Exam 13: Gravitation

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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 object is dropped from an altitude of one Earth radius above Earth's surface.If M is the mass of Earth and R is its radius, the speed of the object just before it hits Earth, neglecting air resistance, is given by:

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Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of the following CANNOT be calculated?

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

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An astronaut in an orbiting space-craft feels "weightless" because she:

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An artificial satellite of Earth nears the end of its life due to air resistance.While still in orbit:

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

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A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed.If R is the radius of Earth, the highest altitude reached, measured from the surface, is:

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Einstein's principle of equivalence states:

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If Earth were to rotate only 100 times per year about its axis:

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A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:

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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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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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A spherical shell has inner radius R1, outer radius R2, and mass M, distributed uniformly throughout the shell.The magnitude of the gravitational force exerted on the shell by a point mass particle of m a distance d from the center, outside the outer radius, is:

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In planetary motion the line from the star to the planet sweeps out equal areas in equal times.This is a direct consequence of:

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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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An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:

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