Planet Zero has a mass of 4.0 1023 kg and a radius of 2.0 106 m. A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 107 J. What maximum distance from the center of Zero is achieved by the probe?
a. 3.2 106 m
b. 4.0 106 m
c. 6.0 106 m
d. 5.0 106 m
e. 2.5 106 m
[Ques. 2] What is the escape speed from a planet of mass M and radius R if M = 3.2 1023 kg and R = 2.4 106 m?
a. 5.5 km/s
b. 4.2 km/s
c. 5.2 km/s
d. 4.8 km/s
e. 3.7 km/s
[Ques. 3] Planet Zero has a mass of 5.0 1023 kg and a radius of 2.0 106 m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 106 m from Zero's center?
a. 3.0 km/s
b. 2.2 km/s
c. 1.6 km/s
d. 3.7 km/s
e. 5.9 km/s
[Ques. 4] Planet Roton has a mass of 4.0 1023 kg and a radius of 2.0 106 m. With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of 3.0 106 m from the center of Roton?
a. 4.2 km/s
b. 3.9 km/s
c. 3.0 km/s
d. 3.4 km/s
e. 6.0 km/s
[Ques. 5] A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 106 m, mass = 6.0 1024 kg)
a. 2.9 108 J
b. 3.5 108 J
c. 4.1 108 J
d. 4.7 108 J
e. 5.9 108 J
[Ques. 6] An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 106 m, R = 5.0 106 m, and M = 4.0 1024 kg.
a. 7.8 km/s
b. 3.5 km/s
c. 5.4 km/s
d. 6.9 km/s
e. 4.8 km/s
[Ques. 7] What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 106 m around the Earth? (Mass of Earth = 6.0 1024 kg.)
a. 5.0 109 J
b. 1.0 1010 J
c. 1.5 1010 J
d. 2.0 1010 J
e. 2.5 109 J
[Ques. 8] A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?
a. GmM/(4R)
b. GmM/R
c. GmM/(2R)
d. GmM/(3R)
e. 2GmM/(5R)
[Ques. 9] A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?
a. GmM/(2R)
b. GmM/(3R)
c. GmM/(4R)
d. GmM/(6R)
e. 3GmM/(4R)
[Ques. 10] What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 106 m, mass = 6.0 1024 kg) with a period of 5.0 h?
a. 88 N
b. 55 N
c. 36 N
d. 98 N
e. 18 N
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