Homework set #1

1. Summarize how Eratosthenes measured the diameter of the Earth.
Eratosthenes used the knowledge of the summer solstice at noon and how the Sun would appear directly overhead, and used vertical sticks to measure the shadows to calculate the diameter of the Earth. The result came to be really close.
2. What observations did Greek philosophers make to support the idea that the Earth is round?
There were many observations that the Greek philosophers made to support the idea that the Earth is round. First was the Lunar Eclipse, when the Earth lines up directly between the sun and the moon and casts a shadow on the moon. Second, they believed that since the sun casts shadows at different angles during the day, and how it was different throughout the year, the earth couldn’t be flat. Also, people in Ancient Greece made observations of the way the stars in the sky were different in each location, and knew that if the Earth were flat, we would see the same stars at the same time.
3. How did knowing the size of the Earth allow for the size of the Moon to be determined?
The diameter of the earth provided the one absolute number on which to base the calculations of the moons on.
4. Outline how the size of and distance to the Moon was estimated.
The ancient philosophers used their knowledge on the Earth’s size and geometry to figure out the size of the Earth's shadow at the distance of the Moon. By watching the Moon travel through the Earth's shadow during a lunar eclipse, they determined the ratio between the size of the shadow at the distance to the Moon and the size of the Moon itself.

5. Summarize how Aristarchus measured the relative distance to the
Sun.
Aristarchus applied geometric methods to measure the size of the sun. With the help from the lunar eclipse, he concluded that the Moon's radius is half that of Earth and measured the Moon's angular diameter to calculate the Earth-Moon distance. By noticing that the Sun and the Moon have equal angular diameters during a solar eclipse, he estimated the Sun's distance from Earth.
6. Outline how the distance to the Sun was estimated in ancient Greece.
In ancient Greece, the sun's distance was estimated by trying to find out when the moon was at exactly at first quarter phase. At this point, the earth-moon-sun angle must be exactly 90 degrees, and he thought that this position was different from when the moon should be halfway between new moon and full moon by 3 degrees. If these 3 degrees is accepted, then the sun is 20 times further than the moon, and also 20 times larger in diameter.
7. Aristarchus proposed a model of the Universe that placed the Sun at the center, rather than the Earth. What arguments were proposed against the Sun-centered model?
Some arguments when Aristarchus proposed a model of the Universe that placed the Sun at the center were:
If the Earth spun on an axis, why didn't objects fly off the spinning Earth?
If the Earth was in motion around the sun, why didn't it leave behind the birds flying in the air?
If the Earth were actually on an orbit around the sun, why didn’t the stars change their position with the respect to the other background stars as the Earth moved about its orbit?
8. Summarize Ptolemy’s Earth-centered model of the Universe. What was the motivation to change the original Earth-centered model to that