YOU'VE asked this question. I've asked this question. Most people have asked this question.
The answer depends on what you're talking about. How many stars we can see in the sky is a surprising amount compared to how many there are in the galaxy or the universe.
It might even be more worthwhile asking how many stars there are in a certain patch of sky or how many there are close enough for us to realistically fly to one day.
How many stars can I see in the sky?
Not many. If you live in a city, town, or suburb, you'll be lucky to see the stars at all.
Even if you were to go to a remote area with perfect conditions on a dark night with no moon, you'd only be looking at around 4,500 stars. Fewer if you have less-than-perfect eyesight.
Even the 'canonical' survey of visible stars in the sky, the Yale Bright Star Catalogue by Dorrit Hoffleit, found only 9,096 stars bright enough for humans to see with the naked eye.
So there's a number you can quote to be profoundly annoying when someone makes a romantic comparison to 'all the stars in the sky'.
How many stars are close enough to travel to in a human lifetime?
Take the closest confirmed star to our own Sun, Proxima Centauri. It's 4.2 light-years away and right next-door to the next to closest stars, Alpha and Beta Centauri at 4.3 light-years.
Ian O'Neill from Universe Today did some calculations to see how long it would take us to send a human to Proxima with current technology.
The most realistic answer is roughly 81,000 years using an ion propulsion drive. 19,000 if we're lucky and the planets line up to slingshot us there. Even if we rode the blast from nuclear bombs the entire way, it would probably take 85 years to get there.
Even then, we wouldn't go because Proxima Centauri is a red dwarf with very little reason for us to go there.
How many stars are there in our local cluster?
While the sun began its life inside an open cluster, we're not sure which one and we've long since left it.
Are there stars close to us? Yes, but there's no gravitational relationship enclosing us together as a neighbourhood.
How many stars are there in the Milky Way galaxy?
To know how many stars there are in the Milky Way, we can't just point our fingers and start counting.
Statistical modeling and painfully accurate observations of our home galaxy have given us a number around 100 billion stars, enough that even if we can't see them individually, we can still see a bright, milky band of light across our sky at night.
How many stars are there in the universe?
Again, we can't just count how many there are. We don't have the telescopes or the time.
What we can do, however, is count them the same way we'd count how many jelly beans there are in a jar or molecules in a container - find out how many there are in an average patch of space and multiply it.
Obviously it's not as simple as that but the concept is there.
Astronomers have also used the known rate of star formation to obtain a figure for the number of stars and this has proven extremely helpful. This was mostly made possible by using the Herschel Space Observatory to look back to different parts of the universe's history.
The Hubble Deep Field Survey also gave us fantastic insight to the density of stars in any given patch of sky.
Combining these kinds of measurements gives us a number approaching one septillion stars. That's a 1 with twenty-four zeros after it.
1,000,000,000,000,000,000,000,000 stars (or thereabouts).
There's honestly no decent way to compare that to anything we can imagine easily. Wolfram Alpha compares it to the number of grains of sand on earth. As of 2013 the World Wide Web was estimated to store 4 Zettabytes of data (1 with 21 zeroes after it and nowhere near the number of stars).
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