Around the Sun, there are about 0.004 stars per cubic light year. Near the center of the galaxy this will be higher, and at the edges it will be lower. To be conservative and try to hit something, let's just say the galactic average is 1000x what it is near the sun: 4 stars / cubic light year. (NOTE that this is pretty absurd.)
The vast majority of stars are smaller than the Sun, but a tiny percentage are way, way bigger. Calling them all Solar-radius might be a decent estimate. But let's go crazy and say an average star has 100x the Sun's radius. (Again, this is absurd, but we're trying to hit something.)
We can ignore planets, black holes, neutron stars, etc. because their cross-sectional areas are just minor corrections to the stars. E.g. the cross-sectional area of all planets in the solar system would just be adding 3 percent to the Sun.
Here’s a question: If you could fly a spacecraft from one end of the galaxy all the way to the other, in a straight line, what are the chances you’d make it through without hitting anything?
That’s the scenario Reddit user bigri23 put forth on the “Ask Science” subreddit. The answer might surprise you: It’s pretty close to 100 percent. In other words, your likelihood of hitting something is zero.
Fellow Redditor astrocubs has the top answer, which explains why the chances of running into something on a flight through the universe are actually very, very small. (This is assuming that “something” is bigger than a pebble, which rules out gas and dust, and only considers something planet-sized or bigger). Here’s how astrocubs got there:
With all that in mind, and all those assumptions—even the ones that exaggerate our chances of hitting something—in place, astrocubs estimates that our theoretical spaceship would have to fly from one end of the galaxy to the other 15,000 times before ever running into anything.
Or, as astrocubs puts it, "you have a 0 percent chance (within rounding errors)" of encountering another object during that trip.
I asked Matthew Francis, a physicist and science writer, whether the answer astrocubs provided was reasonable. Without crunching the numbers himself, he said that it was likely right. “If you don't count tiny stuff like gas particles, the galaxy is a pretty empty place!” he told me in an email. “In fact, when two galaxies collide, the chances of individual stars running into each other are slim, even though the galaxies themselves get all stretched out of shape. If you got in a spaceship and went from one side of the galaxy to the other (assuming you didn't aim right at the black hole at the center), you'd probably miss everything.”
The calculations here are firmly in the world of theory, and don't take into account the actual positions of planets or stars, or the existence of the space junk that we humans are constantly leaving behind. But even though the amount of trash we've deposited is dangerous and ugly, it's tiny compared the size of the universe.
Yet another reminder that space, for all its wonders and marvels, is a very empty place.