Kepler's Laws

Which of the following statement is best in accordance with Kepler's first law of planetary motion?

• A. The orbits of planets form an ellipse, with the Sun at one focus.

• B. Planets orbit in perfect circles, with the Sun slightly off-center.

• C. All planets make one orbit of the Sun in exactly the same time period.

• D. Planets farther from the Sun orbit proportionally faster.

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How do Kepler’s laws of planetary motion compare to Newton’s laws of motion and Newton’s law of universal gravitation?

• A. Kepler described Earth’s orbit around the Sun. Newton described the Moon’s orbit around Earth.

• B. Kepler explained only the shape of Earth’s orbit. Newton explained only Earth’s speed in orbit.

• C. Kepler explained the effect of gravity on Earth’s orbit around the Sun. Newton explained the

  effect of the Moon’s gravity on the Sun.

• D. Kepler described the shape and speed of Earth’s orbit around the Sun. Newton identified the

  forces that cause Earth to orbit the Sun.

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The diagram below shows four points along Earth's orbit as it revolves around the Sun. The shaded area in the sector bounded by Points 1 and 2 is the same as the shaded area in the sector bounded by Points 3 and 4.

Which statement accurately compares the conditions at these four points?

• A. The magnitude of Earth's acceleration is the same at all four points.

• B. The Sun's gravitational pull on Earth is the same at Point 1 as it is at Point 3.

• C. Earth's speed is the same as it goes from Point 1 to Point 2 as when it goes from Point 3 to Point 4.

• D. It takes Earth the same amount of time to go from Point 1 to Point 2 as it does to go from Point 3 to Point 4.

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According to Kepler’s first law, orbiting planets follow an elliptical path with the Sun at one of the focal points of the ellipse. Kepler’s second law states that a line from the Sun to the planet must always pass over an equal amount of area in an equal amount of time. Based on this information,

which statement best describes the relationship between the speed of a planet and its distance from the Sun?

• A. The speed of a planet is constant as it orbits the Sun.

• B. The changes in the speed of an orbiting planet are independent of its distance from the Sun.

• C. Planets move at higher speeds when they are close to the Sun and lower speeds when they are far from the Sun.

• D. Planets move at lower speeds when they are close to the Sun and higher speeds when they are far from the Sun.

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The table below lists the distances of Mercury, Earth, and Saturn from the Sun. Kepler’s third law of motion describes the relationship between the distances of the planets from the Sun and their orbital periods.

Based on the time it takes each planet to complete a ‘year’ around the Sun, rank these planets in order from shortest to longest.

• A. Mercury, Earth, Saturn

• B. Mercury, Saturn, Earth

• C. Earth, Mercury, Saturn

• D. Saturn, Earth, Mercury

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A total eclipse of the Sun occurs when the disc-like shape of the Moon completely covers the Sun, as seen from locations on Earth. However, this depends on the Moon being at its closest point to Earth in its orbit. Some eclipses, known as annular eclipses, show a thin ring of bright sunlight visible around the dark disc of the Moon. What is the relative position of the Moon, the Sun, and Earth during an annular eclipse?

• A. The Moon is at apogee.

• B. The Moon is at perigee.

• C. Earth is at aphelion.

• D. Earth is at perihelion.

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Which statement is a relationship described by one of Kepler's laws?

• A. For every action, there is an equal and opposite reaction.

• B. The acceleration of the Moon depends directly on the net force applied to it by Earth.

• C. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

• D. A line drawn between the Moon and the center of Earth will sweep out equal areas of the plane of the Moon's orbit in equal time periods.

According to Kepler’s Second Law of Planetary Motion, a line drawn from a planet to the Sun sweeps out equal areas in equal time. In this drawing, a planet is orbiting around the Sun. The thinner triangle occurs over the same time period as the wider, shorter triangle. Both triangles have the same

area. How does Newton’s universal gravitation affect the movement of the planet as it approaches the Sun?

• A. The planet’s own gravitational force causes the planet to speed up as it nears the Sun.

• B. The Sun’s gravitational force slows the planet down, keeping it close by for a longer period of time.

• C. The Sun’s gravitational force pulls more strongly on the planet as it approaches, speeding it up in its orbital path.

• D. The planet's speed is unchanged by gravitation from the Sun, but the distance traversed by the planet in its orbit is shorter.

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Because of its changing proximity to the Sun, which property does Kepler's Second Law of Planetary Motion predict will change during a planet's orbit?

• A. orbital speed

• B. orbital period

• C. orbital minor axis

• D. orbital eccentricity

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Which statement is a direct implication of Kepler's Second Law of Planetary Motion?

• A. A planet's acceleration is affected by its mass.

• B. A planet's velocity depends on its position in its orbit.

• C. A planet's total distance from the foci of its orbit is constant.

• D. A planet's period can be predicted from the semimajor axis of its orbit.

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