Homework Assignment 3
Physics 55
Made available: Tuesday, September 13, 2005
Due in class on: Monday, September 19, 2005
Problem 1: Some Shorter Problems
1. Two celestial objects in your local sky have the same direction but altitudes of 59 ◦ 230 500 and 36◦ 420 2700 .
What is the angular separation of these two objects in terms of minutes, arcminutes, and arcseconds?
Hint: You can write 230 500 as 220 6500 since 10 = 6000 . This is similar to “borrowing a 10” when
performing a subtraction like 24 - 19.
2. If the Earth’s rate of rotation about its axis were to decrease, describe how the sidereal day and solar
day would change: do they become longer, shorter, closer in duration? Repeat for the synodic month
versus sidereal month.
3. On November 1 at 8:30 P.M., you see the bright star Bellatrix (a shoulder star of the asterism Orion)
rising from the East. At about what time will Bellatrix rise one week later on November 8?
4. By taking into account the fact that the planet Saturn follows the ecliptic on the celestial sphere,
explain whether or not there is a place on Earth such that Saturn will never appear in the evening sky.
5. What is the altitude and direction of the Sun in your local Durham sky at noon during the winter
solstice? Explain your reasoning and include a drawing as part of your explanation.
6. Jupiter’s moon Ganymede has a greater average distance from Jupiter than Jupiter’s moon Io.
(a) Describe what kinds of phases Ganymede will undergo as seen by someone on Io and describe the
perceived size of Ganymede during its different phases.
(b) Explain whether or not Ganymede will undergo retrograde motion as seen by someone on Io.
7. Do Problem 26 on page 109 of the text.
Problem 2: Practice With Right Ascension and Declination
Answer the following questions by referring to this table of stellar celestial coordinates. Justify each answer
with a brief explanation.
Star
Alpha Centauri
Deneb
Sirius
Spica
Vega
RA
14h 38m
20h 41m
6h 45m
13h 25m
18h 36m
1. Which star is closest to the spring equinox?
1
Dec
−60◦380
+45◦060
−16◦420
−11◦200
+38◦470
2. Which star or stars can never be seen at Durham’s latitude of 36◦ N?
3. Which star remains above the horizon for the longest time each day at Durham’s latitude of 36 ◦ N?
4. Which star will cross your meridian first in Durham, Deneb or Vega?
5. Which star passes nearest to your zenith at Durham’s latitude of 36◦ N?
6. Which star will be nearest to your meridian if you are looking at the sky about midnight on the winter
solstice?
Problem 3: Optional Extra Credit Problems
1. The dividing line between the illuminated and unilluminated halves of the Moon is called the terminator
(no relation to Arnold Schwarzenegger). As you can see from Fig. 2.21 on page 42 of the text, the
terminator appears curved when there is a crescent or gibbous Moon, but appears straight when there
is a first quarter or third quarter Moon. Using these facts, explain why it is not possible for the
phases of the Moon to be caused by the Earth’s shadow falling on the Moon (which is a common
misunderstanding of why the Moon has phases).
2. A sidereal clock such as those used by astronomers at observatories uses 24 hours to span a sidereal
day, just as a solar clock also uses 24 hours. (See Mathematical Insight S1.1 on page 97 of the text.)
While a solar day is defined to be the amount of time from one noon to the next (Sun crossing the
meridian), a sidereal day is defined to be the time from one midnight to the next, where midnight
12:00 is defined to occur when the vernal equinox on the celestial sphere crosses the meridian.
(a) Given this fact, what is the sidereal clock time when the vernal equinox rises in the east?
(b) On what day of the year will a sidereal clock and a solar clock have nearly the same times for
most of that day? When will the two clocks exactly agree on that day?
3. Look up a book on spherical trigonometry. Explain how a triangle ABC can be defined on the surface
of a sphere by interconnecting any three points on a sphere by arcs of great circles. (Such arcs are
the equivalent of straight lines in a plane since such arcs are the shortest curves on a sphere that
lies between any two points on the sphere.) Summarize how various famous results from Euclidean
geometry hold or don’t hold for spherical triangles: are the sum of interior angles equal to 180 ◦ ? Does
a law of sines and law of cosines hold for spherical triangles? If so, give a derivation of these laws.
We will discuss the geometry of triangles on spheres and on other curved surfaces later in the semester
when we discuss Einstein’s general theory of relativity, which says that gravity arises from a nonEuclidean geometrical warping of space-time.
Problem 4: Comments about the Homework and Course
• About how long did this assignment take to complete?
• Do you feel that you are understanding the course material? If not, please indicate what topics or
ideas you would like to understand better.
• Other comments or suggestions about the homeworks, lectures, or observation sessions?
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