Working with others is all right, but do not just copy someone's answer; make sure that you understand the question and your answer. See me if you have any questions. Please hand in your work on time. You will lose credit for late homework as described in the syllabus. The number in parentheses after the problem number is the points allotted for each problem. Give your reasoning when necessary. (52 points total)
1.(2) At what location on Earth does the celestial equator pass through the zenith?
2.(2) At the present time, two stars in the Big Dipper can be used as pointers for the star Polaris (also named alpha Ursae Minoris). Would they be pointers for this star (alpha Ursae Minoris) in the year 2500 BC? Why?
3.(4) (a) The star Sirius is observed to undergo heliacal rising on a particular day. How many days later does it undergo heliacal rising again? (b) The planet Venus is observed to undergo heliacal rising on a particular day. How many days later does it undergo heliacal rising again? Here, heliacal rising refers to first appearance in the morning sky.
4.(6) (a) Where do you have to be on Earth in order to see the south celestial pole directly overhead? (b) What is the maximum possible altitude for the Sun above the horizon at that location? (in degrees) (c) On what date is this maximum altitude achieved?
5.(2) What point in the sky on the celestial sphere remains fixed in the sky relative to an observer's horizon throughout the night.
6.(2) At what time of day does the new Moon rise above the horizon? (on average)
7.(2) What is the phase of the Moon if, on the first day of autumn, the Moon is located at the vernal equinox?
8.(2) A lunar eclipse occurs on June 21. What is the approximate declination of the moon?
9.(2) Astronauts are sent to the moon at the time of new moon. When they look back at the Earth, what is the phase of the Earth's illumination?
10.(2) Over a period of a year, what fraction of the celestial sphere can be observed by a person at the equator? By a person at the North Pole?
11.(2) The latitude of Charlottesville is 38 degrees N. If the obliquity of the Earth were 45 degrees, would the Sun be observed to go through the zenith during the year for an observer here? Why?
12.(2) The change in the declination of the Sun between September 21 and December 21 is approximately how many degrees?
13.(2) What is the phase of the Moon during a total lunar eclipse? During a total solar eclipse?
14.(2) Assume Mars is at opposition on December 21. What is its approximate declination?
15.(4) On what day(s) of the year will your shadow in sunlight at midday be shortest if you live (a) in Sydney, Australia (b) on the Earth's equator?
16.(4) (a) You are on the Arctic Circle. What is the maximum altitude that the Sun ever attains in the sky during a year. (b) You are on the Tropic of Cancer. What is the maximum altitude that the Sun ever attains in the sky during a year.
17.(2) How many times does Venus come into opposition with the Sun in one synodic period for Venus?
18.(4) The declination of Sirius is -17 degrees (17 degrees South). (a) From our latitude (38 degrees North), what is the maximum altitude that Sirius reaches above the horizon? (b) From Sydney, Australia (latitude 34 degrees South), what is the maximum altitude that Sirius reaches above the horizon?
19.(2) At Stonehenge, the full Moon is observed at the very maximum northerly point for the Moon. What is the approximate time of year?
20.(2) In what latitude range do you have to live in order for the Moon to pass directly overhead at some time during a 20 year period? Give your reasoning.