ConceptCheck 3-1: If the noontime position of the Sun on the summer solstice was much closer to being directly overhead, he would assume that Earth was much larger because Earth’s surface between the two cities would be much less curved, implying a much larger, circular Earth.

ConceptCheck 3-2: When astronomers say a planet is moving retrograde, a planet is observed night after night to be slowly drifting from east to west compared to the very distant background stars. This is opposite how it typically appears to move. Regardless, all objects always appear to rise in the east and set in the west on a daily basis.

ConceptCheck 3-3: The Greeks’ ancient geocentric model used a nonspinning, stationary Earth where the stars, planets, and the Sun all moved around Earth.

ConceptCheck 3-4: In the Ptolemaic model, the planets are continuously orbiting in circles such that they appear to move backward for a brief time. However, the planets never actually stop and change their directions.

ConceptCheck 3-5: No. Planets only appear to move in retrograde motion if seen as two planets moving at different speeds passing one another. An imaginary observer on the stationary Sun would only see planets moving in the same direction as they orbit the Sun.

ConceptCheck 3-6: When Venus is visible in the western sky, it is at its greatest eastern elongation and the faster-moving Venus has not yet caught up with Earth, as Earth is momentarily in front of Venus as they orbit the Sun.

ConceptCheck 3-7: Mars has an orbit around the Sun that is larger than Earth’s orbit. As a result, Mars never moves to a position between Earth and the Sun, so Mars never is at inferior conjunction.

ConceptCheck 3-8: In Copernicus’s model, the more distant planets are moving slower than the planets closer to the Sun. As a faster-moving Earth moves past a slower-moving Mars, there is a brief time in which Mars appears to move backward through the sky. However, the planets never actually stop and change their directions.

ConceptCheck 3-9: Slowly moving Jupiter does not move very far along its orbit in the length of time it takes for Earth to pass by Jupiter, move around the Sun, and pass by Jupiter again, giving Jupiter a synodic period similar to Earth’s orbital period around the Sun. In much the same way, slow-moving Jupiter takes more than a decade to move around the Sun back to its original starting place as measured by the background stars, giving it a large sidereal period.

ConceptCheck 3-10: Copernicus’s model was no more accurate at predicting the positions and motions of the planets than Ptolemy’s model. However, Copernicus’s model turned out to be more closely related to the actual motions of the planets around the Sun than was Ptolemy’s model of planets orbiting Earth.

ConceptCheck 3-11: When Venus is on the opposite side of the Sun from Earth, it will be in a full or gibbous phase. The full phase can occasionally be observed because Earth and Venus do not orbit the Sun in the same exact plane.

ConceptCheck 3-12: Galileo was the first person to use and widely share his observations using a telescope, which is necessary in order to observe Jupiter’s tiny moons.

ConceptCheck 3-13: An ellipse with an eccentricity of zero is a perfect circle and, compared to Mars’s e = 0.093, the eccentricity of Venus’s orbit is e = 0.007. Venus has an eccentricity value closer to zero so its orbit is closer to a perfect circle in shape.

ConceptCheck 3-14: Kepler’s second law says that objects are moving slowest when they are farthest from the object they are orbiting, so an Earth-orbiting satellite will move slowest when it is farthest from Earth.

ConceptCheck 3-15: According to Kepler’s third law, planets closer to the Sun move faster than planets farther from the Sun. For objects orbiting Earth, the object closer to Earth’s surface is also moving the fastest, which, in this case, is the space shuttle.

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ConceptCheck 3-16: No. Kepler’s laws of planetary motion apply to any objects in space that orbit around another object, including comets orbiting the Sun, man-made satellites and moons orbiting planets, and even stars orbiting other stars.

ConceptCheck 3-17: According to Newton’s first law, if no outside forces are acting on an object, then it will remain in that state of motion. In other words, a spacecraft in outer space will continue at the same speed as it moves far from our Sun’s gravitational influence.

ConceptCheck 3-18: Newton’s third law states that when one object exerts a force on another object, the second object exerts an equal but opposite force on the first. In other words, if the astronaut touches the door, the door touches the astronaut. The fact that the forces are equal does not mean that the “effects” are equal. If the only force on the door is the one applied by the astronaut, the door will move, following Newton’s laws of motion.

ConceptCheck 3-19: According to Newton’s universal law of gravitation, the gravitational attraction between two objects depends on the square of the distance between them. In this case, if the asteroids drift 3 times closer together, then the gravitational force of attraction between them increases 3² times, or, in other words, becomes 9 times greater.

ConceptCheck 3-20: The International Space Station has an initial forward velocity such that as it falls around Earth, it actually misses Earth because Earth’s round surface is curved away.