Three galaxies, each of mass m = 4.0 1041 kg, lie in a plane at the corners of an equilateral triangle with sides of 5.0 1022 m length. The magnitude of the force the other two galaxies exert on each galaxy is
a. 4.3 1027 N.
b. 6.4 1027 N.
c. 7.4 1027 N.
d. 8.6 1027 N.
e. 4.3 1028 N.
[Ques. 2] The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (R= 6.37 106 m; RMoon= 1.74 106 m; m = 5.98 1024 kg; mMoon = 7.36 1022 kg.)
a. 6.03 103 min.
b. 0.713 min.
c. 84.3 min.
d. 108 min.
e. 140 min.
[Ques. 3] Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.
a. Momentum and energy.
b. Energy and angular momentum.
c. Momentum and angular momentum.
d. Momentum, angular momentum and energy.
e. None of the above.
[Ques. 4] Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have
a. the smaller period.
b. the greater period.
c. the smaller gravitational mass.
d. the larger gravitational mass.
e. the larger universal gravitational constant.
[Ques. 5] A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?
a. There is no gravitational force on the satellite.
b. There is no acceleration toward the center of the Earth.
c. The satellite is in a state of free fall toward the Earth.
d. There is a tangential force that helps the satellite keep up with the rotation of the Earth.
e. The force toward the center of the Earth is balanced by a force away from the center of the Earth.
[Ques. 6] 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. 7] 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. 8] 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. 9] 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. 10] 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
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