Homework #4: Solutions
Astro 10, spring 2010
General Notes to Graders:
If numerical answers are roughly correct, do not take marks off.
Award part marks if the student has made some progress with the question. Be generous.
1. [5 points]
Estimating by eye, the angle covered by the star trails is roughly 30 degrees. In one sidereal
day, the stars make one complete revolution around the North Celestial Pole, so 360 degrees
corresponds to 23 hours and 56 minutes (one sidereal day). Therefore the exposure time is
t
exp
= (1436 min)
·
30
◦
360
◦
= 119
.
7 min
This is a rough estimate though, so we will say that the exposure lasted
about 120 min = 2 hours.
Notes to graders:
This is a rough estimate from a photograph, so any angle between 20 and 40
degrees is ﬁne. This will result in answers between 1 hour, 20 min and 2 hours, 40 min. Answers
within this range should receive full credit. Also, the students need not use the sidereal day to
receive full credit  just 24 hours for 360 degrees is ﬁne.
2. [5 points]
If you see the quarter moon around sunset, it must be the ﬁrst quarter moon. You can see this
by looking at Figure 42 on page 66 in the textbook: the ﬁrst quarter moon is directly overhead
at 6:00 PM while the third quarter moon is directly overhead at 6:00 AM. Therefore, since you
are seeing the ﬁrst quarter moon, in a week (about one quarter of the lunar cycle) the full moon
will be up.
Notes to graders:
Students must have a discussion equivalent to this in content for full credit.
3. [10 points]
The way to think about this is to visualize the whole Moon phase cycle (see page 66 in text
book). If you were on the Moon while it was in its full phase, both the Earth and Sun would be
in the same direction. Thus the Earth would be in a new phase
from your perspective!
. If you
were on the Moon during its new phase, the Earth and Sun would be in opposite directions 
therefore Earth would be in a full phase
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 Spring '06
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 First Quarter Moon

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