Recently I realized that the distance I used for the star Betelgeuse – ninth-brightest star in the night sky and second-brightest in the constellation Orion the Hunter – in a popular blog post here at EarthSky had become outdated. I thought that this would be good time to mention how star distances are determined, while correcting Betelgeuse’s distance estimate. Truth is, finding the distances to even the nearest stars is not easy.
Ancient Greek astronomers knew how to do it but could not, because they lacked the technology. Oddly enough, normal-sighted people use something like this same concept – the concept of parallax, used to find distances to the nearby stars – every day without ever thinking about it.
Here’s what we do, on a human scale. Hold your thumb out at arms’ length and look at it with just one eye. Note the apparent position of your thumb with respect to the background, say a fence in your backyard, a row of distant trees or buildings. Then quickly switch to the other eye. You should note that your thumb seems to jog slightly to one side or the other. That’s because you are looking at your thumb with your two different eyes separated by a couple of inches, seeing a slightly different view with each.
Normally our brains consolidate the two views, and that’s why we have stereoscopic vision. The brain calculates distances based on how much the view differs. It is similar to how a surveyor can measure the distance to some object using triangulation. Our brains do it automatically.
The ancients thought, correctly, that this concept could be used to determine the distances to stars. Instead of using the views from two human eyes, they chose to make separate observations from two different locations. Mathematically, if you can measure the apparent angular offset (also called the parallax angle) of some object when viewed from two different locations separated by a known distance, you can calculate the distance to the object easily. Ancient astronomers, however, could not make it work because no matter how far they extended the distance between the two observations, they could not see any angular displacement. In other words, the view from one place looked exactly the same as a view from another. They failed, but they concluded correctly that the angle must be very small, and the stars very, very far away!
All measurements of stellar parallax (and determination of the distances to stars) failed until German astronomer Friedrich Bessel succeeded in 1838. Instead of just his eye, he used a telescope. And instead of the distance between his eyes, his baseline was the diameter of the Earth’s orbit. He accomplished this huge baseline by measuring once, and then again 6 months later when the Earth was on the other side in its orbit, a distance of roughly 186 million miles (300 million km). Even then, he was barely able to make out a tiny angular displacement. But it was enough to determine a distance of 11 light-years to a nearby star called 61 Cygni.
From Bessel’s time until the 1980s, only a few thousand parallaxes had been determined. The process is hindered by a number of factors including the extremely small angles involved, imperfections in the instruments and perhaps most of all, the murkiness of Earth’s own atmosphere. Observations from the Earth, even from very clear and dark locations such as deserts and mountaintops are blurred by distortions from the atmosphere. It’s a bit like looking up from the bottom of a swimming pool.
In 1989, the European Space Agency (ESA) launched a satellite with a telescope above the Earth’s blurry blanket of air. It was called Hipparcos, named after the famed Greek astronomer Hipparchus, who applied trigonometry to the problem of stellar distances more than 2,000 years ago.
Over several years of observations, Hipparcos provided parallax and distance data for more than 100,000 relatively nearby stars.
This brings me back to the reason for this post. The original Hipparcos data gave a parallax of Betelgeuse of 7.63 milliarcseconds (mas), which is about one millionth the width of a full moon. This equates to a distance of about 430 light-years.
Subsequent studies found an error in the methods of reducing data for variable stars such as Betelgeuse. One effort to correct those errors gives 5.07 mas. Using this figure, Betelgeuse is about 643 plus or minus 46 light-years. This is likely the most accurate current estimate to date.
To give a sense of scale here, if our sun were the size of a BB (a pellet used in a BB gun), Betelgeuse would be roughly the size of a Toyota Camry, and located nearly 12,500 miles (20,000 km) away!
The range is still quite large, and, while it does not seem precise, we are probably safe in saying that Betelgeuse is somewhere between 430 and 690 light years away!
Bottom line: Finding the distances to even the nearest stars is not easy. Here’s how it’s done, and why the distance to the famous star Betelgeuse recently was modified from 430 light-years to 643 light-years (plus or minus 46 light-years).