Deck 9: Gravitation

Question 1

In metric units, the dimensions of the gravitational constant G are

A) [newton]·[meters] / [kilogram].
B) [newton]·[meters] / [kilogram²].
C) [newton]·[meters²] / [kilogram].
D) [newton]·[meters²] / [kilogram²].

Answer 1

[newton]·[meters²] / [kilogram²].

Question 2

The fact that Newton's Law of Gravitation depends inversely on the square of the distance separating two bodies is necessary to account for all of the following except

A) Kepler's First Law.
B) Kepler's Second Law.
C) Kepler's Third Law.
D) Hold it! All of the preceding answers are correct.

Answer 2

Kepler's Second Law.

Question 3

Kepler's law that depends on the gravitational attraction between two bodies being a central force, but is not restricted to the force being of an inverse square nature, is related to the

A) shape of the orbit.
B) rate of area swept out in the orbit.
C) period of the orbit.
D) Hold on. None of the above answers is correct.

Answer 3

rate of area swept out in the orbit.

Question 4

Kepler's Third Law, where k is a proportionality constant, is

A) T² = kr³.
B) T² = kr.
C) T² = kr².
D) T = kr³ .

Question 5

In Kepler's Third Law, the proportionality constant between the period of the motion and the orbital radius depends

A) directly on the mass of the orbiting body.
B) directly on the mass of the orbited body.
C) inversely on the mass of the orbiting body.
D) inversely on the mass of the orbited body.

Question 6

The fact that Newton's Law of Gravitation depends inversely on the square of the distance separating two bodies is sufficient to account for all of the following except for

A) the shape of the planetary orbits.
B) the fact that there is no force on a test mass placed anywhere inside a hollow, spherically symmetric body.
C) the relation between the orbital period and the semimajor axis of the ellipse.
D) the numerical magnitude of the gravitational constant.

Question 7

The gravitational potential energy U is related to the gravitational force F by an equation of the form

A) $U \propto \int \vec { F } \cdot d \vec { r }$
B) $U \propto \int F _ { r } d t$
C) $U \propto r F _ { y }$
D) $U \propto t \vec { F } _ { \gamma }$

Question 8

The gravitational potential energy U for an orbiting body depends on the distance r between it and the orbited body as

A) r⁺¹.
B) r⁺².
C) r^-1.
D) r^-2.

Question 9

The mass of Mercury is 3.3 $\times$ 10²³ kg, and its radius is 2440 km. The acceleration due to gravity on the surface of Mercury is

A) 9.8 m/s².
B) 4.5 m/s².
C) 3.7 m/s².
D) 2.2 m/s².

Question 10

The relationship between the gravitational constant G and the acceleration due to gravity is

A) G = gM/r².
B) g = GM/r².
C) G = gMr².
D) g = GMr².

Question 11

Assume a flat Earth and an acceleration due to gravity with a constant magnitude and direction. Ignoring friction, the path of a projectile launched at a speed less than the escape velocity at its surface is

A) a circle.
B) an ellipse.
C) a hyperbola.
D) a parabola.

Question 12

Assume a round Earth. Ignoring friction, the path of a projectile launched at a speed less than the escape velocity at its surface is

A) a circle.
B) an ellipse.
C) a hyperbola.
D) a parabola.

Question 13

Ignoring friction, the path of a projectile launched at a speed equal to the escape velocity at a planet's surface is

A) a circle.
B) an ellipse.
C) a hyperbola.
D) a parabola.

Question 14

Ignoring friction, the path of a projectile launched at a speed greater than the escape velocity at a planet's surface is

A) a circle.
B) an ellipse.
C) a hyperbola.
D) a parabola.

Question 15

If a rocket is launched at the escape velocity on the surface of a planet, the limiting value of its kinetic energy as the distance from the planet (due to the motion of the rocket) approaches infinity is

A) positive.
B) negative.
C) zero.
D) undefined.

Question 16

An object released from a point a few feet above the Earth at the equator falls to the Earth. From this simple observation, ignoring friction, one can deduce that the orbital period (time to complete an orbit) for a satellite skimming around the surface of the Earth is

A) less than a day.
B) about equal to a day.
C) larger than a day.
D) unknown; insufficient information is given to determine the answer.

Question 17

The gravitational force on a satellite in a highly elliptical orbit, after it passes the point of closest approach to the Earth and before it reaches the point of farthest separation from the Earth, has a component

A) in the same direction as the velocity of the satellite.
B) in the direction opposite to the velocity of the satellite.
C) Either of the previous answers is correct.
D) Neither of the previous answers is correct.

Question 18

The speed of a satellite in a highly elliptical orbit, after it passes the point of closest approach to the Earth and before it reaches the point of farthest separation from the Earth, is

A) increasing.
B) decreasing.
C) changing in a way such that both of the previous answers apply over different portions of the path.
D) constant.

