Exam 13: Gravitation

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Two planets are orbiting a star in a distant galaxy. The first has a semimajor axis of 150 * 106 km, an eccentricity of 0.20, and a period of 1.0 Earth years. The second has a semimajor axis of 250 *106 km, an eccentricity of 0.30, and a period of:

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Four particles, each with mass m, are arranged symmetrically about the origin on the x axis. A fifth particle, with mass M, is on the y axis. The direction of the gravitational force on M is: Four particles, each with mass m, are arranged symmetrically about the origin on the x axis. A fifth particle, with mass M, is on the y axis. The direction of the gravitational force on M is:

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A mass m is located at the origin; a second mass m is at x = d. A third mass m is above the first two so the three masses form an equilateral triangle. What is the net gravitational force on the third mass?

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A planet in another solar system orbits a star with a mass of 4.0 * 1030 kg. At one point in its orbit it is 250* 106 km from the star and is moving at 35 km/s. Take the universal gravitational constant to be 6.67 * 10-11 m2/s2 .0 kg and calculate the semimajor axis of the planet's orbit. The result is:

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A particle might be placed A particle might be placed   Rank these situations according to the magnitude of the gravitational force on the particle, least to greatest. Rank these situations according to the magnitude of the gravitational force on the particle, least to greatest.

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Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *104 m/s. What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one?

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Two particles, each of mass m, are a distance d apart. To bring a third particle, with mass 2m, from far away to a resting point midway between the two particles, an external agent must do work equal to:

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A rocket ship is coasting toward a planet. Its captain wishes to know the value of g at the surface of the planet. This may be inferred by:

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Of the following where would the weight of an object be the least?

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Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium". The statement is:

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Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation. Then, the relationship between K and U:

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Suppose you have a pendulum clock which keeps correct time on Earth (acceleration due to gravity = 9.8 m/s2). Without changing the clock, you take it to the Moon (acceleration due to gravity = 1.6 m/s2). For every hour interval (on Earth) the Moon clock will record:

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An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they land together shows that:

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A spring scale, calibrated in newtons, is used to weigh sugar. If it were possible to weigh sugar at the following locations, where will the buyer get the most sugar to a newton?

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The speed of a comet in an elliptical orbit about the sun:

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Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below. Rank the configurations according to the magnitude of the gravitational force on M, least to greatest. Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below. Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.

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In Einstein's theory of gravitation, gravity is due to:

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An artificial Earth satellite of mass m is moved from a circular orbit with radius R to a circular orbit with radius 2R. If the mass of the Earth is ME, the work done by the gravitational force is:

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An artificial satellite of the Earth releases a bomb. Neglecting air resistance, the bomb will:

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The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet?

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