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Sputnik I was launched into orbit around Earth in 1957.It had a perigee (the closest approach to Earth,measured from Earth's center) of 6.81 × 106 m and an apogee (the furthest point from Earth's center) of 7.53 × 106 m.What was its speed when it was at its perigee? The mass of Earth is 5.97 × 1024 kg and G = 6.67 × 10-11 N • m2/kg2.


A) 7180 m/s
B) 7840 m/s
C) 8230 m/s
D) 11,000 m/s
E) 13,400 m/s

F) B) and E)
G) A) and E)

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Neptune circles the Sun at a distance of 4.50 × 1012 m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 1012 m.What is the orbital period of Saturn?


A) 304 y
B) 121 y
C) 109 h
D) 88.6 y
E) 29.4 y

F) A) and E)
G) A) and B)

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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

F) C) and D)
G) D) and E)

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Spaceman Speff orbits spherical asteroid X with his spaceship.To remain in a circular orbit at 421 km from the asteroid's center,he should maintain a speed of 80 m/s. What is the mass of planet X? (G = 6.67 × 10-11 N • m2/kg2)


A) 4.0 × 1019 kg
B) 5.1 × 1017 kg
C) 4.0 × 1016 kg
D) 5.1 × 1014 kg

E) A) and B)
F) A) and D)

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The gravitational acceleration on a planet's surface is 16.0 m/s2. What is the gravitational acceleration at an altitude of one planet diameter above the SURFACE of the planet?


A) 5.33 m/s2
B) 1.78 m/s2
C) 1.60 m/s2
D) 4.00 m/s2
E) 8.00 m/s2

F) C) and E)
G) C) and D)

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A certain planet has an escape speed V.If another planet has twice size and twice the mass of the first planet,its escape speed will be


A) 2V.
B) A certain planet has an escape speed V.If another planet has twice size and twice the mass of the first planet,its escape speed will be A)  2V. B)    V. C)  V. D)  V/2. E)  V/  V.
C) V.
D) V/2.
E) V/ A certain planet has an escape speed V.If another planet has twice size and twice the mass of the first planet,its escape speed will be A)  2V. B)    V. C)  V. D)  V/2. E)  V/

F) A) and C)
G) All of the above

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From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.9200g? The radius of the earth is 6.38 × 106 m.


A) 272 km
B) 260 km
C) 554 km
D) 510 km

E) A) and B)
F) A) and C)

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Ekapluto is an unknown planet that has two spherical moons in circular orbits.The table summarizes the hypothetical data about the moons.Both moons have low axial spin rates. (G = 6.67 × 10-11 N • m2/kg2) Ekapluto is an unknown planet that has two spherical moons in circular orbits.The table summarizes the hypothetical data about the moons.Both moons have low axial spin rates. (G = 6.67 × 10<sup>-11</sup> N • m<sup>2</sup>/kg<sup>2</sup>)    The acceleration due to gravity at the surface of Moon B is A)  0.10 m/s<sup>2</sup>. B)  0.15 m/s<sup>2</sup>. C)  0.20 m/s<sup>2</sup>. D)  0.25 m/s<sup>2</sup>. E)  0.30 m/s<sup>2</sup>. The acceleration due to gravity at the surface of Moon B is


A) 0.10 m/s2.
B) 0.15 m/s2.
C) 0.20 m/s2.
D) 0.25 m/s2.
E) 0.30 m/s2.

F) B) and D)
G) B) and E)

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The weight of spaceman Speff at the surface of planet X,solely due to its gravitational pull,is 389 N.If he moves to a distance of 1.86 × 104 km above the planet's surface,his weight changes to 24.31 N.What is the mass of planet X,if Speff's mass is 75.0 kg? (G = 6.67 × 10-11 N • m2/kg2)


A) 2.99 × 1024 kg
B) 2.99 × 1018 kg
C) 2.99 × 1017 kg
D) 1.59 × 1018 kg

E) B) and C)
F) C) and D)

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

F) C) and D)
G) B) and C)

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A certain planet has an escape speed V.If another planet of the same size has twice the mass as the first planet,its escape speed will be


A) 2V.
B) A certain planet has an escape speed V.If another planet of the same size has twice the mass as the first planet,its escape speed will be A)  2V. B)    V. C)  V. D)  V/2. E)  V/  V.
C) V.
D) V/2.
E) V/ A certain planet has an escape speed V.If another planet of the same size has twice the mass as the first planet,its escape speed will be A)  2V. B)    V. C)  V. D)  V/2. E)  V/

F) C) and E)
G) B) and D)

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Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r,and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?


A) 20 d
B) 40 d
C) 80 d
D) 160 d
E) 320 d

F) B) and E)
G) A) and E)

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Planet Z-34 has a mass equal to 1/3 that of Earth,a radius equal to 1/3 that of Earth,and an axial spin rate 1/2 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) 3g.
C) 6g.
D) g/9.
E) 9g.

F) A) and C)
G) All of the above

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If the mass of the earth and all objects on it were suddenly doubled,but the size remained the same,the acceleration due to gravity at the surface would become


A) 4 times what it now is.
B) 2 times what it now is.
C) the same as it now is.
D) 1/2 of what it now is.
E) 1/4 of what it now is.

F) A) and B)
G) C) and E)

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A meteoroid,heading straight for Earth,has a speed of 14.8 km/s relative to the center of Earth as it crosses our moon's orbit,a distance of 3.84 × 108 m from the earth's center.What is the meteroid's speed as it hits the earth? You can neglect the effects of the moon,Earth's atmosphere,and any motion of the earth.(G = 6.67 × 10-11 N • m2/kg2,Mearth = 5.97 × 1024 kg)


A) 18.5 km/s
B) 21.5 km/s
C) 32.4 km/s
D) 87.3 km/s

E) None of the above
F) B) and D)

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Beings on spherical asteroid Π have observed that a large rock is approaching their asteroid in a collision course.At 7514 km from the center of the asteroid,the rock has a speed of 136.0 m/s and later at 2823 km it has a speed of 392.0 m/s.Use energy conservation to find the mass of asteroid Π.You can neglect any effects due to the parent star of the asteroid.(G = 6.67 × 10-11 N • m2/kg2)


A) 4.582 × 1021 kg
B) 9.164 × 1027 kg
C) 6.112 × 1028 kg
D) 4.582 × 1020 kg

E) None of the above
F) A) and B)

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A small-sized 155-kg mass is located 1.50 m from a small-sized 275-kg mass,with both masses fixed in place.Where should you place a third small-sized mass so that the net gravitational force on it due to the original two masses is zero?

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0.643 m from the 155...

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Find the orbital speed of an ice cube in the rings of Saturn.The mass of Saturn is 5.68 × 1026 kg and the rings have an average radius of 100,000 km.(G = 6.67 × 10-11 N • m2/kg2)


A) 19.5 km/s
B) 27.5 km/s
C) 13.8 km/s
D) 1.95 km/s

E) None of the above
F) A) and B)

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The reason an astronaut in an earth satellite feels weightless is that


A) the astronaut is beyond the range of the earth's gravity.
B) the astronaut is falling.
C) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
D) this is a psychological effect associated with rapid motion.
E) the astronaut's acceleration is zero.

F) None of the above
G) A) and D)

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Ekapluto is an unknown planet that has two moons in circular orbits.The table summarizes the hypothetical data about the moons. Ekapluto is an unknown planet that has two moons in circular orbits.The table summarizes the hypothetical data about the moons.   The orbital period of Moon B is closest to A)  5.6 × 10<sup>6</sup> s. B)  6.0 × 10<sup>6</sup> s. C)  6.4 × 10<sup>6</sup> s. D)  6.9 × 10<sup>6</sup> s. E)  7.3 �× 10<sup>6</sup> s. The orbital period of Moon B is closest to


A) 5.6 × 106 s.
B) 6.0 × 106 s.
C) 6.4 × 106 s.
D) 6.9 × 106 s.
E) 7.3 × 106 s.

F) C) and D)
G) A) and B)

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