How do you know how far away something is when you cannot travel to it? For instance, how do we know how far away stars are from the Earth? One way to find out is by using the principle of parallax.
When we look up into the sky at night and we see the moon, it seems as if we stretch enough we might just be able to touch it. But we know this is just an illusion; the moon is in orbit around the Earth, and it takes days to get there even by rocket. A long time ago, people didn't know this, so how did they figure out that it was so far away?
The answer is parallax. When you look at an object with both eyes, you get a sense of how far away it is. This is partially based on cues in your environment - things further away tend to look smaller - but also through parallax. Choose a stationary object near you. Look at it with both eyes. Now look at it with just one eye open, then just the other. The object you chose appears to move in relation to the objects behind it but nothing is actually moving. This difference in perspective is constantly telling your brain how far away objects are. The more different the images are, the closer the object is.
To measure the distance to the moon, two observations can be taken from two different locations, viewing the distance from the moon to a relatively fixed position in the sky, like a constellation. The position of the constellation will also change, but this change is so small as to make the position of the constellation fixed in comparison to the moon. Knowing the distance between observation points, the difference in distance between the two observed positions of the moon and the constellation, and incorporating a little right angle trigonometry, it is possible to extrapolate the distance from the Earth to the moon.
To determine the distance from the Earth to the stars, a similar method is used, but instead of using two locations on the Earth, we can use the Earth itself as two different locations. This is possible because the Earth travels a great distance around the Sun every year. We know the distance to the Sun using parallax, so we then know approximately the diameter of the Earth's orbit around the Sun. By taking observations spaced half a year apart, we can measure the parallax of nearby stars against stars that are further away. This method works for stars less than 1600 light years away. Beyond that the measurements become too small to make accurate calculations. Other methods have been developed to measure distances greater than that, but they are all calibrated using parallax on nearby stars.
