Eratosthenes and the Circumference of the Earth

Portrait of Eratosthenes

Eratosthenes was an astronomer, historian, geographer, philosopher, poet, theatre critic and mathematician, who lived in the 3rd century BC in the greatest metropolis of the age, the Egyptian city of Alexandria. His envious contemporaries called him ‘Beta’, the second letter of the Greek alphabet, because they said, Eratosthenes was second best in the world in everything.

However, it was quite an underevaluation of the greatness of the man.

He was the first person to use the word “geography” and invented the discipline of geography as we understand it. He also invented a system of latitude and longitude.

He was the first person to calculate the circumference of the earth with remarkable accuracy. He was also the first to calculate the tilt of the Earth’s axis (also with remarkable accuracy).

The story of the calculation of Earth’s circumference is very interesting. Eratosthenes was also the director of the great library of Alexandria. There, one day he read in a book that in the southern frontier outpost of the ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on June 21 at noon, the Sun would appear at the zeith, which means directly overhead. Thus on this day at this time at this location, a vertical stick would cast no shadow. On the summer solstice, June 21 (the longest day of the year), as the hours crept towards noon, the shadows of the temple columns drew shorter and shorter. At noon precisely, the reflection of the Sun could be seen in the water at the bottom of a deep well.

This was a fairly simply observation that someone else might easily have ignored. What significance could sticks, shadows, reflections and wells  have on the simple everyday matters? But Eratosthenes was a scientist and his musings on these commonplaces changed the world; in a way they made the world.

Eratosthenes had the presence of mind to do an experiment, actually to observe whether vertical sticks cast any shadows at noon on June 21 in Alexandria as well. And his discovery was that they do.

Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow while a stick in Alexandria, could cast a pronounced shadow.  In case, at both places had there been no shadows, or had the shadows been of equal lengths, it would have been easy to explain considering the earth to be a flat surface and the Sun’s rays to be inclined in both cases at equal angles. This would have been easily explainable. But this was clearly not the right explanation under the present observation.

Hence, the only possible answer that he saw was that the surface of the Earth was curved. Not only that, the greater the curvature, the greater would be the difference in the shadow lengths.  Since the Sun was so far away, its rays falling on any two locations on the Earth can be considered parallel for all practical purposes. Thence, according to the difference in shadow lengths between the two observations, Eratosthenes was able to calculate that the angular separation of Alexandria and Syene to be of 7 degrees along the surface of the Earth and this 7 degrees was approximately 1/50th of 360 degrees, which was the total angular circumference of the Earth. Knowing the distance between the two cities was approximately 800 Kms, because he hired a man to pace it out, Eratosthenes was able to calculate that 800 Kms times 50 is 40,000 Kms and so that must be the circumference of the Earth.

It was a brilliant deduction, especially in an age where the only tools he had available for this scientific experiment were a few sticks, eyes, feet and brains. Most importantly, he had a taste for experimentation, a thirst for knowledge and a curiosity to understand the basic tenets of nature, which were all ahead of his own age.

The story of Eratosthenes and how one man changed our understanding of our world is an awe inspiring example of the power of scientific inquiry and inquisitiveness. He drew his conclusions objectively from the observed facts of the world and not according from his personal wishes and preferences.

 

 

Further Reading:

“Cosmos” by Carl Sagan (book)

http://www.pbs.org/wnet/hawking/cosmostar/html/cstars_eratho.html (online reading)

 

Advertisements

The Voyagers

The Voyager Spacecraft

Jupiter’s Great Red Spot – Photographed by Voyager

In 1977, NASA launched the twin Voyager 1 and 2 spacecrafts whose primary mission was the exploration of Jupiter and Saturn. After making a string of discoveries there — such as active volcanoes on Jupiter’s moon Io and intricacies of Saturn’s rings — the mission was extended. Voyager 2 went on to explore Uranus and Neptune, and is still the only spacecraft to have visited those outer planets.

Saturn rings with “spoke” features in B-ring. Aug. 22, 1981. 2.5 million miles.

Their extended mission is now called the Voyager Interstellar Mission (VIM). As of this mission, the Voyager spacecrafts, which have drifted to the edge of the Solar system beyond Pluto, will continue to explore the outermost edge of the Sun’s domain. And beyond.

The Voyagers are currently in the Heliosheath, – the outermost layer of the heliosphere where the solar wind is slowed by the pressure of interstellar gas. It is basically the zone beyond which, the Sun’s influence ends and we reach the interstellar space. And they are still sending scientific information about their surroundings back to Earth.

