Measuring distance near and far

Time is one dimensions of spacetime. The other three are measurements of distance. We recognize the world around us as occupying height, width, and depth or x,y, and z or some variation of coordinates which tell us about the physical universe.

The history of measuring distance is related to time in our most ancient history.

With no standardized units, no one would say “travel so many kilometres” but rather “travel for half a day west” or “travel east until sunset.”

Such measurements are horribly imprecise as not everyone moves at the same pace.

Standardized units for length first appeared in Western culture with the rise of Mesopotamia and evolved over time with the Egyptian civilization.

Measurements were based on the human body – the length of the forearm or stride or perhaps someone’s actual foot.

Pretty much every ancient civilization developed some method of measuring distance.

Concurrently, builders developed methods to translate measurements

into workable plans. And from this arose geometry. Most students I have talked to question the utility of learning trigonometry but without it, we wouldn’t have many of the ancient wonders of the world.

Or, for that matter, pretty much any of the advances of modern civilization.

For example, if you want to lay out a perfectly square foundation, how do you go about doing it?

The answer is to make sure all four sides are the same length and each diagonal is exactly the same length as the other. Simple geometry.

But how do you determine the height of an object?

Move away from the object until you are looking at the top at exactly a 45 degree angle.

The height of the object is the distance you are from it – with your own eye level taken into account.

Of course, we would now just use a tape measure.

But what if the distance was too large for a tape measure?

For example, how does one measure the circumference of the Earth?

Eratosthenes of Cyrene was a Greek polymath as he engaged in a number of different intellectual disciplines, including both geometry and geography.

He is credited with being the first person to accurately determine the circumference of the Earth.

He did this by measuring the angle a shadow makes in both Alexandria and Syene on a midsummer’s day.

At Syene, the sun was directly overhead and cast no shadow whereas at Alexandria it was onefiftieth of a full circle.

As the distance between the two cities was 5,000 stadia – equivalent to about 925 km – he was able come to a value equivalent to about 40,000 kilometres which is pretty much the distance we have today. (And he also proved the Earth is round!)

But how does one go about measuring even larger distances, such as the distance to the sun?

This was achieved by measuring the transit of Venus across the sun from various known locations across the globe and applying trigonometry to again calculate the triangles.

The astounding figure obtained was about 153 million kilometres – only slightly larger than the presently accepted value of 149.6 million kilometres.

How do you measure even larger distances, such as the distance to the stars?

This is where it gets tricky and geometry finally begins the fail.

We can use Earth-based measurements taken six months apart to construct the base of a triangle by measuring the apparent motion of stars against the background of the night sky.

This system of parallax works for closer stars but eventually the angular differences become too small to measure.

Enter Henrietta Swan Leavitt, a computer at the Harvard Astronomical Observatory in the early 1900s.

She was tasked with measuring the photographs of stars called Cepheid variables in the Small and Large Magellanic Clouds and determined a relationship between their apparent luminosity and the period of their oscillating brightness.

Initially, her relationship was all relative but when the absolute distance to local Cepheid stars was determined, her stars became standard candles.

By measuring their period, astronomers could determine their absolute luminosity and by measuring their apparent luminosity, astronomers can determine their exact distances.

It was by measuring Cepheid Hubble was able to show the Andromeda Nebula was actually a galaxy two million light years away.

In a report last week, astronomers have remeasured 2500+ Cepheid variable stars and using the distance measurements obtained, they were able to recalculate our map of the Milky Way.

The data provides a galaxy which is not as flat as we thought. It is curled up and down – much like a vinyl record which has been left too long near heat.

Whether their calculations hold up to further analysis and the Milky Way is a non-planar galaxy remains to be seen. But one thing is clear – we have come a long way from guesstimating distances based on time to measuring the physical universe from one end to the other.