Walking through the mind of Aristarchus of Samos
If you’ve never heard of Aristarchus of Samos, you’re missing out on one of history’s most brilliant minds. A mathematician, astronomer, and philosopher, he was the first to propose a heliocentric model of the universe — placing the Sun, not the Earth, at the center.
At a time when the geocentric model was widely accepted, Aristarchus not only challenged conventional beliefs but also attempted to measure the relative sizes and distances of the Sun and Moon.
On the Sizes and Distances of the Sun and Moon
On the Sizes and Distances of the Sun and Moon is the only surviving work of Aristarchus. In this work, he is able to derive these following results:
- Sun is around 19 times farther away.
- Earth is approximately 3 times bigger than the moon and is roughly six times smaller than the sun.
Also, keep in mind that during these results, geocentric model was still widely accepted. So I personally find it really interesting and enlightening that he was able to even employ the methods he employed to get to these results.
Now, although we know these values to be incorrect, what makes his work remarkable is not the numbers themselves, but the method he used to arrive at them — and, more importantly, the mindset behind it. His willingness to challenge established beliefs and rely on logical reasoning was groundbreaking, demonstrating a level of scientific thinking that was centuries ahead of his time.
How did he calculate the distances?
Now, let’s talk about what methods he used to get to these results. He had available the following observations:
Observation A: Angle between the sun and moon during a half moon is 90°.
Observation B: The apparent size of the sun and moon in the sky.
Observation C: Size of earth’s shadow relative to moon during a lunar eclipse.
Part I: Calculating distances
Let’s look at observation A, “The angle between the sun and moon during a half moon is 90°”. You might have come across this observation if you’ve ever deeply thought about the phases of the moon — or ever questioned how the moon appeared half somedays.
When the moon appears half, the position of moon — sun — earth looks something like this:
so, the angle at moon is 90 degrees, now if we find the other two angles (angle at earth and sun), we can in principle calculate the distances.
For the angle centered at earth, we can obtain it by observing the angular distance from the moon to the sun which is called the lunar elongation. He calculates this angle to be 87°.
Angular distance
Now, we have a right angled triangle, with one of the angle being 87 degree, in principle from here you would think aristarchus could calculate the ratio of the distances using the secant:
And could infact get to this result — Sun is 19.1 times farther than the moon (sec87°=19.1)
But, since trignometry hadn’t even been invented, the only tools he had was geometric reasoning and using it he was able to establish a maximum and minimum limit that the sun is between 18–20 times farther than the moon.
Conclusion
Part-I only discusses the distance calculation, in next blog I’ll go through how aristarchus calcuated the sizes which is even more interesting.
Even though the result of distance discussed in this article is wrong, I found the story of aristarchus so interesting that I had to write this article.
During his time on this earth, everyone believed in a geocentric model — they believed that the sun revolved around the earth. I find it really interesting how he not only challenged this preconcieved notion but was able to stay critical enough and had the intellectual courage to believe in a heliocentric model and calculate these values.
In our age, where information is abundant and we take everything at face value, this type of mindset is not only welcomed but also needed. I strongly believe questioning , being critical of things , finding answers, staying curious are the very characteristic of being a human and we should always try to embrace it.
Aristarchus’s work should reminds us that questioning established ideas is the foundation of progress and brings us closer to the truth. Even though his calculations weren’t perfect, his method laid the groundwork for scientific reasoning — an approach we should embrace today.
❤️ SUPRIYA