The Golden Record

But that is not all that is wonderful about these crafts. NASA has also placed a very ambitious message aboard the Voyagers 1 and 2. Each craft contains a 12-inch gold-plated copper disc, called a phonograph. This disc contains sounds and images that are selected to portray the diversity of life on Earth. The contents of the record were selected for NASA by a committee chaired by the great astronomer and astronomy populariser, late Dr. Carl Sagan of Cornell University. They have included a variety of natural sounds like wind, thunder, birds, etc. along with musical selections from different cultures and eras and spoken greetings from Earth-people in 55 languages. And a lot more.

The extremely ambitious hope is that sometime in the future, some extraterrestrial beings might discover the Voyager and will look at it and discover the Golden Record. They might not understand the strange sounds that the record will make. We don’t know if those beings will even have the same sense of sounds as we do or will their “ears” be differently capable? Will they have vision like us or will that also be like something we cannot even imagine? We don’t know. And they will never be able to figure out where this came from, which edge of our galaxy, which direction, which planetary system around which of the billions of stars inhabiting the milkyway. None of this will ever be known to them. And we don’t even know if there ever will be a “them” to discover our message.

At the time of writing this blog, I checked NASA’s website (http://voyager.jpl.nasa.gov/where/index.html) and found that the Voyager 1 is currently 18.169 billion kms away from the Sun. When you think about it, the vastness of this distance trumps our brains. Can we imagine a distance of 18+ billion kms? It is unlike anything we have ever measured on earth of course. Yet, in the context of the size of the Milky Way itself, this distance is nothing but a fraction of a fraction of a small dot.

The Voyager spacecrafts are both beyond Pluto and they find themselves in empty space now. There is nothing there to see, except darkness. There is no upcoming planet, no moon and no source of light as well. The Voyagers will continue their slow and patient journey for the next thousands of years or maybe much more.

Eventually, the Voyagers will pass other stars. In about 40,000 years, Voyager 1 will drift within 1.6 light years (9.3 trillion miles) of AC+79 3888, a star in the constellation of Camelopardalis. In some 296,000 years, Voyager 2 will pass 4.3 light years (25 trillion miles) from Sirius, the brightest star in the sky. The Voyagers are destined—perhaps eternally—to wander the Milky Way.

Will we ever hear from the voyagers when they reach there? That’s not possible. Will humanity even exist after such a long time? Extremely improbable. But whether humans exist or not, and whether some other extraterrestrials even find and read our message or not, we have already communicated to the cosmos announcing that we existed and dared to look up at the sky. We looked at the distant stars and contemplated the vastness of the universe. We understood and are still trying to understand what we see when we look up at the night sky.

Thousands of years into the future, we may not exist but this message will exist and probably through this, we will continue to live in a poetic sense. I am sure that the majority of people on our planet don’t even know about the voyagers and what I have described above. Most of those who do might never understand the depth of this endeavour. But it is important that we do know and that is why I am even writing this.

Does this adventure of the voyagers make any difference to someone when they are going about their lives trying to make a living, maintaining relationships, planning for their future, worrying about daily stuff, etc.? Maybe not. But then, neither does any form of poetry. Still most people are greatly moved by poetry and this lonely and courageous journey of the voyagers is nothing less than poetic. We may not be able to travel such interstellar distances ourselves because we are humans and need food to survive and we do not even live for so long. But we have made something that will carry out this journey on our behalf.

Knowing that the universe is largely a lonely place with nothing for trillions of miles and no one to contact is a saddening thought. Knowing that our efforts, however grand we might think them to be, are really never going to be good enough when you contemplate the vastness of the universe is a very humbling thought. Yet, we should take great pride in the fact that we know our limitations very well but we do not fear failure.

As Carl Sagan has noted, “The spacecraft will be encountered and the record played only if there are advanced spacefaring civilizations in interstellar space. But the launching of this bottle into the cosmic ocean says something very hopeful about life on this planet.”

We may not have all the answers to all the mysteries of the universe but we do represent a thirst for knowledge that defines being human. And this thirst for knowledge, adventure, courage, hope and ambition for unravelling the mysteries of the universe will always be the symbol of being human. And having a common understanding of the grandness of the cosmos will only bring us all together. We will learn to care about the planet and our species because for over trillions and trillions of miles, we will not find another like us.

P.S: I am not a scientist or a science writer by any stretch of imagination, but what I do represent is my own thought and  understanding of the world. There certainly are better knowing people than me and I do not claim to be an authority on this subject and most of the factual data in my blog is sourced from NASA’s website: voyager.jpl.nasa.gov. What I have added are my personal feelings about this.

%d bloggers like this: