Deck 12: Gravity

Question 1

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to decrease the forward speed of the rocket, what will happen?

Answer 1

The spacecraft will be put into an elliptical orbit with an apogee equal to the original radius.The average radius of this orbit is smaller,so it will take less time to complete one revolution.So if the speed increment is calculated correctly,when he completes one revolution,bringing him back to the original radius,he could be caught up with the station.At that point,a forward burst could put him in the same circular orbit as the station.

Question 2

State Kepler's First Law of Orbital Motion

Answer 2

The orbits of the planets are ellipses,with the Sun at one focus.

Question 3

Our Moon revolves about Earth in the same direction as Earth's direction of rotation about its own axis. The gravitational attraction of the Moon causes tides on Earth, which gradually slow down its rotation about its own axis. What consequences does this have for the Moon?

Answer 3

Since the angular momentum of the Earth-Moon system has to be conserved,a decrease in the angular momentum of Earth about its axis must be balanced by an increase of the Moon's angular momentum about that axis.The radius of the Moon's orbit will thus gradually increase until it escapes from the gravitational field of Earth.

Question 4

There are daily variations in the barometric pressure, which occur because of tidal effects.

Question 5

Why are planets and stars approximately spherical, whereas asteroids and meteorites are shaped like ordinary rocks?

Question 6

Triton, the largest of Neptune's moons has a retrograde rotation. This means that it revolves about Neptune in the opposite direction to Neptune's direction of rotation about its own axis. The gravitational attraction of Triton causes tides on Neptune, which gradually slow down its rotation about its own axis. What consequences does this have for Triton?

Question 7

A star is in an elliptical orbit around a black hole (which can't be seen). You have been observing the motion of the star through a telescope and have followed the motion long enough to establish that it is elliptical. How can you determine on which focus of the ellipse the black hole is located?

Question 8

For a satellite in orbit around Earth, the product of its speed times the distance from the center of Earth has the same value when the satellite is at the perigee, its closest approach to Earth, and at the apogee, its furthest point from Earth. Is the product the same at other points on the orbit?
Why?

Question 9

The gravitational force that the Sun exerts on Earth is much larger than the gravitational force that Earth exerts on the Sun.

Question 10

A mass is attached to a fixed point by means of an ideal spring with zero unstretched length and is free to move in two dimensions. What would be the equivalent statement of Kepler's third law for this situation in the case of circular orbits around the fixed point?

Question 11

State Kepler's Third Law of Orbital Motion

Question 12

The reason that when an object falls towards Earth, Earth does not move toward the object, is that the force exerted by Earth on the object is so much bigger.

Question 13

Tidal locking is what makes the Moon rotate about its own axis at the same rate that it revolves around Earth. Using as a model of a moon two identical masses of mass m connected by a light rod, explain how the forces on the masses would tend to keep this satellite in a fixed orientation.

Question 14

A binary system has two stars of mass M circling their common center of mass on opposite sides of a circle of radius R. What is the potential energy of the system?

Question 15

Four identical bodies of mass M, at the vertices of a square with a diagonal 2R, orbit their common center of mass in a circular motion with a radius R. How much energy is required to separate the four stars so they are an infinite distance apart?

Question 16

The Schwarzchild radius is defined for a given mass M as the radius for which the escape velocity would be exactly equal to the speed of light, c. What is the expression for this radius in terms of G, M, and c?

Question 17

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to increase the forward speed of the rocket, what will happen?

Question 18

The ground rises and sinks regularly because of tidal effects.

Question 19

Tides are approximately 24 hours apart.

Question 20

State Kepler's Second Law of Orbital Motion

Question 21

How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare?

A) The escape velocity for the lighter rocket is smaller than that for the heavier rocket.
B) The escape velocity for the lighter rocket is the same as that for the heavier rocket.
C) The escape velocity for the lighter rocket is greater than that for the heavier rocket.
D) It is impossible to compare the two escape velocities.

