How did Eratosthenes calculate the tilt of the Earth?

[myshadow]

Eratosthenes was a Greek mathematician who calculated the circumference of the Earth in 240 BC by using shadows and geometry. That's already ridiculous, but then I read he also calculated the tilt of the Earth! How did he do that?

This guy was definitely a time traveller from the future. lol.

 

[Nugatory]

I'm sorry, I may have misunderstood the question you're asking. I had thought that you were asking how to calculate the tilt of the Earth from measurements that could be made with technology available in 240 BC... In which case the answer is of course that it's half the difference between the height of the sun at high noon on the longest day of the year and the shortest day of the year (and of course there are a half dozen or so explanations of why in the first page of google results).

I just found it amusing that this thread had made it onto that first page in less than twenty minutes after you started it. Apparently the google page ranking algorithm takes physicsforums.com very very seriously.

 

[mesa]

"this thread had made it onto that first page in less than twenty minutes after you started it. Apparently the google page ranking algorithm takes physicsforums.com very very seriously."

This really is pretty remarkable, I just did a Google search and it came up on my first page too at only a few hours old; bots (spiders or whatever Google calls the program these days) are working overtime.

You guys should try this, ha ha!

 

[Ryan_m_b]

Keep it civil people

 

[pmacias]

I can assure you that Eratosthenes was not a time traveller from the future. He was a brilliant mathematician and astronomer who lived in ancient Greece and made significant contributions to our understanding of the Earth's shape and tilt.

To calculate the tilt of the Earth, Eratosthenes used a method called the "gnomon" or "shadow stick" method. He observed that on the summer solstice, the sun was directly overhead in the city of Syene, located near the Tropic of Cancer. At the same time, he measured the angle of the sun's shadow in his hometown of Alexandria, which was not directly overhead.

By comparing these two angles, Eratosthenes was able to calculate the difference in the sun's angle of incidence at the two locations. He then used this difference to determine the angle of the Earth's tilt. This method, while simple, was based on accurate observations and mathematical calculations, making it a reliable way to determine the Earth's tilt.

So, while it may seem "ridiculous" or even unbelievable that Eratosthenes was able to calculate the tilt of the Earth with such accuracy, it is a testament to his intelligence and scientific methods. It is important to recognize and appreciate the achievements of scientists throughout history, rather than dismissing them as time travellers or mere luck.