They are some of the most spectacular sights in the sky: globular clusters, tight collections of hundreds of thousands or even millions of stars. Now, using the Hubble Space Telescope — and ancient math — astronomers have accurately measured the distance to one of the oldest ones in our universe.

Until now, astronomers have used the brightness, or luminosity, of stars to calculate the age of globular clusters. But this method has produced readings that are inaccurate by 10 to 20 per cent. That's enough to make some estimates come in older than the universe itself.

Calculating these distances is crucial to our understanding not only of how the universe formed but of how we got here ourselves.

"All this can fold into how the galaxy formed," Don VandenBerg, co-author of the new study published in The Astrophysical Journal Letters and professor at the University of Victoria, told CBC News. "It's all part of the origin of things."

Researchers looked at globular cluster NGC 6397 within our galaxy and used a novel method to calculate its distance, employing math as old as science itself: trigonometry.

A simple way of understanding this method is to hold your index finger out in front of you at arm's length. Close your right eye and note the position of your finger against a background. Open it and then do the same with your left eye. You will notice that your finger seems to move against the background, though in reality it didn't move at all. This is called parallax.

Every six months, over a period of two years, as Earth orbited the sun, the team of astronomers used the Hubble Space Telescope to study this apparent shift of NGC 6397. Capturing the stars as they moved across the telescope's view, they measured the distance of 40 stars within the globular cluster to be about 7,800 light-years away, with just a three per cent margin of error — far better than the previous margin of 10 to 20 per cent.

The shifts, or wobbles, of the stars were only 1/100th of a pixel on the telescope's camera and were measured to a precision of 1/3,000th of a pixel.

"This is like standing on Earth and measuring the size of a car tire on the moon to within one-inch accuracy," Tom Brown an astrophysicist at the Space Telescope Science Institute and lead author of the paper, told CBC News.

You get a sense of just how distant the cluster is in the video below.

And, amazingly, the astronomers calculated that this particular globular cluster was ancient: 13.4 billion years old, to be precise. Looking at it, we see it as an infant in a galaxy that is roughly 13.8 billion years old.

Jewels in the cosmos

Globular clusters are found in halos around galaxies. The stars within them are gravitationally bound and look like a fuzzy ball of light in small telescopes. But in powerful telescopes you can see thousands upon thousands of individual stars, believed to be created at the early stages of the universe's formation.

Since they're so old, astronomers have been seeking to use them to better measure the distance to other objects as well as understand their evolution.

The globular cluster Omega Centauri, with as many as 10 million stars, is seen in all its splendour in this image captured from the La Silla Observatory in Peru. The image shows only the central part of the cluster. (European Southern Observatory)

Astronomers had been using open clusters — stars that were formed from the same cloud of gas and dust and that are loosely held together by gravity — to measure distances. But these younger, closer stars didn't provide much accuracy.

This new research changes all that.

"This helps give the foundation to models that are used in many parts of astronomy — not just looking at stars but also looking at distant galaxies," Brown said. "And this particular cluster is the anchor in one of the most widely used models in astronomy for interpreting distant galaxies."

The research team hopes to further refine the accuracy of the measurement of the distance to NGC 6397 to within one per cent when the European Space Agency's Gaia space telescope releases its second round of collected data, scheduled for later this month.