How Aristarchus found moon's diameter?

[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.

 

[SteamKing]

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

 

[Drakkith]

Have you tried wikipedia's article? https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus)

 

[prashant singh]

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

 

[Drakkith]

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.

 

[prashant singh]

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

 

[Drakkith]

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.

 

[sophiecentaur]

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?

 

[prashant singh]

No its not a H.W problem but thanks for explaining

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?

 

[sophiecentaur]

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!