Question 22

Most asteroids are oblong in shape. Approximate an asteroid as being made up of two identical spheres of mass M and radius R that are just touching each other, in a figure eight. In terms of G, M, and R, what is the escape velocity for a spaceship taking off from the top of the figure eight?

A) (2GM/R)^1/2
B) (4GM/3R)^1/2
C) (8GM/3R)^1/2
D) (3GM/R)^1/2
E) (7GM/5R)^1/2

Question 23

The gravitational force between two objects is proportional to

A) the distance between the two objects.
B) the square of the distance between the two objects.
C) the product of the masses of the two objects.
D) the square of the product of the masses of the two objects.
E) none of the above

Question 24

Kepler's second law tells us that planets sweep out equal areas in equal times. If you compare the amount of area per time swept by Earth with the one of Jupiter, you would conclude:

A) They sweep the same area per time.
B) They sweep different areas per time.
C) Jupiter sweeps a larger area per time because it has much more mass than Earth.
D) Earth sweeps a larger area per time because it has much less mass than Jupiter.

Question 25

A satellite is orbiting Earth in a circular orbit of radius r when it fires its rockets and acquires speed rapidly. Following this, the satellite's orbit

A) becomes hyperbolic.
B) stays circular but with a larger radius.
C) stays circular but with a smaller radius.
D) becomes elliptical.
E) none of the above

Question 26

The acceleration due to gravity on the surface of Earth is g. Calling R the radius of Earth, at what distance from Earth's center would the acceleration due to gravity drop to g/16?

A) 16 R
B) R/16
C) R/4
D) 4 R
E) 2 R

Question 27

Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force

A) is cut to one fourth.
B) is cut in half.
C) doubles.
D) quadruples
E) remains the same

Question 28

Two bodies, one of mass M and the other of mass m, are subject only to their mutual gravitational attraction. One possible motion is for both of them to revolve in concentric circles about their center of mass. What is the connection between the period of the revolutions and the separation R between the two bodies in this case?

A) 2πR^3/2/[G(M+m)]^1/2
B) 2πR^3/2(M+m)^1/2/(GMm)^1/2
C) 2πR^3/2(M+m)^1/2/[G(M²+m²)]^1/2
D) 2πR^3/2(M+m)/(G)^1/2 (Mm)^3/4
E) 4πR^3/2(M+m)/(G)^1/2 (Mm)^3/4

Question 29

You have discovered a star system consisting of three equally spaced stars of equal mass arranged in a straight line. The two outermost stars, Zenith and Nadir, revolve synchronously around the central star, Janus. What is the period of revolution for this system in terms of M, the mass of each of the stars, and R, the radius of the circular orbit of Zenith and Nadir?

A) [2πR^3/2/(GM)^1/2] × (3/2)^1/2
B) [2πR^3/2/(GM)^1/2] × (2/3)^1/2
C) [2πR^3/2/(GM)^1/2] × (4/5)^1/2
D) [2πR^3/2/(GM)^1/2] × (5/4)^1/2
E) [2πR^3/2/(GM)^1/2] × (7/5)^1/2

Question 30

What is the ratio of potential energy to kinetic energy for a comet that has just enough energy to escape from the Sun's gravitational field?

A) 1/2
B) 1
C) 2
D) -1
E) -2

Question 31

A satellite completes one full orbit around Earth. The work performed by Earth's gravitational force on the satellite is

A) always positive.
B) zero J.
C) always negative.
D) positive most of the time.
E) negative most of the time.

Question 32

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity at the satellite, as compared to the acceleration of gravity on the surface of Mars, is

A) one-ninth as much.
B) zero.
C) the same.
D) one-third as much.
E) one-sixteenth as much.

Question 33

Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

A) g/3.
B) 3 g.
C) 6 g.
D) g/9.
E) 9 g.

Question 34

During the period of one day, the number of high tides on the East or West coast is usually

A) five.
B) one.
C) two.
D) four.
E) three.

Question 35

What is the ratio of potential energy to total energy for a planet in a circular orbit around the Sun?

