Question 1

Which of the following best describes the geocentric model of the universe as advocated by Ptolemy?

Accepted Answer

The Earth is at the center, and all celestial bodies orbit the Earth using deferents and epicycles.

Question 2

According to Newton’s Law of Universal Gravitation, what happens to the gravitational force between two masses if the distance between them is tripled?

Accepted Answer

The force becomes one ninth as strong.

Question 3

Which equation correctly expresses Newton’s Law of Universal Gravitation?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 4

If the mass of the Earth were doubled, but its radius remained the same, how would the acceleration due to gravity at the surface change?

Accepted Answer

It would double.

Question 5

Kepler’s first law states that planetary orbits are:

Accepted Answer

Ellipses with the Sun at one focus.

Question 6

A GPS satellite orbits the Earth at an altitude where its period is 12 hours. If the radius of the Earth is $$R_E$$ and its mass is $$M_E$$, which equation would you use to find the orbital radius $$r of $$the satellite?

Accepted Answer

$$T^2$$ = \frac{4\$$pi^2$$ $$r^3$$}{G M_E}$$

Question 7

Which of the following observations by Galileo provided strong evidence for the heliocentric model?

Accepted Answer

The phases of Venus.

Question 8

If the distance between the Earth and the Moon were doubled, what would happen to the gravitational force between them?

Accepted Answer

It would become one quarter as strong.

Question 9

Which principle allows us to calculate the net gravitational force on an object when multiple bodies exert gravitational forces on it?

Accepted Answer

The principle of superposition.

Question 10

A lunar rover has a mass of 225 kg. Given the Moon’s mass $$M_M = 7.34 	imes 10$$^{22}$$ kg and radius R_M = 1.74$$ 	imes $$10^6 m$$, what is the acceleration due to gravity on the Moon’s surface?

Accepted Answer

$$g_M = G \frac{M_M}{R_M^2$}$$

Question 11

Kepler’s second law states that:

Accepted Answer

A planet sweeps out equal areas in equal times.

Question 12

Which experiment allowed the measurement of the universal gravitational constant $$G$$?

Accepted Answer

The Cavendish experiment.

Question 13

If a planet has a mass 3.57 times that of Earth and a radius 1.60 times that of Earth, what is the acceleration due to gravity on its surface?

Accepted Answer

$$g = g_E \frac{3.57}{(1.60)^2$}$$

Question 14

Which of the following is a consequence of the inverse-square law of gravitation?

Accepted Answer

Doubling the distance between two masses reduces the force by a factor of four.

Question 15

Which of the following best explains why comets were not considered atmospheric phenomena after Tycho Brahe’s observations?

Accepted Answer

Parallax measurements showed comets were farther than the Moon.

Question 16

What is the correct formula for the mass of the Earth, given the acceleration due to gravity $$g$$ and the radius $$R$$?

Accepted Answer

$$M_E = \frac{g R^2$}{G}$$

Question 17

Which of the following statements about the gravitational force between the Earth and the Moon is correct?

Accepted Answer

They pull on each other equally.

Question 18

A satellite orbits at a distance $$r$$ from the center of the Earth. Which equation gives its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{\frac{G M_E}{r}}$$

Question 19

Kepler’s third law relates the period $$T of a $$planet’s orbit to its mean distance $$r$$ from the Sun. Which of the following expresses this law?

Accepted Answer

$$T^2$$ \propto $$r^3$$

Universal Gravitation and the Foundations of Orbital Motion

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