# How Aristarchus found moon's diameter?

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• prashant singh
In summary, Aristarchus found that Earth's diameter is 2.5 times the moon's diameter. He made some wrong calculations in his calculations, and this led to the disagreement between him and Archimedes.
prashant singh
how aristarchus found that Earth's diameter = 2.5 × moon's diameter . What wrong things he did to calculate the size of moon just like the shodow part.

prashant singh said:
how aristarchus found that Earth's diameter = 2.5 × moon's diameter . What wrong things he did to calculate the size of moon just like the shodow part.
You could look him up on the Internet. There are several fine articles there which discuss Aristarchus and his work.

prashant singh
Mathematical parts and diagrams

Yes I have tried wikipidia, it didnt helped me , there was only one image and equations , I need some brief explanation .

Well, that's exactly what you asked for earlier... Did you scroll down to the "Illustrations" section and check out the links to the interactive illustrations? Or check out the references for the page? I found this video as a reference for the article which supposedly explains the method, but I do not speak whatever language is being spoken in the video.

I want to know why they took (L/S) = (l/s) and how they got (L/t) =(l/t)(180/(pi × theta) and what is theta here

prashant singh said:
I want to know why they took (L/S) = (l/s) and how they got (L/t) =(l/t)(180/(pi × theta) and what is theta here

I'd have to work through the whole process to understand it and I don't have time for that right now. Sorry.
Until then, I'd recommend looking up what similar triangles mean and carefully working your way through the process as best you can (if you haven't done so already).

prashant singh
Can u explain me only first part please.

prashant singh said:
Can u explain me only first part please.
Similar triangles?
PF will respond so much better when you appear to have put some effort in, yourself.
What have you actually learned from that Wiki article?
I have spent less than five minutes on the recommended Wiki article and I found:
"The error in this calculation comes primarily from the poor values for x and θ. The poor value for θ is especially surprising, since Archimedes writes that Aristarchus was the first to determine that the Sun and Moon had an apparent diameter of half a degree. This would give a value of θ = 0.25, and a corresponding distance to the moon of 80 Earth radii, a much better estimate. The disagreement of the work with Archimedes seems to be due to its taking an Aristarchos statement that the lunisolar diameter is 1/15 of a "meros" of the zodiac to mean 1/15 of a zodiacal sign (30°), unaware that the Greek word "meros" meant either "portion" or 7°1/2; and 1/15 of the latter amount is 1°/2, in agreement with Archimedes' testimony."

Is this a homework assignment?

No its not a H.W problem but thanks for explaining
sophiecentaur said:
Similar triangles?
PF will respond so much better when you appear to have put some effort in, yourself.
What have you actually learned from that Wiki article?
I have spent less than five minutes on the recommended Wiki article and I found:
"The error in this calculation comes primarily from the poor values for x and θ. The poor value for θ is especially surprising, since Archimedes writes that Aristarchus was the first to determine that the Sun and Moon had an apparent diameter of half a degree. This would give a value of θ = 0.25, and a corresponding distance to the moon of 80 Earth radii, a much better estimate. The disagreement of the work with Archimedes seems to be due to its taking an Aristarchos statement that the lunisolar diameter is 1/15 of a "meros" of the zodiac to mean 1/15 of a zodiacal sign (30°), unaware that the Greek word "meros" meant either "portion" or 7°1/2; and 1/15 of the latter amount is 1°/2, in agreement with Archimedes' testimony."

Is this a homework assignment?

prashant singh said:
No its not a H.W problem but thanks for explaining
Ouch. That was hardly an explanation - not one that could satisfy me, in any event.
But you really have to hand it to those ancients who managed to measure some of those astronomical angles and distances a lot better than you or I would do, using tools from our shed and some bits of good quality timber!

Drakkith and prashant singh

## 1. How did Aristarchus determine the diameter of the moon?

Aristarchus used a method called parallax to determine the diameter of the moon. He measured the angle between the moon and the sun during a half-moon phase, and then repeated the measurement when the moon was at a quarter phase. By comparing the two angles, he was able to calculate the diameter of the moon.

## 2. What tools did Aristarchus use to make his calculations?

Aristarchus likely used basic instruments such as a protractor and a ruler to make his calculations. He may have also used a sundial to measure the angle between the sun and the moon.

## 3. How accurate were Aristarchus's calculations of the moon's diameter?

Aristarchus's calculations were quite accurate for the tools and methods available at the time. His estimate of the moon's diameter was within 20% of the actual value, which was a significant achievement considering the limited technology of the ancient Greeks.

## 4. How did Aristarchus's findings impact our understanding of the solar system?

Aristarchus's calculations of the moon's diameter were a key step in understanding the size and scale of the solar system. His work paved the way for future scientists to make more accurate measurements and calculations of other planets and celestial bodies.

## 5. Can modern technology confirm Aristarchus's calculations of the moon's diameter?

Yes, modern technology and instruments such as telescopes and satellites have confirmed Aristarchus's calculations of the moon's diameter. In fact, scientists have been able to measure the moon's diameter with even greater precision, thanks to advancements in technology.

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