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Exam 12: Gravity

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Question 41

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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

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Question 42

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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

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Question 43

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

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?

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.

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?

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.

The gravitational force between two objects is proportional to

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 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 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?

State Kepler's Third Law of Orbital Motion

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

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

A 700-kg satellite is in an elliptical orbit around Earth with a perigee (the point of closest approach) of 7.50 × 10⁶ m from the center of Earth and an apogee (the furthest point from the center of Earth) of 11.5 × 10⁶ m. What is the total energy of the satellite? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg².

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?

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 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.

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.

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