A) 1/2
B) 1
C) 2
D) -1
E) -2

Question 36

How does the escape speed from Mars compare with that of the Earth?
[ M_Earth=9.31∗ M_Mars ; R_Earth=1.88 ∗ R_Mars ]

A) 222.%
B) 22.5%
C) 44.9%
D) 66.2%
E) 20.2%

Question 37

Because Earth's orbit is slightly elliptical, Earth actually gets closer to the Sun during part of the year. When Earth is closer to the Sun its orbital speed is

A) less than when Earth is farthest away from the Sun.
B) the same as when Earth is farthest away from the Sun.
C) greater than when Earth is farthest away from the Sun.
D) sometimes greater sometimes smaller than when Earth is farthest away from the Sun.

Question 38

If Earth were twice as massive but it revolved at the same distance from the Sun, its orbital period would be

A) 4 years.
B) 3 years.
C) 2 years.
D) 1 year.
E) 6 months.

Question 39

The gravitational force between two objects is inversely proportional to

A) the distance between the two objects.
B) the square of the distance between the two objects.
C) the product of the masses of the two objects.
D) the square of the product of the masses of the two objects.
E) none of the above

Question 40

An astronaut is in a capsule in a stable orbit, about two Earth radii from the center of Earth. Her weight is

A) zero N.
B) the same as on the surface of Earth.
C) about one-half of her weight on the surface of Earth.
D) about one-third of her weight on the surface of Earth.
E) about one-quarter of her weight on the surface of Earth.

Question 41

A satellite orbits just above the Earth's surface. (a) Calculate the period of the satellite. (b) Calculate the speed of the satellite.

Question 42

What is the gravitational force between two 7.00-kg balls, when they are 35.0 cm apart?
G = 6.67 x 10^-11 N·m²/kg².

Question 43

What is the distance from the moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 10²⁴ kg, the mass of the Moon is 7.35 × 10²² kg, the distance between Earth and the Moon is 3.84 × 10⁸ m, and G = 6.67 x 10^-11 N·m²/kg².

A) 3.45 × 10⁸ m
B) 3.83 × 10⁷ m
C) 4.69 × 10⁶ m
D) 3.83 × 10⁶ m
E) 4.69 × 10⁷ m

Question 44

An experiment for determining the value of the universal gravitational constant G was devised by Jolly. He placed a 5.00-kg sphere on a balance and, after it was balanced, he moved a 5775-kg lead sphere under the 5.00-kg sphere, causing the balance to tilt off its equilibrium position. The distance between the centers of the two spheres was 0.569 m. Knowing that G = 6.67 x 10^-11 N·m²/kg², what mass did he need to add to the other side of the scale to bring it back in balance?

A) 0.606 mg
B) 5.94 mg
C) 3.39 mg
D) 0.345 mg
E) 0.912 N

Question 45

During a lunar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon has a mass of 7.36 × 10²² kg; the Earth has a mass of 5.98 × 10²⁴ kg; and the Sun has a mass of 1.99 × 10³⁰ kg. The separation between the Moon and the Earth is given by 3.84 × 10⁸ m; the separation between the Earth and the Sun is given by 1.496 × 10¹¹ m.
(a) Calculate the force exerted on the Earth by the Moon.
(b) Calculate the force exerted on the Earth by the Sun.
(c) Calculate the net force exerted on the Earth by the Moon and the Sun.

Question 46

The identical 50-kg masses are held at the corners of an equilateral triangle, 30 cm on each side. If one of the masses is released, what is its initial acceleration, if the only forces acting on it are the gravitational forces due to the other two masses?

A) 3.7 × 10^-8 m/s²
B) 2.5 × 10^-8 m/s²
C) 1.9 × 10^-8 m/s²
D) 4.2 × 10^-8 m/s²
E) 6.4 × 10^-8 m/s²

Question 47

The mass of Pluto is 1.25 × 10²² kg and its radius is 1.14 × 10⁶ m. What is the value of g at the surface of Pluto? G = 6.67 x 10^-11 N·m²/kg².

