Table of Contents
- 1 How did they calculate the diameter of the Earth?
- 2 How did Eratosthenes estimate the size of Earth in 240 BC?
- 3 Why did Aristarchus’s critics think that the Earth was stationary?
- 4 How did the Greeks calculate the Earth’s circumference?
- 5 Who first determined the size of the Earth?
- 6 How did Eratosthenes calculate the circumference of the Earth?
How did they calculate the diameter of the Earth?
On the day the Sun shone on the bottom of the wells in Syene, Eratosthenes measured the Sun’s position in the sky over Alexandria. It was seven degrees away from the zenith, meaning Syene must be seven degrees away from Alexandria as measured on the circle that is Earth’s circumference.
How did Eratosthenes estimate the size of Earth in 240 BC?
How did Eratosthenes estimate the size of the earth in 240 bc? By comparing whether sun light could reach water down in water wells in two cities at different latitudes and using simple trigonometry. On the vernal equinox the spin axis of the earth and a line between the earth and the sun are perpindicular.
How did Eratosthenes calculate the size of the Earth?
Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 kilometers. He could then use simple proportions to find the Earth’s circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers.
What is the formula of Earth?
The formula for calculating the circumference of a sphere is 2 x pi x radius. So, the radius of the Earth is 6371 km. Plug that into the formula, and you get 2 x 3.1415 x 6378.1 = 40,074. It would be more accurate if you use more digits for pi.
Why did Aristarchus’s critics think that the Earth was stationary?
The ancient Greeks knew about parallax, so why did Aristarchus’s critics think Earth was stationary? (Select all that apply.) They didn’t realize that stars could be very, very far away. (They didn’t understand that stars could be so far away, making their parallax undetectable.)
How did the Greeks calculate the Earth’s circumference?
In the third century BCE , Eratosthenes, a Greek librarian in Alexandria , Egypt , determined the earth’s circumference to be 40,250 to 45,900 kilometers (25,000 to 28,500 miles) by comparing the Sun’s relative position at two different locations on the earth’s surface.
What is the real diameter of the Earth?
Both of these values are very close to the accepted modern values for the Earth’s circumference and radius, 40,070 km and 6378 km respectively, which have since been measured by orbiting spacecraft. The diameter of a circle is twice the radius, giving us a diameter for Earth of 12,756 km.
How do you calculate the circumference of the Earth?
Moreover, it bulges at the equator due to the Earths rotation. However, derived from NASA’s value of the (presumably) average diameter of the Earth, 12,756 km, we can approximately calculate is circumference, using equations of the relationship between the diameter or radius of a circle, to its circumference, also incorporating π.
Who first determined the size of the Earth?
In 1906, the German geodesist Friedrich Robert Helmert determined that the earth was a global ellipsoid and calculated it to within 100 meters, 0.002\% of modern measurements. O’Connor, J., & Roberston, E. Aryabhata the Elder .
How did Eratosthenes calculate the circumference of the Earth?
Because seven degrees is about one 50th of a full circle (360 degrees), Eratosthenes simply multiplied the distance from Alexandria to Syene — believed to have been about 515 miles (830 km) — by 50. He calculated Earth’s circumference at 26,000 miles (42,000 km), only five percent away from the modern accepted value of 24,901 miles (40,074 km).