Planetary Orbits: Kepler's Laws

The actual shape of the Earth’s orbit around the Sun is best described as

• a very eccentric ellipse

• a slightly eccentric ellipse

• an oblate spheroid

• a perfect circle

Answer explanation

The Earth's orbit is not a perfect circle but a slightly eccentric ellipse, meaning it has a small deviation from circularity. This is why 'a slightly eccentric ellipse' is the correct choice.

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The constructed ellipse below is a true scale model of the orbit of a planet in our solar system. The eccentricity of this orbit is approximately

Mathematical Equivalence

ON

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The diagram below represents the construction of a model of an elliptical orbit of a planet traveling around a star. The focal point and the center of the star represent the foci of the orbit. The eccentricity of this orbit is approximately

• 1.3

• 0.8

• 0.5

• 0.3

Answer explanation

The eccentricity of an orbit measures its deviation from a perfect circle. An eccentricity of 0.8 indicates a highly elliptical orbit, which aligns with the characteristics of many planetary orbits, making 0.8 the correct choice.

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Which object is located at one foci of the elliptical orbit of Mars?

• the Sun

• Earth

• Betelgeuse

• Jupiter

Answer explanation

In an elliptical orbit, one foci is occupied by the Sun, which is the central body that the planets, including Mars, orbit around. Therefore, the correct answer is the Sun.

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Which planet has an orbital eccentricity most like the orbital eccentricity of the Moon?

• Jupiter

• Mars

• Saturn

• Mercury

Answer explanation

Saturn has an orbital eccentricity of about 0.056, which is similar to the Moon's eccentricity of approximately 0.054. In contrast, the other planets listed have significantly higher eccentricities.

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When the distance between the foci of an ellipse is increased, the eccentricity of the ellipse will (a)   .

• decrease

• increase

• remain the same

Answer explanation

As the distance between the foci of an ellipse increases, the shape becomes more elongated, leading to a higher eccentricity. Therefore, the eccentricity of the ellipse will increase.

Which planet’s orbit around the Sun is nearly circular?

• Mercury

• Neptune

• Pluto

• Venus

Answer explanation

Mercury's orbit is the most circular among the planets, with an eccentricity of only 0.2056. In contrast, Neptune, Pluto, and Venus have more elliptical orbits, making Mercury the correct choice for a nearly circular orbit.

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The diagram below shows four positions of a planet in its orbit around the Sun. At which position is the planet’s orbital speed greatest?

• A

• B

• C

• D

Answer explanation

The planet's orbital speed is greatest at position B, which is closest to the Sun. According to Kepler's laws, a planet moves faster when it is nearer to the Sun due to the stronger gravitational pull.

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The diagram below represents the Earth's orbit path around the Sun. The Earth takes the same amount of time to move from A to B as from C to D. Which values are equal within the system?

• The shaded sections of the diagram are equal in area.

• The distance from the Sun to the Earth is the same at point A and at point D.

• The orbital velocity of the Earth at point A equals its orbital velocity at point C.

• The gravitational force between the Earth and the Sun at point B is the same as the gravitational force at point D.

Answer explanation

The shaded sections represent equal time intervals in the Earth's orbit, thus they cover equal areas according to Kepler's second law. This makes the first choice correct.

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The diagram below shows a satellite in four different positions as it revolves around a planet. Which graph best represents the changes in this satellite's orbital velocity as it revolves around the planet?

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