A) 0.642 m/s²
B) 9.81 m/s²
C) 1.62 m/s²
D) 3.72 m/s²
E) 1.40 m/s²

Question 48

The highest tides occur when

A) the Sun and the Moon are on the same side of Earth.
B) the Sun and the Moon are on opposite sides of Earth.
C) the Sun, Moon, and Earth form a right-angled triangle with Earth at the 90° vertex.
D) the Sun, Moon, and Earth form a right-angled triangle with the Moon at the 90° vertex.
E) the Sun, Moon, and Earth form a right-angled triangle with the Sun at the 90° vertex.

Question 49

At their closest approach, Venus and Earth are 4.20 × 10¹⁰ m apart. The mass of Venus is 4.87 × 10²⁴ kg, the mass of Earth is 5.97 × 10²⁴ kg, and G = 6.67 x 10^-11 N·m²/kg². What is the force exerted by Venus on Earth at that point?

A) 1.10 × 10¹⁸ N
B) 4.62 × 10²⁸ N
C) 5.43 × 10²⁶ N
D) 6.30 × 10²⁰ N
E) 1.72 × 10¹⁹ N

Question 50

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 × 10⁶ m.

A) 9.81 m/s²
B) 9.78 m/s²
C) 9.75 m/s²
D) 9.72 m/s²
E) 9.69 m/s²

Question 51

At what altitude should a satellite be placed into circular orbit so that its orbital period is 48.0 hours? The mass of the earth is 5.976 × 10²⁴ kg and the radius of the earth is 6.378 × 10⁶ m.

A) 4.22 × 10⁷ m
B) 7.58 × 10⁷ m
C) 8.22 × 10⁷ m
D) 6.07 × 10⁷ m
E) 6.71 × 10⁷ m

Question 52

The mass of the Moon is 7.4 × 10²² kg and its mean radius is 1.75 × 10³ km. What is the acceleration due to gravity at the surface of the Moon?

A) 2.8 × 10⁶ m/s²
B) 9.8 m/s²
C) 4.9 m/s²
D) 1.6 m/s²
E) 0.80 m/s²

Question 53

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.976 × 10²⁴ kg and the radius of the earth is 6.378 × 10⁶ m.
(a) Assuming a circular orbit, what is the period of the International Space Station's orbit?
(b) Assuming a circular orbit, what is the speed of the International Space Station in its orbit?

Question 54

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

A) 580 N
B) 290 N
C) 1160 N
D) 118 N
E) 1200 N

Question 55

A spaceship with a mass of 2.8 × 10⁶ kg is traveling toward two asteroids, each with a mass of 5.0 × 10¹⁶ kg, which are 40 km apart. Its path is perpendicular to the line joining the asteroids and aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? G = 6.67 x 10^-11 N·m²/kg².

A) 12,000 N
B) 8000 N
C) 16,000 N
D) 6200 N
E) 18,000 N

Question 56

The hydrogen atom consists of a proton of mass 1.67 × 10^-27 kg and an orbiting electron of mass 9.11 × 10^-31 kg. In one of its orbits, the electron is 5.3 × 10^-11 m from the proton. What is the mutual attractive gravitational force between the electron and proton?

A) 1.8 × 10^-47 N
B) 3.6 × 10^-47 N
C) 5.4 × 10^-47 N
D) 7.0 × 10^-47 N
E) 9.3 × 10^-47 N

Question 57

An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 10⁶ m and that G = 6.67 x 10^-11 N·m²/kg². From this information, she can conclude that the mass of Mars is

A) 3.30 × 10²³ kg.
B) 6.62 × 10²³ kg.
C) 4.62 × 10²³ kg.
D) 8.09 × 10²³ kg.
E) 9.95 × 10²³ kg.

Question 58

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

A) 580 N
B) 290 N
C) 1160 N
D) 2320 N
E) 1200 N

Question 59

The radius of the Earth is R. At what distance above the Earth's surface will the acceleration of gravity be 4.9 m/s²?