Question 19

The Moon orbits the Earth with a period of about 28 days. The two bodies are separated by a distance ~ 250,000 miles. An Earth satellite at a distance ~125,000 miles would have a period (in days) of

A) $( 1 / \sqrt { 16 } ) \times 28$ days.
B) $( 1 / \sqrt { 8 } ) \times 28$ days.
C) $( 1 / \sqrt { 4 } ) \times 28$ days.
D) $( 1 / \sqrt { 2 } ) \times 28$ days.

Question 20

As formulated by Isaac Newton, the Inverse Square Law of Gravitational Attraction applies to all infinitesimal parts of two masses

A) if they are point particles.
B) if they have spherical symmetry.
C) regardless of their shape, size, or the presence of other bodies.
D) Hold it! All of the previous answers are correct.

Question 21

An Earth satellite in an elliptical orbit "speeds down" (that is, as it comes closer to the Earth, its speed increases). This is consistent with the fact that the gravitational potential energy U of the satellite-Earth system at points closer to the Earth is

A) larger than U at points farther from the Earth.
B) equal to U at points farther from the Earth.
C) less than U at points farther from the Earth.
D) Hold it! None of the above responses is correct.

Question 22

For a large spherical mass and a small test mass, the force between them is at a maximum when the test mass is located

A) very far from the center of the spherical mass.
B) on the surface of the spherical mass.
C) at the center of the spherical mass.
D) Hold it! None of the above answers is correct.

Question 23

For a large spherical mass and a small test mass, the gravitational potential energy between them is at a minimum when the test mass is located

A) very far from the center of the spherical mass.
B) on the surface of the spherical mass.
C) at the center of the spherical mass.
D) Hold it! None of the above answers is correct.

Question 24

Consider the tidal forces on body A as it orbits body B in a particular configuration and state of motion. Each of the following independent changes would increase these forces except if

A) the radius of the orbit is reduced.
B) the radius (but not the mass) of body A is increased.
C) the radius (but not the mass) of body B is increased.
D) Hold it! There are no exceptions.

Question 25

If frictional drag due to the atmosphere acts on an Earth satellite in a low orbit, the net effect on its orbital speed will be

A) to increase it.
B) to decrease it.
C) to leave it unchanged.
D) unknown; insufficient information is given to work out the answer.

Question 26

Two objects with masses M₁ and M₂ are originally separated by a distance r. The distance between the two masses is increased to 3r. The force between the two objects will

A) increase by a factor of 3.
B) decrease by a factor of 3.
C) increase by a factor of 9.
D) decrease by a factor of 9.

Question 27

Two masses, M₁ = 10²² kg and M₂ = 10³⁰ kg, are separated by a distance of 10¹¹ m. The magnitude of the gravitational force between the two masses is

A) 10²⁰ N.
B) 10³¹ N.
C) 10²⁸ N.
D) 10²² N.

Question 28

Atomic oxygen is one of the major constituents of the upper atmosphere in the region of low Earth orbit (LEO). LEO is approximately 150 miles $( 240 \mathrm {~km} )$ above the surface of the Earth. The radius and mass of the Earth are $6.4 \times 10 ^ { 6 } \mathrm {~m}$ and $5.98 \times 10 ^ { 24 } \mathrm {~kg}$ . The mass of atomic oxygen is $16 \times \left( 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$ . The kinetic energy at which the atomic oxygen strikes the surface of the space shuttle is

A) 8.0 $\times$ 10^-18 J.
B) 8.0 $\times$ 10^-19 J.
C) 8.0 $\times$ 10^-20 J.
D) 8.0 $\times$ 10^-21 J.

Question 29

The Earth's radius is 6.4 $\times$ 10⁶ m. The acceleration due to gravity (in g's) that is experienced by an object at a distance of 150 miles (240 km) above the Earth's surface is

A) zero because the object is in space (0 g).
B) 0.51 g.
C) 1.0 g.
D) 0.92 g.

Question 30

The mass of Mars is 6.42 $\times$ 10²³ kg, and the radius of the planet is 3.40 $\times$ 10⁶ m. The acceleration due to gravity on the surface of Mars is

A) 3.7 cm/s².
B) 37 cm/s².
C) 370 cm/s².
D) 37 m/s².

Question 31

Two planets have masses M and M/2 respectively. The distance between the two planets is r. The relative distance from the first planet where the gravitational force on a third body due to the two planets would be zero is

A) 0.414 r.
B) 0.500 r.
C) 0.586 r.
D) 3.414 r.

Question 32

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.40 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The time it takes a space shuttle in LEO to travel around one orbit

A) is 90.0 minutes.
B) is 105 minutes.
C) is 120 minutes.
D) cannot be determined without knowing the mass of the shuttle.

Question 33

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The velocity of the space shuttle in LEO

A) is 7.9 km/s.
B) is 7.7 km/s.
C) is 7.9 m/s.
D) cannot be determined without knowing the mass of the shuttle.

