Sayed Shafaat Mahmud
4 min readSep 3, 2020

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Distances in Astronomy

To an early Greek Astronomer, the night sky couldn’t have been more than a 2 dimensional surface of a gigantic semi-sphere dotted with tiny points of light. The milky-way might not have been anything more than a dusty patch of ‘cosmic cloud’. However, today we know that the night sky is vast. It tells us the story that occurred billions of years ago, it tells us our origin, it tells us how it all happened in the first place.

The first essential step towards the distance calculation can be awarded to Johannes Kepler. Kepler, with his patient observation of the wanderers of the night sky (the planets), deduced a beautiful relationship between the distance and the period of revolution of a planet revolving the sun. The formula looks like the following:

(Period of Revolution)² = (Average Distance of Revolution) ^3

This simple relationship changed our understanding of the universe from 2D to 3D overnight. So, now that we know how far the planets are, how do we infer the distance to the nearby stars?

To estimate the distance to a nearby star (i.e. Sirius) we just take the parallax angle of the star and some basic trigonometry is sure to give a decent assumption. How do we measure the parallax? If we stretch our thumb to an arm-length and shut our one eye and repeat it with the other, it can be seen that the thumb appears to move by a slight ’angle’ relative to the background. This same principle applies to the stars. Let’s say, we record the position of the star in January and in May. By May, the earth would be opposite to the position it was in June with the Sun being in between. This creates a slight ‘angular shift’ of Sirius concerning the background stars. Dividing that star by 1-radian angle and the distance between the Earth and the Sun gives us its Distance!

Parallax Measurement

The Parallax technique works at best to a distance of 300 light-years. With modern equipment, such as the Hubble Telescope, the range increases to 3000 light-years but we know a ton more.

The 3rd way of measuring Distance came from a Harvard ‘computer’ named Henry Leavitt. Leavitt used to observe pulsating variable stars known as the Cepheid Variables. These stars would pulsate at a wide range of periods. However, as she started to observe a huge range of pulsating variables, she came to realize that if we draw a graph of luminosity vs. Period of Pulsation, we will realize that the luminosity increases along with the increase of pulsation period. This led to a stunning conclusion. Now, we can confidently state that stars appearing fainter but with larger periods are not close but extremely far away and, stars appearing brighter but with shorter periods wasn’t bright but it was closer.

period-luminosity relationship

This elegant implication, later on, expanded our view that the tiny distant blobs that we see in the sky through a telescope, aren’t nebulae. They are Galaxies, islands of billions of stars much like our own Milky Way separated by millions of light-years of distance. This counterintuitive realization was proved by Edwin Hubble in the early 1920s. Using, the variable stars as ‘Standard Candles’, he collected the spectrograph of a large number of galaxies. He realized that the wavelengths of the spectrum collected from most galaxies were enormously red-shifted meaning that they were extremely distant and were moving away at speeds close to the speed of light.

In the current age, we can trace back billions of light-years into the past and actually ‘see’ the initial conditions of the Universe. We can understand how these galaxies formed, we understand why they appear to move away from us and what’s more to regular matter in the galaxies. So much for only a century of hard work, isn’t it?

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