A) 0.41 R
B) 0.50 R
C) 1.0 R
D) 1.4 R
E) 2.0 R

Question 60

A satellite of mass 500 kg orbits the Earth with a period of 6000 s. The Earth has a mass of 5.98 × 10²⁴ kg. (a) Calculate the magnitude of the Earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's surface.

Question 61

Three masses are located as follows: a 3.5-kg mass is at the origin, a 4.2-kg mass at (0.0 m, 7.0 m), and a 6.5-kg mass at (24.0 m, 0.0 m). What is the gravitational energy of the system of masses?
G = 6.67 x 10^-11 N·m²/kg².

A) -2.8 × 10^-10 J
B) -2.0 × 10^-10 J
C) -1.4 × 10^-10 J
D) -3.2 × 10^-10 J
E) -3.9 × 10^-10 J

Question 62

Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a moon, which has been named Dactyl. From the dimensions of Ida and its general features, one can estimate the mass of Ida to be 4.5 × 10¹⁶ kg, and the distance between Dactyl and Ida is approximately 90 km. Assuming a circular orbit, what would be the orbital speed of Dactyl? G = 6.67 x 10^-11 N·m²/kg².

A) 5.8 m/s
B) 11 m/s
C) 2.3 m/s
D) 2.9 m/s
E) 30 m/s

Question 63

A space exploration satellite is orbiting a spherical asteroid whose mass is 4.65 × 10¹⁶ kg and whose radius is 39,600 m, at an altitude of 12,400 m above the surface of the asteroid. Mission Control sends it a signal to fire a short burst of its retro rockets to bring its speed to zero m/s. What is the speed of the satellite when it hits the surface of the asteroid?

A) 6.11 m/s
B) 7.18 m/s
C) 8.29 m/s
D) 5.74 m/s
E) 4.36 m/s

Question 64

An 825-kg space vehicle is circling Earth in a circular orbit with a radius of 10,300 km. Its orbit is to be changed to a larger circle with a radius of 17,400 km. How much energy is required to accomplish this? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 1.00 × 10⁹ J
B) 1.30 × 10¹⁰ J
C) 6.51 × 10⁹ J
D) 4.45 × 10⁹ J
E) 4.50 × 10¹⁰ J

Question 65

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 1.04 × 10⁷ m
B) 2.26 × 10⁹ m
C) 1.60 × 10⁸ m
D) 3.41 × 10⁸ m
E) 7.45 × 10⁸ m

Question 66

Uranus completes one revolution about its own axis every 17.24 hours. What is the radius of the orbit required for a satellite to revolve about Uranus with the same period? Uranus has a mass of 8.69 × 10²⁵ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 8.27 × 10⁷ m
B) 3.41 × 10⁸ m
C) 2.56 × 10⁸ m
D) 9.03 × 10⁷ m
E) 1.04 × 10⁷ m

Question 67

In Gulliver's Travels, Jonathan Swift wrote about a country where astronomers had found that Mars had two moons. (The moons of Mars were unknown at that time.) "They have likewise discovered two lesser stars, or satellites, which revolve about Mars, whereof the innermost is distant from the center of the primary planet exactly three of his diameters, and the outermost five; the former revolves in the space of ten hours, and the latter in twenty-one and a half..." If this information were correct, what would the mass of Mars be? The radius of Mars is 3,393,500 m and G = 6.67 x 10^-11 N·m²/kg².

A) 3.86 × 10²⁴ kg
B) 6.45 × 10²³ kg
C) 5.67 × 10²¹ kg
D) 2.83 × 10²¹ kg
E) 4.78 × 10²⁰ kg

Question 68

A projectile is shot from the surface of Earth by means of a very powerful cannon. If the projectile reaches a height of 35,000 m above Earth's surface, what was the speed of the projectile when it left the cannon?

