Problem Set Number 1
Due in recitation Friday, September 12 or Monday, September 15
- (10 points) On the following sketch of the celestial sphere, add
- The axes.
- The celestial equator.
- The north and south celestial poles.
- The ecliptic.
- The vernal and autumnal equinoxes.
- The stars Vega, Sirius, Betelgeuse, and Alpha Centauri (note
that you'll need to look up their coordinates in your textbook).
- The path of the Sun over the course of a year (be sure to
indicate the direction of motion).
- The position of the Sun on the day you complete this problem
- The part of the sky that is dark on that same day.
- (10 points) Describe the approximate direction, in horizon
of the sunrise from the following locations on the given dates. Tell a
about why this sunrise might be unusual (if at all). Also estimate how
it takes for the Sun to clear the horizon (the Sun has an angular
about 0.5 degrees).
Why might people at the North Pole be very happy about sunrise on March
And why might astronomers at the South Pole also be happy on that same
- Sunrise from here in Ames on September 21.
Rises due East (Azimuth 90
degrees) and takes a few minutes to rise (a bit more than 2 minutes)
and rises at an angle of 48 degrees to the horizon.
- Sunrise viewed from the Earth's equator on September 21.
Also rises due East (azimuth
90 degrees), and rises faster than in Ames (2 minutes) as it goes
- Sunrise from the North Pole on March 21.
Well... the Sun's motion away
from the horizion is caused by the changing angle with the Earth; so it
takes about 2 days to rise (23.5 degrees covered in 3 months from
equinox to solstice, so 2 days to cover the 1/2 degree).
- Sunrise from the South Pole on September 21.
Same as part c.
After 6 months below the horizon,
that first view of the sun must be almost miraculous! Similarly,
astronomers at the South Pole say goodbye to the sun and can look
forward to several months of nightime observing with no breaks (except
for clouds, snowstorms, and rampaging penguin attacks).
- (4 points) It is an unwritten rule in baseball that the
the diamond points northeast - that is, the line starting at home
running in the direction of second base, usually points to an azimuth
about 45 degrees. Speculate on why that might be, given the usual
of the batter and fielders and the direction of their gazes. Remember
baseball traditions mostly originated before stadium lights were
i.e. think of day games.
The most vulnerable player on the
field is the batter - s/he faces the pitcher and must hit (or run away
from) the pitch coming at him/her at high speeds. The batter must
not have the sun in his/her eyes, and if the field points to the
northeast, the sun will always be behind the hitter. The right
fielder must simply cope.
- (10 points) What is the altitude of the noon Sun on the following
dates at these locations?
- Ames, IA (lat 42 deg N, long 93 deg W) on March 21, June 21,
September 21, December 21
48 degrees (90 - latitude);
48+23.5=71.5 degrees; 48 degrees; 48-23.5=24.5 degrees
- Tromso, Norway (lat 72 deg N, long 21 deg E) on March 21,
June 21, September 21, December 21
18 degrees (90 - 72);
18+23.5=41.5 degrees; 18 degrees; 18-23.5=-5.5 degrees (below the
- Key West, FL (lat 23.5 deg N, long 80 deg W) on March 21,
June 21, September 21, December 21
66.5 degrees (90-23.5); 90
degrees (right overhead!); 66.5 degrees, 66.5-23.5=43 degrees
- (6 points) Explain why the sidereal month is shorter than the
month. You will need to explain the meaning of the two months in your
answer. Why is the difference between the two types of months 2 days,
not, say, 4 or 6?
The siderial month is the time it
takes the moon to orbit the Earth relative to the stars. Once it
does so, however, the Sun has moved farther East and so some more time
is needed for the moon to catch up to the Sun - the synodic
month. As it takes 27.3 days for a siderial month, in that time
the sun has moved about 26 degrees farther East. At the rate
the moon moves (13 degrees per day) it takes the moon 2 more days
to catch up the lost ground.