Homework 6: Due Wednesday, February 25, 2004

1. Is the full moon at midnight high in the sky in the summer or the winter? Justify your answer.

The full moon is opposite the sun in the sky. So when the sun is high in the sky (as it is in the summer), the full moon is low. When the sun is low in the sky (as it is in the winter), the full moon is high. Think about a moonlit night during a snowy winter. Part of the reason that moonlit nights are so spectacular in the winter is the fact that the full moon is so high.

2. If you lived on the Moon

a. would you see the Sun rise and set, or would it always be in the same place in the sky? Explain.


The sun would rise and set but it would take roughly a month to do so.

b. Would you see the Earth rise and set, or would it always be in the same place in the sky? Explain.

The earth would always be visible although the moon would see the lit earth part of a month and a dark earth part of a month.

3. Suppose it is the first day of spring in the northern hemisphere. What is the phase of the Moon if the Moon is located at a) The vernal equinox?
   

   Look at the diagram above. The Sun is in front of the vernal equinox on the day of the vernal equinox. The moon is in front of the vernal equinox--this was given in the problem. In this case the moon is new.

   b) the summer solstice?


Look at the diagram above. The sun is in front of the vernal equinox because the date is the vernal equinox. The moon is in front of the summer solstice. In this configuration the moon is at first quarter.
4. Suppose that Sirius is at your zenith at 9 P.M. Greenwich sidereal time. Where on earth are you located? (Give both latitude and longitude).

   The declination of Sirius is -16^o45'. So we are at 16^o 45' S latitude. The right ascension of Sirius is 6 hrs 45 minutes. Therefore the sidereal time is 6 hrs 45 minutes. The sidereal time in Greenwich is 21 hours. This means that we are 9 hours 45 minutes east of Greenwich. Now

   9.75/24=x degrees longitude/360^o. Thus x=146^o East.

5. a). Calculate, using a diagram, the length of a synodic month given that a sidereal month is 27.32 days b) Given that a sidereal month is 27.32 days, how much earlier does the moon rise everyday. I want to see your calculation here, not just an answer. Does your result agree with the Sky-Gazer's Almanac?
   -+

   Consider the diagram above. In 27.3 days the earth goes roughly 27 degrees around the sun. This is one sidereal month. In order to go from new to new (a synodic month), the moon must revolve an extra 27 degrees around the earth. The moon takes 27.3 days to go 360 degrees. 27.3/360=x days/27. x=2 days. So a synodic month is roughly 2 days longer than a sidereal month. If you look on your Star Gazer's Almanac, you will see that it takes roughly 29 days to go from full to full (a synodic month) so our calculation looks good.

   How much earlier does the moon rise every day?

   In one day the moon revolves (1/27.3) x 360 degrees=13 degrees. It takes the earth (13/360) x 24 hours = .87 hours = 52 minutes to rotate through 13 degrees. So the moon rises roughly 50 minutes later each day.