Science of Easer Problem Set – Due 18 April 2013
Goals: 1) Solve a different cultures astronomy problem. 2) Look at the interaction between science, religion and culture. 3) Practice making scientific models based upon observations.
1) (25 points) A major problem in Medieval European astronomy was to predict when Easter would occur. This involved finding when the lunar calendar (cycle) would sync up with the solar calendar (cycle). This problem was not unique to Medieval Europe. Often a culture’s oldest calendar is a lunar calendar. Then most cultures adopt a solar calendar. The culture will want to celebrate the old holidays (tied to the phase of the moon) at the same time of year (spring, summer, etc.) Medieval European astronomers were asked to predict when the first full moon will be after the first day of spring (vernal equinox). During this time Europe used the Julian year. The Julian calendar reform established a cycle of 3 years of 365 days followed by a leap year of 366 days so that the average year in a four year period would be 365.25 days long, i.e. the time from one vernal equinox to the next is 365.25 days. We will use the same solar calendar. For the time from one full moon to the next we will use a more exact number, 29.53059 days. The main question is, do these two calendars sync up with each other? Namely are there two integers, M and N, such that M years and N months have the same number of days? If so then after M years Easter will once again occur on the same day. It turns out there is not an exact answer to this problem. THE TRIVAL SOLUTION (0 YEARS, 0 MONTHS) IS NOT AN ACCEPTABLE ANSWER.
A) Find two sets of (M,N) such that the number of days in M Julian years and N months are nearly equal with the additional conditions that M is less than 100 and both M and N are integers. M1 and M2 not multiples of each other.
B) Pick one of the two sets as the correct answer. What is (are) your reasons for doing so?
2) Medieval astronomers found out that the real year is slightly less than the Julian year. To four decimal places the real year is 365.2422 days long while the Julian year is 365.25 days long. (10 points)
a) In one year, what is the percent error in the Julian calendar?
b) In one year, what is the absolute (in minutes and seconds!) error in the Julian calendar?
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Science of Easer Problem Set – Due 18 April 2013
3) Medieval astronomers also determined the length of the seasons. How long, in days, are each of the astronomical seasons? Note: Spring is the time from the vernal equinox (first day of spring) to the summer solstice (first day of summer), Summer is the time from the summer solstice to the autumnal equinox (first day of fall), etc. (10 points)
4) Greek astronomy, which formed the basis for medieval astronomy, tried to build a cosmology consistent with the following assumptions/observations:
a) The Earth does not move.
b) The Earth is the center of the solar system.
c) Objects in the sky move in circular paths. N.B. circular path not necessarily the same as a complete circle.
d) Objects in the sky moved with uniform circular motion along those circular paths.
Can you build a model of the Sun – Earth system considering only the annual motion of the Sun that is consistent with your answer in (3) and the above assumptions? If not, build one that is consistent with as many as possible of the above assumptions. Which one(s) do you have to violate, and why? (25 points)
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