Greek Estimates

What was the key observation Eratosthenes used to measure the Earth's circumference?

• The angle of the Sun's rays at noon in Alexandria

• The length of the shadow cast by the Great Pyramid

• The difference in star positions between Alexandria and Syene

• The time it took for the Sun to set in different locations

How did Eratosthenes calculate the Earth's circumference using the angle of the Sun's rays?

• By measuring the distance between two cities and using the angle to calculate the circumference

• By using the angle to calculate the Earth's radius directly

• By deriving the angle of the shadow in Syene using math

• By using the angle to determine the Earth's diameter

What assumption did Eratosthenes make about the Earth to calculate its circumference?

• The Earth is a perfect sphere

• The Earth is flat

• The Earth is an oblate spheroid

• The Earth is a cube

Aristarchus used the concept of similar triangles to estimate the distance to the Moon. What was one of the key observations he made?

• The angle between the Earth, Moon, and Sun during a specific lunar phase

• The length of the shadow of the Earth on the Moon during a lunar eclipse

• The time it takes for the Moon to orbit the Earth

• The brightness of the Moon compared to the Sun

How did Aristarchus use the concept of similar triangles to estimate the distance to the Sun?

• By comparing the surface area of the Earth to the diameter of the Sun

• By comparing the distance to the Moon with the distance to the Sun

• By measuring the angle of the Sun's rays at different times of the day

• By using the angle of the Earth's shadow during the Winter Solstice

Which option is closest to the ratio that Aristarchus found for the distances to the Sun and Moon?

• 1:1000

• 1:200

• 1:400

• 1:10

What method did Aristarchus use to estimate the distances to the Sun and Moon?

• Trigonometric parallax

• Pythagorean Theorem

• Similar triangles

• Law of cosines

Eratosthenes' method relied on the assumption that the Sun's rays are:

• Divergent

• Convergent

• Parallel

Eratosthenes measured the distance between Alexandria and Syene to be approximately:

• 500 km

• 800 km

• 1000 km

• 1200 km

What aspect of the animation shown here played a key role in Aristachus' method for finding the distances to the Sun and Moon?

• The speed at which the Moon eclipses the Sun

• The speed at which the Sun eclipses the Moon

• The phase of the Moon during an eclipse

• The relative size of the Sun and Moon in the sky