Question 34

The orbit of Io, a moon of Jupiter, is found to have a period of 1.769 days, and its average distance from the center of Jupiter is 420,000 km. The mass of Jupiter

A) is 1.9 $\times$ 10²⁷ kg.
B) is 2.2 $\times$ 10³⁷ kg.
C) is 8.0 $\times$ 10²⁷ kg.
D) cannot be determined without knowing the mass of Io.

Question 35

The period of a planetary orbit about a star is one Earth year, whereas the average distance between the planet and the star is 1.5 AU (astronomical units). A second planet is orbiting the star at a distance of 6.0 AU. The period of the second planet orbiting the same star is

A) 4.0 years.
B) 6.0 years.
C) 8.0 years.
D) unknown; the period cannot be determined from the information given.

Question 36

The period of a planetary orbit about a star is 1.5 Earth years, whereas the average distance between the planet and the star is 2.0 AU (astronomical units). A second planet is orbiting the star with a period of 12 Earth years. The orbital radius of the second planet is

A) 9.0 AU.
B) 16 AU.
C) 8.0 AU.
D) unknown; the orbital radius cannot be determined from the information given.

Question 37

A planet in another solar system is found to have twice the radius of the Earth and a mass that is double that of the Earth. The acceleration due to gravity on this other planet is

A) 0.50 g.
B) 1.0 g.
C) 1.5 g.
D) 2.0 g.

Question 38

A planetary orbit follows an ellipse in which the star is located at one of the foci. At the location of the second focus is

A) the planet.
B) another star.
C) nothing.
D) a little green creature.

Question 39

A comet is found to move in an elliptical orbit. When the comet's aphelion distance is 2.5 AU, it has a velocity of 100 m/s. The point of closest approach is 0.5 AU from the Sun. The velocity of the comet at the point of closest approach is

A) 2.5 km/s.
B) 80 m/s.
C) 5.0 $\times$ 10² m/s.
D) unknown; more information about the orbit is necessary to answer this question.

Question 40

The orbital angular momentum of Io was calculated to be approximately 1.55 $\times$ 10²⁷ kg·m²/s at perihelion. The angular momentum at the aphelion

A) increases.
B) decreases.
C) remains the same.
D) cannot be determined from the information given.

Question 41

The gravitational potential energy of a planet orbiting around a star is U₀ when the distance between the two objects is r₀. If the distance between the planet and the star is increased to 2r₀, the gravitational potential energy is

A) U₀/4.
B) U₀/2.
C) 2U₀.
D) 4U₀.

Question 42

The Moon has a mass of 7.35 $\times$ 10²² kg and a mean radius of 1.74 $\times$ 10⁶ m. The velocity required by the Apollo landing capsule to escape from the gravitational attraction of the Moon is

A) 2.40 km/s.
B) 1.70 km/s.
C) 1.45 $\times$ 10³ m/s.
D) unknown; we cannot answer this problem without knowing the mass of the orbiter.

Question 43

An object passes through the solar system with a zero total energy. The trajectory it will follow is

A) elliptical.
B) parabolic.
C) hyperbolic.
D) circular.

Question 44

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The escape velocity of an object in LEO is

A) 10 km/s.
B) 11 km/s.
C) 2.0 $\times$ 10² m/s.
D) unknown; we cannot determine the answer without knowing the mass of the object.

Question 45

The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. Assume that a meteor starts at infinity with zero velocity and is attracted to the Earth. Neglecting friction, the speed at which it will strike the Earth is

A) 36 km/h.
B) 11 km/h.
C) 100 km/h.
D) unknown; we cannot determine the answer without knowing the mass of the object.

Question 46

The mass of a planet is 1/9 the mass of Earth, and its radius is 1/3 the radius of the Earth. The acceleration due to gravity on this planet is

A) (3)g.
B) (1/3)g.
C) (2/3)g.
D) g.

Question 47

The mass of the Moon is 7.348 $\times$ 10²² kg, and the mass of the Earth is 5.974 $\times$ 10²⁴ kg. The average distance from the center of the Earth to the center of the Moon is 384,400 km. Between the two bodies is a point where the gravitational attractions on a third body will cancel. The distance from the center of the Earth to this point is approximately

A) 288,300 km.
B) 438,000 km.
C) 384,400 km.
D) 343,000 km.

Question 48

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.37 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. If an object in LEO has a mass of 20 kg, its weight is

A) 0 N.
B) 9.1 N.
C) 9.8 N.
D) 3.5 N.

Question 49

An object has a weight of 100 N on the surface of the Earth. If the object is moved to 2R_E above the surface of the Earth, its weight is

A) 25.0 N.
B) 11.0 N.
C) 0 N.
D) 100 N.

Question 50

An asteroid has a mass of approximately 10¹⁵ kg and a diameter of 10 km. The escape velocity for an object at the surface of the asteroid is

A) 7.1 $\times$ 10² m/s.
B) 27 m/s.
C) 3.6 $\times$ 10² m/s.
D) 19 m/s.