Question 1

According to Kepler's First Law, what is the shape of a planet's orbit around the Sun, and where is the Sun located within this shape?

Accepted Answer

An ellipse with the Sun at one focus

Question 2

Kepler's Second Law states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. What does this imply about the planet's speed in its orbit?

Accepted Answer

The planet moves faster when it is closer to the Sun

Question 3

Which of the following best describes the relationship given by Kepler's Third Law for planets orbiting the Sun?

Accepted Answer

$$T^2$$ \propto $$a^3$$

Question 4

If a planet's semi-major axis is doubled, by what factor does its orbital period change according to Kepler's Third Law?

Accepted Answer

It becomes $$2^{3/2} = 2.83$ times as long

Question 5

A planet is at perihelion (closest to the Sun) in its elliptical orbit. Which of the following is true about its velocity and kinetic energy at this point?

Accepted Answer

Both velocity and kinetic energy are at their maximum

Question 6

Which of the following equations correctly expresses the conservation of angular momentum for a planet orbiting the Sun under zero net torque?

Accepted Answer

$$mvr = 	ext{constant}$$

Question 7

Given the table of planetary data, which of the following is a correct conclusion about the ratio $$T^2/a^3$ for planets in the solar system?

Accepted Answer

It is approximately the same for all planets

Question 8

In the context of planetary orbits, what does the term 'focus' refer to?

Accepted Answer

One of two fixed points inside the ellipse, one of which is occupied by the Sun

Question 9

If the area swept out by the line joining a planet and the Sun is greater in one month than another, what can you conclude?

Accepted Answer

The planet moved faster during that month

Question 10

Which of the following statements is NOT consistent with Kepler's Laws?

Accepted Answer

The Sun is at the center of every planet's circular orbit

Question 11

A comet has a highly eccentric orbit around the Sun. According to Kepler's Second Law, how does its speed change as it moves from aphelion to perihelion?

Accepted Answer

It increases

Question 12

If a planet's orbital period is 8 years, what is the length of its semi-major axis in astronomical units (AU)? (Assume $$T^2$$ = $$a^3 in AU $$and years.)

Accepted Answer

$$a = 4 AU$$

Question 13

Which of the following best explains why the Sun is not at the center of a planet's elliptical orbit?

Accepted Answer

An ellipse has two foci, and the Sun occupies only one

Question 14

If the semi-major axis of Mars is 1.52 AU, what is its orbital period in Earth years? (Use $$T^2$$ = $$a^3.)$$

Accepted Answer

1.87 years

Question 15

Which of the following is a direct consequence of the fact that the gravitational force between the Sun and a planet produces zero torque about the Sun?

Accepted Answer

The planet's angular momentum about the Sun is conserved

Kepler’s Laws and Simple Harmonic Motion: Foundations of Planetary Motion and Oscillatory Systems

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