Answers

ConceptChecks

ConceptCheck 3-1: Because the Sun is always shining on the Moon, the Moon is always half illuminated and half dark. Except in the rare events of eclipses, discussed later, the Moon’s apparent changing phases are due to observers on Earth seeing differing amounts of the Moon’s half illuminated surface.

ConceptCheck 3-2: The Moon goes through an entire cycle of phases in about four weeks, so if it is currently in the waxing crescent phase, in one week it will be in the waxing gibbous phase, and after two weeks it will be in the waning gibbous phase.

ConceptCheck 3-3: The Moon is shown at four points of its orbit in Figure 3-4b. In the left position, the far side is fully dark.

ConceptCheck 3-4: If the Moon is full, then after one week, it would reach the third quarter phase, and the point that used to be in the center of the Moon’s visible surface at full moon would now fall into darkness that would last for two weeks. This scenario can be seen in two figures: In Figure 3-4b, this scenario is shown by the red dot on the leftmost depiction of the Moon, and the Moon’s position a week later at the bottom of the figure. In Figure 3-2, this scenario occurs between positions E and G.

ConceptCheck 3-5: Increase. If Earth was moving around the Sun faster than it is now, Earth would move farther around the Sun during the Moon’s orbit and it would take longer for the Moon to reach the position where it was in line with the Sun and Earth, increasing its synodic period. This is illustrated (for the new moon) in Figure 3-5.

ConceptCheck 3-6: Lunar eclipses only occur when the Sun, Earth, and Moon all lie exactly on a line; this line is called the line of nodes. As shown in Figure 3-7, during a full moon the Sun, Earth, and Moon are not necessarily lined up because the Moon orbits in a different plane than the ecliptic. Usually, the full moon is above or below the ecliptic plane of Earth’s orbit around the Sun and misses being covered by Earth’s shadow.

ConceptCheck 3-7: No. Before the Moon passes into the full shadow (the umbra), where the Sun is completely blocked by Earth, the Moon must pass through the penumbra where only part of the Sun is blocked. This is illustrated by Path 2 in Figure 3-8.

ConceptCheck 3-8: Total solar eclipses are only observed in the small region where the Moon’s tiny umbral shadow lands on Earth (see Figure 3-11), whereas when the Moon enters Earth’s much larger umbral shadow, anyone on Earth who can see the Moon can observe it in Earth’s shadow.

ConceptCheck 3-9: A total lunar eclipse can last for more than an hour whereas a total solar eclipse lasts only a few minutes.

ConceptCheck 3-10: If the noontime position of the Sun on the summer solstice was much closer to being directly overhead, it means that on the curved surface of Earth, the overhead directions at both Syene and Alexandria are pointing in similar directions. This scenario does not occur on Earth and would only do so if Earth were much larger. (Keep in mind that the distance between these two cities is assumed to be constant for this question, no matter what the size of Earth.)

CalculationCheck

CalculationCheck 3-1: Because their diameters must be in the same proportion as their distances, if Aristarchus assumed the Sun to be 100 times farther away when the Sun and Moon appeared to be the same diameter in the sky, he would have proposed that the Sun is 100 times wider than the Moon. Today we know that the Sun is about 400 times farther away from Earth and 400 times wider than the Moon.