Answer
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Work Step by Step
a) For any observer, a full moon will be rising when the sun is on the opposite side of the moon when the sun, earth, and moon are positioned in one straight line. Here, the sun fully illuminates the moon's surface as seen by the observer and when the sun is setting, the full moon is just rising.
b) Figure 5-31b shows the positions of the sun, moon, and earth one day later. Because it takes the moon 24 hours and 50 minutes to reach the same position in the sky each day, the moon is not yet visible.
c) At b, the red dot is on "top" of the earth because after 24 hours, the earth completes one revolution about its axis. At (e), 29.53 days have passed, so the earth has completed a little more than half of a revolution meaning the same location must be near the bottom as shown.
D) at (d), the earth has completed 27.32 revolutions. It takes approximately 365.25 days to complete 360 degrees, which means 1 day is equal to $0.986^o$. This multiplied by 27.32 days is $26.96^o$. Therefore, the angle between the lines that connect from the center of the sun to the center of the earth at points a and d is $26.96^o$.
The earth takes 1 day to complete 1 revolution. $1 d = 360^o$
$0.32d=115.2^o$
The location of the red dot will be $115.2^o+26.96^o=142.16^o$ from the location of the tangent to the earth's surface which is parallel to the line through the moon, sun, and earth in part a. Therefore, it will be where the small black arrow is pointing.