## How we Measure the Distance to Stars

Someone asked me last week how we know how far away the stars are if we can’t travel to them. Whenever someone asks me an astronomy/physics related question I try to give a clear concise answer to the best of my knowledge. Afterwards, I always think of better ways I could have explained the answer. Now I’ll take the liberty of using my blog as a medium for explaining this concept. First look at the following diagram.

There are actually a few different ways to measure the distance to stars but the first method scientists used is called stellar parallax. This method only works for close stars (relatively speaking) and uses a phenomenon with which we can experiment with our own eyes. Hold your finger at arms length and look at it with one eye open. Note what lies behind it in the background. Now switch eyes and see how your finger has “moved” with respect to the background. That is called parallax. Do it with the stars and it’s called *stellar* parallax. If you can measure the angular distance that your finger has “moved”, and you know the distance between your eyes, you can calculate the distance from your eyes to your finger. The way we do it with the stars only differs in that we use the orbit of the Earth around the Sun to observe the “movement” of a star against a background of more distant stars. We know the distance from the Earth to the Sun to be ~93 million miles. We measure the annual amount of movement a star makes in arcseconds (an arcsecond is 1/60th of an arcminute which in turn is 1/60th of a degree. You end up using only half of that angle so as to achieve a right angle). Knowing that opposite angles are equal, we now have a right angle for which we know the length of one of its legs and the measure of one of its angles (in addition to the 90 degree angle). Using basic trigonometry we can take the tangent of the observed angle (called the parallax angle) and solve for the length of the unknown leg.

**tangent = opposite/adjacent **, therefore

**tangent(parallax angle) = (93 million miles)/(parallax angle)**

The answer to this equation is the distance to the star. Scientist, however, typically forego this calculation and just measure stellar distance in a simpler unit called parsecs (**par**allax **sec**onds). To measure in parsecs, simply invert the parallax angle (1/arcseconds). Then if a more layman unit is needed use a conversion factor. For example, 1 parsec is roughly equal to 19 trillion miles. The star with the largest known parallax angle and therefore the closest to our star is Proxima Centauri which exhibits a parallax angle of 0.77 arcseconds corresponding to a distance of 1.29 parsecs or about 24 trillion miles.