.

But that’s a story for another day.