The problems below are all related to "Stargazers to Starships." They are arranged in the order of the relevant sections, whose numbers are given in brackets [ ]. Re denotes Earth radius. |
Teachers using this material in class may obtain a list of solutions by regular mail, by sending a personal request on school letterhead to
Dr. David P. Stern, Code 695, Goddard Space flight Center, Greenbelt, MD 20771, USA
-  Suppose you look down on the solar system from somewhere north of it (from the direction of the star Polaris). You note that the Earth orbits around the Sun in a counterclockwise direction. If you assume the Earth is fixed and the Sun moves ("apparent motion of the Sun")--does the Sun circle the Earth clockwise or counterclockwise?
-  You have a telescope, mounted on an equatorial axis, with a clockwork to track the stars. It has crosshairs and a scale going through the middle of your image.
You suspect that the positions of stars near the horizon are shifted by refraction of light through the atmosphere. (Air refracts light much less than water or glass--but light from a star near the horizon must pass through a very thick layer.) How can you check this out, and measure the effect if it exists?
-  You are in a lifeboat boat close to the equator, somewhere south of Hawaii. The pole star is too close to the horizonto be seen, but Orion is in the sky, rather close to the horizon, too, and you know that the 3 conspicuous stars in a line, forming Orion's "belt," straddle the celestial equator. How do you find where north is?
-  Rudyard Kipling in his poem "The Road to Mandalay" (Mandalay is in Burma-Myanmar) wrote "...And the sun comes up like thunder/On the road to Mandalay."
- Is sunrise any faster in the tropics--or actually slower--or else, latitude really makes no difference? Explain.
- You are on a seashore in the tropics, watching sunset. If the bending of light in the atmosphere is neglected, and the visual size of the sun's disk is half a degree in diameter, how much time (approximately) passes from the moment the disk just touches the horizon to when the disk disappears completely?
- [2a] Can a sundial work correctly if its gnomon casts its shadow not on a horizontal surface but on a vertical one, e.g. the wall of a house? Explain.
- [2a] Suppose you have built a really big sundial, big enough to have divisions for minutes between the hour lines. You have corrected it for your position in your time zone and are taking the equation of time into account. What else may affect its accuracy?
-  A synchronous satellite keeps its position above the same spot on Earth. Is its period 24 hours or 23 hrs. 56.07 min ("star day")?
-  In one of the eclipses of 1999 the Moon is unable to cover the entire Sun. In the middle of the eclipse zone, where one would expect a total eclipse, a narrow ring of light remains, extending all the way around the dark disk of the Moon. Not knowing anything more about that eclipse, in what part of the year would you think it is most likely to be?
- (a) [8b] Could Hipparchus have used a sundial to check if the eclipses at the Hellespont and in Alexandria reached their peak at the same time?
(b) [8c] A sundial obviously won't work at night, but could Hipparchus have used an instrument tracking the positions of the stars (the way a sundial tracks the position of the Sun) to tell the duration of a lunar eclipse?
(c) [8c] Let the duration of a lunar eclipse be the time between the moment the Moon goes completely dark to the moment it begins to be uncovered; it is visible, of course, all over the Earth's night side.
Similarly, the duration of a solar eclipse would be the time between the beginning of totality anywhere on Earth and the end of totality anywhere (at a different location!). What would you think lasts longer, and why: the longest lunar eclipse or the longest solar eclipse?
- [8c] How many km equal a parsec? A light year? Take the radius of the Earth's orbit as 300 million km, the velocity of light as 300,000 km/sec. (This calculation is best done using the scientific notation for large numbers).
-  Tycho's nova had right ascension RA = 0 h, 22 m, declination d = 63° 53'. Look up a star chart--in which constellation did it occur?
-  Section #8b, about using a total solar eclipse to estimate the distance of the Moon, includes a map of the eclipse of August 11, 1999. The path of totality across the Black Sea is shown, as are samples of the region of totality at selected times. You will notice that region is nearly circular.
However, on a map of the complete path of totality (which by the way is available at the web site cited there), you will find that as you follow that path, the patch of totality becomes more and more ellipstical and elongated. By the time the eclipse ends, at sunset in India, the patch is a rather lengthy ellipse. Why? And why do you suppose the duration of the eclipse is shorter there?
-  From a handbook, the periods T in days and the distances r in millions of kilometers, for the 4 main satellites of Jupiter (known as the "Galilean satellites" since Galileo discovered them) are: