Question 1

Neptune has a radius of 2.48 × 107 m and an escape velocity of 23,300 m/s. What is the mass of Neptune? G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  1.01 × 1026 kg 
B)  2.02 × 1026 kg 
C)  3.03 × 1026 kg 
D)  4.04 × 1026 kg 
E)  5.05 × 1026 kg 
A)  1.01 × 1026 kg 
B)  2.02 × 1026 kg 
C)  3.03 × 1026 kg 
D)  4.04 × 1026 kg 
E)  5.05 × 1026 kg

Question 2

Halley's comet has an elliptical orbit around the Sun with a period of 76.0 years. At its closest approach (perihelion) it is 8.82 × 1010 m from the Sun and has a speed of 54.6 km/s. How fast is it moving at its furthest point from the Sun (aphelion)? The mass of the Sun is 2.00 × 1030 kg and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  604 m/s 
B)  802 m/s 
C)  1070 m/s 
D)  1540 m/s 
E)  1860 m/s 
A)  604 m/s 
B)  802 m/s 
C)  1070 m/s 
D)  1540 m/s 
E)  1860 m/s

Question 3

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?

Accepted Answer

The speed of the star would be

Question 4

The ground rises and sinks regularly because of tidal effects.

Accepted Answer

A) True 
 B)False

Question 5

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.

Accepted Answer

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 
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

Question 6

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

Accepted Answer

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

Question 7

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.

Accepted Answer

(a)1.99 × 10²⁰ N,towar

Question 8

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?

Accepted Answer

A)  2πR3/2/[G(M+m)]1/2 
B)  2πR3/2(M+m)1/2/(GMm)1/2 
C)  2πR3/2(M+m)1/2/[G(M2+m2)]1/2 
D)  2πR3/2(M+m)/(G)1/2 (Mm)3/4 
E)  4πR3/2(M+m)/(G)1/2 (Mm)3/4 
A)  2πR3/2/[G(M+m)]1/2 
B)  2πR3/2(M+m)1/2/(GMm)1/2 
C)  2πR3/2(M+m)1/2/[G(M2+m2)]1/2 
D)  2πR3/2(M+m)/(G)1/2 (Mm)3/4 
E)  4πR3/2(M+m)/(G)1/2 (Mm)3/4

Question 9

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.

Accepted Answer

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 
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 10

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?

Accepted Answer

The answer of The Schwarzchild radius is defined for a...

Question 11

An astronaut is orbiting a black hole with a mass of 2.0 × 1031 kg at a distance of 126 km from its center. The astronaut is positioned in the spacecraft so that his 0.10-kg cheeks are 0.050 m on either side of the orbital circle. What is the net tidal force pulling his cheeks apart?
G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  1,000 N 
B)  2,000 N 
C)  10,000 N 
D)  20,000 N 
E)  100,000 N 
A)  1,000 N 
B)  2,000 N 
C)  10,000 N 
D)  20,000 N 
E)  100,000 N

Question 12

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?

Accepted Answer

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

Question 13

Halley's comet has an elliptical orbit around the Sun with a period of 76.0 years. At its closest approach (perihelion) it is 88.6 x 1010 m from the Sun and has a speed of 54.8 km/s. How far is it from the Sun at its furthest point (aphelion)? The mass of the Sun is 2.00 × 1030 kg and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  12.8 × 1012 m 
B)  32.3 × 1012 m 
C)  5.42 × 1012 m 
D)  31.4 × 1012 m 
E)  52..3 × 1012 m 
A)  12.8 × 1012 m 
B)  32.3 × 1012 m 
C)  5.42 × 1012 m 
D)  31.4 × 1012 m 
E)  52..3 × 1012 m

Question 14

State Kepler's Second Law of Orbital Motion

Accepted Answer

Planets sw

Question 15

An asteroid approaches Earth so that when it is very far away it is traveling with a speed of 6500 m/s along a line that would miss the center of Earth by 8,500,000 m. Because of the gravitational attraction of Earth, it departs from this straight line and curves towards Earth, colliding with it. What is the speed of the asteroid when it hits Earth? The mass of Earth is
5)97 × 1024 kg and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  11400 m/s 
B)  12900 m/s 
C)  13700 m/s 
D)  15800 m/s 
E)  16400 m/s 
A)  11400 m/s 
B)  12900 m/s 
C)  13700 m/s 
D)  15800 m/s 
E)  16400 m/s

Question 16

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.00600 m/s2 and the escape velocity is only 9.95 m/s. What is the radius of Eros?

Accepted Answer

A)  8250 m 
B)  16,000 m 
C)  1600 m 
D)  800 m 
E)  400 m 
A)  8250 m 
B)  16,000 m 
C)  1600 m 
D)  800 m 
E)  400 m

Question 17

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

Accepted Answer

In large bodies,the gravitational forces

Question 18

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

Accepted Answer

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

Question 19

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.

Accepted Answer

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 
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 20

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. In order to make a soft landing, Mission Control sends it a signal to fire a short burst of its retro rockets to change its speed to one that will put the satellite in an elliptical orbit with a periapsis (the distance of closest approach, as measured from the center of the asteroid) equal to the radius of the asteroid. What is the speed of the satellite when it reaches the surface of the asteroid?
G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  4.32 m/s 
B)  6.11 m/s 
C)  7.18 m/s 
D)  9.43 m/s 
E)  5.74 m/s 
A)  4.32 m/s 
B)  6.11 m/s 
C)  7.18 m/s 
D)  9.43 m/s 
E)  5.74 m/s

Exam 12: Gravity

Neptune has a radius of 2.48 × 107 m and an escape velocity of 23,300 m/s. What is the mass of Neptune? G = 6.67 x 10-11 N·m2/kg2.

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?

The ground rises and sinks regularly because of tidal effects.

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

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.

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?

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?

State Kepler's Second Law of Orbital Motion

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.00600 m/s2 and the escape velocity is only 9.95 m/s. What is the radius of Eros?

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

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

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.

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Neptune has a radius of 2.48 × 10⁷ m and an escape velocity of 23,300 m/s. What is the mass of Neptune? G = 6.67 x 10^-11 N·m²/kg².

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.

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.00600 m/s² and the escape velocity is only 9.95 m/s. What is the radius of Eros?

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.