l) A solar day is the time it takes the Earth to rotate once on its axis so that the Sun returns to the same place in the sky. The solar day is exactly 24 hours long. Because the Earth travels in its orbit around the Sun a little bit each day, it takes the stars a little bit less time to return the same position in the sky, about 3 minutes and 56 seconds less. The time for the Earth to rotate so the stars are in the same position is called a sidereal day. If you have a clock with a pendulum of length 1.000000m that is keeping perfect solar time, What length pendulum do you need for the clock to have it run on sidereal (star) time? (a) (4pt) First calculate the new period in terms of the old: this is the ratio of seconds in a sidereal day to seconds in a solar day. (b) (4pt) Now calculate the new length of the pendulum. e) (Zpt) Suppose you have calibrated this clock to run at sidereal time at sea level. Most observatories are on high mountain tops, like Mauna Kea in Hawaii, which has an elevation of 14,000 feet. If you put your sidereal clock there, how will you need to adjust its pendulum length to continue keeping sidereal time? Why