1. In 240 BC, Eratosthenes (c. 276 BC-c. 194 BC) measured the At Alexandria, the
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Question
1. In 240 BC, Eratosthenes (c. 276 BC-c. 194 BC) measured the At Alexandria, the midday Sun Earth's circumference and came within 95% of the modern casts a shadow indicating the Sun is from true vertical, value. Using the diagram, calculate the circumference of the Earth in stadia. Then, convert stadia to kilometers 130 pts total Show your work in the box. TWork 10 pts Measurements (known values): Syene to Alexandria is a distance 5,000 stadia. The angle 7°. Also, a Greek stadium is 1/6 km. At Syene, the midday [Hint Convert 116 km to a decimal.] The modern value of Earth's Sun casts no shadow. circumference is 40,100 km. Compare your (Eratosthenes) answer to this. Note this proportion: 70/360 -5000 stadia/circumference of Earth in stadia By simple geometry the distance from Syene to is of the 360° circumference of the Earth. Ancient stadium could vary from 157 m (515 ft to 209 m (686 ft. Circumference in stadia: Round to a whole number. 10 ptsl Circumference in kilometers: Round to a whole number. 10 pts] 2. With only naked eye observation and a simple measuring instrument, you can determine the relative distance of the inner planets to the Sun (in terms of astronomical units, AU) A measurement of the greatest eastern elongation of Mercury (the maximum angle in degrees between the Earth-Sun line and the Earth- planet line) shows it to be 22.8°. Calculate Mercury's distance from the Sun. Right triangle 1 AU E- El S-Sun Caution! Make sure that your scientific calculator's mode is set for Sci (not ENG). You want degrees (DEG), not radians (RAD). Show your work in the box. Worl 10 pts Mercury's distance: AU Mercury's distance: km (use scientific notation) (Round to 2 decimals) [10 pts] (Round to 1 decimalExplanation / Answer
1. Distance between two cities = 5000 Stadia
7o = 1/51.4 of circle (7o / 360)
circumference in stadia = 51.4*5000
= 2,57,000 stadia
1 stadia = 1/6 km
circumference of the Earth in km = 2,57,000 *1/6
= 42,833 km
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