For many years astronomers thought this assumption was reasonable.

This is a good estimate for the total mass of the Galaxy only if hardly any mass lies outside the Sun’s orbit. Our estimate tells us how much mass is contained in the volume inside the Sun’s orbit. More sophisticated calculations based on more sophisticated models give a similar result. Thus, for all practical purposes, the result (about 100 billion times the mass of the Sun) is the mass of the Milky Way. However, the mass of the Sun is completely trivial compared to the mass of the Galaxy.

Plugging numbers into Kepler’s formula, we can calculate the sum of the masses of the Galaxy and the Sun. This is the sort of situation to which Kepler’s third law (as modified by Newton) can be directly applied. For our calculation, then, we can assume that all the mass that lies inward of the Sun’s position is concentrated at the center of the Galaxy, and that the Sun orbits that point from a distance of about 26,000 light-years. Long ago, Newton showed that if you have matter distributed in the shape of a sphere, then it is simple to calculate the pull of gravity on some object just outside that sphere: you can assume that gravity acts as if all the matter were concentrated at a point in the center of the sphere. Let’s assume that the Sun’s orbit is circular and that the Galaxy is roughly spherical, (we know the Galaxy is shaped more like a disk, but to simplify the calculation we will make this assumption, which illustrates the basic approach). We can use the information about the Sun’s orbit to estimate the mass of the Galaxy (just as we could “weigh” the Sun by monitoring the orbit of a planet around it-see Orbits and Gravity). This means that we have gone only a tiny fraction of the way around the Galaxy in all the time that humans have gazed into the sky. It is a long time compared to human time scales during the entire lifetime of Earth, only about 20 galactic years have passed. We call the period of the Sun’s revolution the galactic year. The speed of the Sun in its orbit is about 200 kilometers per second, which means it takes us approximately 225 million years to go once around the center of the Galaxy. Our star’s orbit is nearly circular and lies in the Galaxy’s disk. The Sun, like all the other stars in the Galaxy, orbits the center of the Milky Way. Let’s see how this surprising discovery was made.

When we described the sections of the Milky Way, we said that the stars are now known to be surrounded by a much larger halo of invisible matter.

Interpret the observed rotation curve of our Galaxy to suggest the presence of dark matter whose distribution extends well beyond the Sun’s orbit.

Describe historical attempts to determine the mass of the Galaxy.

By the end of this section, you will be able to:

Calculating the stars