Aristarchus measure the distance to the sun

April 20, 2020
In ancient days, Peoples didn't have any telescope or observatory to study our solar system. They used their naked eye to observe the position of planets and stars. Historically, Greeks astronomers had a remarkable talent. They were the first who said the Earth is spherical.

 Aristotle was a famous Greek astronomer, he believed that Earth is at the center of our solar system. Another astronomer not famous as Aristotle, Aristarchus claimed that the Sun is at the center and today, we know that Aristarchus was right.

 Aristarchus was the first person (around 250 B.C.) who gave a proper method to find the distance between earth and sun, his measurement was not so accurate but the method he used was brilliant. He took that position when the moon was half-illuminated and then he noticed that the sun, moon, and earth was forming a right angle. He estimated the angle 87° not far from the actual value 89.83°.
earth to sun distance, how many kilometers between earth and sun, aristarchus model of solar system, earth and sun png, measure diameter of sun, aristarchus, measure distance between earth and sun, greek astronomer.how did aristarchus measure the distance from the earth to the sun, aristarchus timeline, how was the distance to the moon first calculated, aristarchus biography, how did aristarchus estimate the relative distances of the moon and sun quizlet, eratosthenes, how to measure distance between moon and earth, aristarchus was able to prove that, the synodic month for the moon is, hipparchus distance to the moon, observer's triangle relation, how to measure the diameter of the moon, ptolemy and epicycles, how did aristarchus die, why was aristarchus’s model not accepted, aristarchus timeline, aristarchus quotes, nicholas kepler, heliocentric frame, copernicus religion, aristarchus size of the sun, sizes of the moon, how do they measure distance in space, how do we know the size of the sun, distance from earth to sun in km, mars current distance from sun, distance between earth and moon, how long would it take to get to the sun, how is the earth-sun distance measured, distance between sun and moon, aristarchus family, define heliocentric theory, why is the heliocentric theory important, archimedes distance to the moon,

 At his time, there was no geometry. So, he used a similar way -
d = distance between moon and earth
D = distance between earth and sun

d\D = 3° / 57.29° = 1/20
⇒ d = 20 ✕ D

 i.e. the distance between sun and earth is 20 times the distance between earth and moon. This is not true, it is 400 times but the idea was remarkable. Of course, he didn't know the distance between the moon and earth. He only compared both distances and nobody knows, how he estimated the angle.

 let's know how he measured the diameter of the sun. First of all, he took that position when earth, moon, and sun were linear. He saw that they form a triangle -
earth to sun distance, how many kilometers between earth and sun, aristarchus model of solar system, earth and sun png, measure diameter of sun, aristarchus, measure distance between earth and sun, greek astronomer,how did aristarchus measure the distance from the earth to the sun, aristarchus timeline, how was the distance to the moon first calculated, aristarchus biography, how did aristarchus estimate the relative distances of the moon and sun quizlet, eratosthenes, how to measure distance between moon and earth, aristarchus was able to prove that, the synodic month for the moon is, hipparchus distance to the moon, observer's triangle relation, how to measure the diameter of the moon, ptolemy and epicycles, how did aristarchus die, why was aristarchus’s model not accepted, aristarchus timeline, aristarchus quotes, nicholas kepler, heliocentric frame, copernicus religion, aristarchus size of the sun, sizes of the moon, how do they measure distance in space, how do we know the size of the sun, distance from earth to sun in km, mars current distance from sun, distance between earth and moon, how long would it take to get to the sun, how is the earth-sun distance measured, distance between sun and moon, aristarchus family, define heliocentric theory, why is the heliocentric theory important, archimedes distance to the moon,

earth to sun distance, how many kilometers between earth and sun, aristarchus model of solar system, earth and sun png, measure diameter of sun, aristarchus, measure distance between earth and sun, greek astronomer,how did aristarchus measure the distance from the earth to the sun, aristarchus timeline, how was the distance to the moon first calculated, aristarchus biography, how did aristarchus estimate the relative distances of the moon and sun quizlet, eratosthenes, how to measure distance between moon and earth, aristarchus was able to prove that, the synodic month for the moon is, hipparchus distance to the moon, observer's triangle relation, how to measure the diameter of the moon, ptolemy and epicycles, how did aristarchus die, why was aristarchus’s model not accepted, aristarchus timeline, aristarchus quotes, nicholas kepler, heliocentric frame, copernicus religion, aristarchus size of the sun, sizes of the moon, how do they measure distance in space, how do we know the size of the sun, distance from earth to sun in km, mars current distance from sun, distance between earth and moon, how long would it take to get to the sun, how is the earth-sun distance measured, distance between sun and moon, aristarchus family, define heliocentric theory, why is the heliocentric theory important, archimedes distance to the moon,
With the help of two triangles above figure-

Dm / (Re - R) = Ds / (Rs - Re)

Dm = Distance between moon and earth

Ds = Distance between earth and sun

Re = Radius of earth

Rs = Radius of sun

Rm = Radius of moon

R = distance between shadow area of earth on radius of moon's position

Dm / Ds = Rm / Rs

⇒ Rm / Rs =  (Re - R) / (Rs - Re)

⇒ (Rs - Re) / Rs = (Re -R) / Rm

⇒ 1 - (Re / Rs) = (Re / Rm) - (R / Rm)

⇒ 1 + (R / Rm) = (Re / Rm) + (Re / Rs)

⇒ 1 + (R / Rm) = Re / Rs ((Rs / Rm) + 1)

⇒ Rs / Re = ((Rs  / Rm) + 1) / (1 + (R / Rm))

⇒ Rs / Re = ( 20 + 1) / ( 2 + 1 ) = 21 / 3 = 7
Rs = 7 Re

(He already calculated that R / Rm = 2.) 
Therefore he said that, "the diameter of the sun is 7 times the diameter of the earth". Of course today we know that it's 109 times. In this way Aristarchus measure the distance to the sun 


Powered by Blogger.