ConceptCheck 1-1: While a hypothesis is a testable idea that seems to explain an observation about nature, a scientific theory represents a set of well-tested and internally consistent hypotheses that are able to successfully and repeatedly predict the outcomes of experiments and observations.

ConceptCheck 1-2: No, Jupiter does not need to be within the dot-to-dot asterism of the bull’s body; rather, Jupiter would only need to be within the semirectangular boundaries of the Taurus constellation.

ConceptCheck 1-3: As locations on Earth rotate from the dark, nighttime side of the planet into the bright, daytime side of the planet, the easternmost cities experience sunrise first. New York is the farthest east of the cities listed, so the Sun rises there first.

ConceptCheck 1-4: The Sun would still only rise and set once each day, but each year would have 3 times more days (365 × 3 = 1095 days each year).

ConceptCheck 1-5: The celestial equator is an extension of Earth’s equator up into the sky. In order for this imaginary line to pass directly overhead, one would need to be standing somewhere on Earth’s equator.

ConceptCheck 1-6: No, they would not; in this imaginary scenario, the Sun would rise and set every 12 hours all year long. Earth’s tilted axis means that observers at Earth’s north pole will experience six months where the Sun never rises (when it is tilted away from the Sun) and then six months when the Sun never sets (when it is tilted toward the Sun).

ConceptCheck 1-7: The Sun slowly moves toward the eastern part of the sky a little each day, taking 365¼ days to return to the same place it was one year earlier.

ConceptCheck 1-8: As the Sun’s position on the celestial sphere slowly moves back and forth between the northern and southern solstice points over the course of a year, the noontime Sun will be directly overhead and cast no shadow for an observer at Earth’s equator only twice each year, on the March and September equinoxes.

ConceptCheck 1-9: Because the Moon is always illuminated by the Sun, it is always half illuminated and half dark. Except in the rare events of eclipses, the Moon’s apparent changing phases are due to observers on Earth seeing differing amounts of the Moon’s half-illuminated surface.

ConceptCheck 1-10: 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 1-11: 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.

ConceptCheck 1-12: 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.

ConceptCheck 1-13: Lunar eclipses only occur when the Sun, Earth, and Moon are all exactly in a line, the line of nodes. 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 1-14: The eclipsing Moon spends more time in the penumbral shadow because Earth’s penumbra is much larger than the umbra.

ConceptCheck 1-15: Total solar eclipses are only observed in the small region where the Moon’s tiny umbral shadow lands on Earth, 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 1-16: A total lunar eclipse can last for more than an hour, but a total solar eclipse lasts only a few minutes.

CalculationCheck 1-1: Earth rotates once in about 24 hours, so when the stars of Cygnus rise in the east at sunset, they take about 12 hours to go from one side of the sky to the other. As a result, it takes about half that time, or six hours, for stars of Cygnus to move halfway across the sky.

CalculationCheck 1-2: The northern solstice occurs on about June 21 and the March equinox occurs about March 21, so there are about nine months or 270 days between these two events.

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