A) 355 m/s
B) 505 m/s
C) 827 m/s
D) 710 m/s
E) 906 m/s

Question 69

Suppose that the Sun were to collapse under its own gravitational pull. To what radius would it have to be reduced in order for the escape velocity to be equal the speed of light, 3.00 x 10⁸ m/s? The mass of the Sun is 2.00 x 10³⁰ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 2.96 km
B) 1.48 km
C) 1.52 km
D) 2.10 km
E) None of the other choices is correct.

Question 70

A satellite is in an elliptical orbit around Earth. At one point on the ellipse, it is 25 × 10⁶ m from the center of Earth and has a speed of 12,000 m/s. What is its speed when it is at another point on the ellipse, 95 × 10⁶ m from the center of Earth? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 12000 m/s
B) 11000 m/s
C) 10000 m/s
D) 9000 m/s
E) 8000 m/s

Question 71

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

A) 4.50 × 10⁷ m
B) 3.90 × 10⁷ m
C) 9.24 × 10⁷ m
D) 8.00 × 10⁷ m
E) 7.27 × 10⁷ m

Question 72

A satellite is in an elliptical orbit around Earth. At one point on the ellipse, it is 40 × 10⁶ m from the center of Earth and has a speed of 10,000 m/s. At another point on the ellipse its speed is 9100 m/s. How far from the center of Earth is the second point? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 2.9 × 10⁸ m
B) 4.3 × 10⁸ m
C) 6.7 × 10⁷ m
D) 8.6 × 10⁷ m
E) 9.1 × 10⁷ m

Question 73

A space vehicle is orbiting Earth in a circular orbit with a radius of 10,300,000 m. What is the minimum increase in speed that is needed for the vehicle to escape Earth's gravitational field? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 6220 m/s
B) 2580 m/s
C) 3110 m/s
D) 2840 m/s
E) 7440 m/s

Question 74

What is the period of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10²³ kg, its radius is 3.40 × 10⁶ m, and G = 6.67 x 10^-11 N·m²/kg²

A) 1.75 hours
B) 1.25 hours
C) 1.15 hours
D) 1.00 hours
E) 1.45 hours

Question 75

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the period of revolution of Phobos to that of Deimos?

A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Question 76

Sputnik I was launched into orbit around Earth in 1957. It had a perigee (the distance from the point of closest approach to the center of Earth) of 6.61 × 10⁶ m and an apogee (the distance from the furthest point in the orbit to the center of Earth) of 7.33 × 10⁶ m. Its mass was 83.5 kg. What was the difference in kinetic energy as it moved from perigee to apogee? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

A) 8.27 × 10⁷ J
B) 6.44 × 10⁷ J
C) 1.93 × 10⁸ J
D) 3.50 × 10⁸ J
E) 4.94 × 10⁸ J

Question 77

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the orbital speed of Phobos to that of Deimos?

A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Question 78

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

A) 60.8 hours
B) 12.0 hours
C) 33.1 hours
D) 9.80 hours
E) 27.0 hours

Question 79

Three masses are located as follows: a 3.0-kg mass is at the origin, a 4.5-kg mass at (0.0 m, 4.0 m), and a 2.5-kg mass at (3.0 m, 0.0 m). What is the gravitational energy of the system of masses?
G = 6.67 x 10^-11 N·m²/kg².

A) -3.8 × 10^-10 J
B) -3.9 × 10^-10 J
C) -5.4 × 10^-10 J
D) -3.2 × 10^-10 J
E) -3.5 × 10^-10 J

Question 80

Sirius A and Sirius B constitute a binary star pair in which the stars orbit their common center of mass with a period of 49.9 years. The stars are 2.40 × 10¹² m apart. Assume that the two stars have equal masses and that they move in a circle about their common center of mass. What is the mass of each star? G = 6.67 x 10^-11 N·m²/kg².

A) 5.41 × 10³⁰ kg
B) 2.70 × 10³⁰ kg
C) 7.55 × 10³⁰ kg
D) 3.30 × 10³⁰ kg
E) 1.65 × 10³⁰ kg