Question 6: How is the second statement important to the measurement of the relative size of the Moon to the Earth? (Hint: Consider what would happen to the shadow of the Earth if the Sun was placed very close to the Earth.)
Question 7: What evidence did the ancient Greek Astronomers have that the Moon orbits the Earth? (Give as many as you can think of.)
Question 8: How much time does it take the Moon to move 0.5 degrees in the sky? This is the time that the Moon requires to sweep out its own diameter on the sky. To determine this remember that it takes the Moon 28 days to sweep out 360 degrees (once around the Earth). Use the following ratio to determine this:
Time for the Moon to move its own diameter on the sky 0.5 degrees ----------------------------------------------------- = ----------- Time for the Moon to go 360 degrees (in hours) 360 degrees
Question 9: How much time did it take the Moon to sweep out Earth's shadow during the lunar eclipse (take the difference of the two times you recorded)? Divide this time by the time it takes the Moon to sweep out its own diameter, which you determined above. This number is approximately how much bigger the Earth is than the Moon.
|Although Aristarchus used a timing method, we can get a crude estimate of the relative size of the Moon to the Earth by looking at the curvature of the Earth's shadow during a lunar eclipse. All of the above model statements are still important to this conceptually simpler method.||
Umbra and Penumbra during a Lunar Eclipse
Question 10: Why would this method have been difficult for the ancient Greek Astronomers to perform, and why was the timing method more favoured?
Question 11: How does your answer using the timing method compare to what you got by looking at the curvature of Earth's shadow during the lunar eclipse?
Question 12: Use the radius of the Earth that you determined from rung 1 of our distance ladder along with the relative size of the Moon determined to find the radius of the Moon in kilometers.
Radius of the Moon: _____________________ km.
Question 13: Calculate the distance to the Moon using its absolute diameter and its angular diameter. For help with the geometry of this problem and with the trigonometry involved with this calculation, take a peek at this hint.