Galileo taught us an important fact about nature, that two objects dropped from the same height will hit the ground at the same time in the absence of air friction. This property of gravity holds on Earth, on the Moon (as we saw in the last post), and just about anywhere else within reason.
How does gravity work on the enormous Milky Way galaxy? To find out, let's go back to what we know about gravity in our solar system.
One of the best ways to measure the mass of an object in space is by looking at how it accelerates neighboring objects. When we ask what is the mass of the Sun by the gravitational pull it has on Earth, we get an answer of about 1 million Earths.
When we now go and ask what is the mass of the Sun as seen by its gravitational pull a different planet like, say, Jupiter, we get the same answer. Ok, you say, this is not so surprising as we'd better get the same answer for what is the mass of the Sun each time we measure it, just as we get the same answer for our weight each time we measure it (and assuming lunch did not come in between).
We can move on to measure the masses of other stars by looking at how other their stars accelerate the planets that orbit them. If we take this concept further, we can even apply this technique to measure the mass of our entire, huge and very heavy Milky Way galaxy! Let us see what happens when we do that.
When we take a look at how the Milky Way accelerates the Sun, we get a certain (very large) answer. When we now take a look at how the Milky Way pulls gravitationally on another star which is at a different distance (farther away or closer) than the Sun, then surprisingly we get a very different answer.
In fact, stars orbit the Milky Way in a way that is completely different from how planets orbit their star. This was a shocking discovery, which over time we have come to interpret by saying that there must be some kind of unseen matter pulling on the stars which is not present in the solar system. We now call that matter 'Dark Matter,' and it was Galileo who first set us on the right track for its discovery.