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| Overview of the Sky |
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1. | What is the declination of a star that lies on the celestial equator? |
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2. | The Small Magellanic Cloud lies at a right ascension of approximately 1 hr 30 min and a declination of -75°. In which hemisphere of the sky is the Small Magellanic Cloud found? Can it ever be seen from 36° N latitude? (Why or why not?) Sketch its location on the celestial sphere. How long after the vernal equinox crosses the celestial meridian will the Small Magellanic Cloud cross the celestial meridian? |
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3. | What is the angular speed (in degrees per day) of the Sun's eastward motion relative to the stars? |
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4. |
You may have some familiarity with the story of the Titanic, which sank in the
North Atlantic about 400 miles off Newfoundland at 2:20 AM local time on April 15,
1912. (See
http://titanic.eb.com
for a Brittanica summary.)
The survivors spent over an hour on the ocean before being rescued by the
Carpathia at about 4 AM.
Many remembered seeing very bright stars low in the south after the sinking,
which were especially clear because the Moon was very close to new.
The Mount Wilson Observatory maintains an interactive star map generator. This can be used to produce an image of the sky as seen by the lifeboat passengers after the sinking of the Titanic. You need only enter the date 04151912 (15 April 1912), the Universal Time (time in London: 0600 will suffice), and the latitude in degrees (41.5) and longitude (50.2), choose "Equator" reference lines, and select "Submit Query." The map is about 250 K. It is in Postscript format, which can be viewed with a Postscript viewer or printed with a Postscript-capable printer. If your computer doesn't have a Postscript viewer installed, you may download the viewer Ghostview for free. Once the map downloads, note the phase of the Moon and the bright southern stars. Can you identify the bright constellations seen just above the southern horizon? |
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5. | Of the seven planets of the ancients, which ones never undergo retrograde motion? Why not? |
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6. | What is the angle in our sky between Venus and the Sun when Venus is at full phase? When will Venus be seen in quarter phase? |
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7. | Sketch the alignment of the Sun, Venus, and the Earth when Venus is in the new phase. If Venus' sidereal period is 225 days and its synodic period is 584 days, how often will Venus be in new phase? |
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8. | Draw a sketch showing why Venus could never be at an angle of 90° or 180° from the Sun. Could Mars? |
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9. | What phase will Jupiter be in when it is at conjunction? At opposition? Why? |
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10. | What is the angle in our sky between Mars and the Sun when Mars is at opposition? At opposition, what times will Mars rise and set? |
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11. | If Mars is at quadrature, what is the angle between Mars and the Sun in our sky? When will Mars rise and set if it is at quadrature and lies east of the Sun? West of the Sun? |
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12. | What is the maximum elongation of Mercury? At maximum elongation, how long after sunset will Mercury set? Is it east of the Sun or west of the Sun if it sets after the Sun sets? |
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13. | What is the maximum elongation of Venus? How long before sunrise will Venus rise if it is a "morning star"? Is it east or west of the sun? Considering that astronomical twilight lasts at least 45 minutes, which of these two planets is more easily seen in a dark sky? |
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14. | Suppose you observe a crescent Moon in the Northern Hemisphere. If you went immediately to the Southern Hemisphere, would you expect the appearance of the Moon in the sky to change? |
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15. | If the star Procyon is located on your celestial meridian, what is the sidereal time at your location? |
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16. | According to our clocks, the stars rise about four minutes earlier each night. Why? |
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17. | What is the average speed of the Moon on its orbit around the earth in km/sec? Hint: assume the orbit to be a circle. |
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18. | How long does it take the Moon to move five times its diameter on the celestial sphere relative to the background stars? |
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19. | What is the angular speed of the Moon's eastward motion relative to the stars? How far does the Moon move in one hour? |
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20. | Because of tidal interaction with the Moon, the Earth is slowing in its rate of rotation and the day is gradually lengthening by about 0.002 seconds per day each century. At this rate, how long until our clocks will need 25 hours rather than 24? |
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21. | What is the angular size of the Sun and the Moon in our sky? What does this fact tell us about the relationships of their distances? |
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22. | What is the size of the Moon's shadow on Earth under the best alignment conditions producing a solar eclipse? |
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23. | Why do we not have eclipses every month? |
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24. | Go to the Dome of the Sky. Use the information available there to determine the linguistic origin of the names for the following stars: Betelgeuse, Sirius, Altair, Regulus, Acrux, and Rigel Kentaurus. |
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25. | Go to the Dome of the Sky. Use the information available there to determine the linguistic origin of the names for the following constellations: Pisces, Orion, Andromeda, Pavo, and Tucana. |
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26. |
We will use the
Earth Viewer
for this exercise.
You can simulate the view of the Earth from the Sun by going to the Earth Viewer address
which will give on each view the latitude and longitude directly under the Sun. Likewise, the address
will give the same information for a view of the Earth from the Moon. Use a latitude-longitude map of the Earth and plot the position of the Moon and the Sun on it over a period of a month. The more "observations" the higher the quality of the plot, but you should try to make at least three or four approximately equally spaced observations for each day. (Note: the size of the Earth in these views is not to scale.) |
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27. | At closest approach to Earth, Mercury has an angular diameter of 13 seconds of arc and the distance is 0.52 AU. Use this to calulate the diameter of Mercury, assuming it to be spherical. |
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28. | Calculate the angular diameter of the Moon on the celestial sphere at apogee and perigee. |
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29. | Suppose you were to stand on the Moon and view the Earth from a fixed spot for several days. Describe the motion of the Earth. |
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30. | Use the links to tidal stations to keep a daily record of high and low tides at several tidal stations. Use the Solar System Live link to determine whether tides are abnormally high or low when the Sun reinforces or counteracts the tidal effect of the Moon (spring and neap tides) |
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31. | There is evidence that ancient astronomers knew about Mercury, but thought that it was two planets. Why do you think they thought that? |
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32. | Under the most favorable circumstances, how long could Mercury be visible between sunset and when it sets? What about Venus? |
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33. | What do you think was the longest natural time scale commonly observable in the sky for the Ancients? |
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34. |
Is the following image of Saturn taken from Earth or from a
spacecraft (Hint: the image contains all the information
that you need to answer the question.)
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35. | What would be the standard Bayer system name for the fifth brightest star in the constellation Canis Minor? What about the third brightest star in Aquarius? |
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36. | In old alamanacs the full Moons for each month were given certain names. A few such names, like the Harvest Moon, which is the first full Moon after the autumnal equinox, still are used. One old name for a full Moon in December was the Long Night Moon. Can you think of a good reason for that name? |
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37. | Consider the general expression for the synodic period of a planet as viewed from Earth. What happens to the synodic period in the two limits that the sidereal period is either much larger or much smaller than that for the Earth? Which limit is more important in the Solar System? |
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38. | Consider the general expression for the length of the solar day for a planet. Describe the following two limits of the expression for the solar day, both mathematically and in physical terms: (a) the sidereal rotational period is much longer than the sidereal period of revolution; (b) the sidereal rotational period is much shorter than the sidereal period of revolution. Can you see a condition that would cause the length of the solar day to become infinite? Can you give a physical interpretation for this case? |