Exam 4: Gravity and Orbits

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According to the scales in the figure, about how many times stronger is gravity on Earth than on the Moon? According to the scales in the figure, about how many times stronger is gravity on Earth than on the Moon?

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  Figure 1 -According to Figure 1, the approximate amount of time between two high tides at a given location is: Figure 1 -According to Figure 1, the approximate amount of time between two high tides at a given location is:

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You discover a moon orbiting a planet. The moon has an orbital period of three weeks, and the average distance between the moon and planet is 1.2 * 106 km. What is the planet's mass? Compare its mass to that of Jupiter, which is 1.9 * 1027 kg.

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Astronauts orbiting Earth in the space shuttle feel weightless in space because:

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Explain why the Moon rotates in the same amount of time as it takes to orbit once around the Earth.

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Suppose you are suddenly transported to a planet with 1/4 the mass of Earth but the same radius as the Earth. Your weight would _________ by a factor of _________.

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Mass and weight are different names for the same physical property of matter.

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All objects on Earth, regardless of the size of their mass, fall with the same acceleration.

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How does the force of gravity between the Sun and Mercury compare to the gravitational force between the Sun and the Earth? Note that the semimajor axis of Mercury's orbit is 0.4 AU, and Mercury's mass is 0.06 times the mass of the Earth.

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You find a moon orbiting a planet. The moon has a period of 10 days, and the average distance between the moon and planet is 106 km. What is the planet's mass? Note that the mass of Jupiter is 1.9 * 1027 kg.

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The distance between Earth and the Moon:

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Consider the figure below that illustrates the tidal bulge on the Earth's oceans due to the Moon and four people at different longitudes on the Earth from the point of view of an observer looking down on the North Pole of the Earth. If you were to arrive at the beach and find that the Moon was visible in the western half of the sky, then is the tide most likely to be coming in and the water level rising; or is the tide going out and the water level going down? Explain the rationale for your answer. Consider the figure below that illustrates the tidal bulge on the Earth's oceans due to the Moon and four people at different longitudes on the Earth from the point of view of an observer looking down on the North Pole of the Earth. If you were to arrive at the beach and find that the Moon was visible in the western half of the sky, then is the tide most likely to be coming in and the water level rising; or is the tide going out and the water level going down? Explain the rationale for your answer.

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Saturn has 95 times the mass of Earth, and its atmosphere extends outward 9.5 times the Earth's radius. How does the acceleration due to gravity at the edge of Saturn's atmosphere compare to that on the Earth?

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The Hubble Space Telescope orbits at an altitude of 600 km above the Earth's surface. Assuming it is in a stable circular orbit, what is its velocity? For reference, the Earth's radius is 6,400 km and Earth's mass is 6 *1024 kg.

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More massive objects fall faster in the Earth's gravitational field than less massive objects.

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The Earth's rotation rate is slowing because of:

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In a system with three gravitating bodies, there are _________ stable locations called _________ points for the third object to orbit in lockstep with the two more massive objects.

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Show that the tidal force on Earth from the Moon is approximately two times the tidal force on Earth from the Sun. For reference, Moon's mass is 7.3 *1022 kg, the Sun's mass is 2 * 1030 kg, the Earth-Moon distance is 3.8 * 105 km, and the Earth-Sun distance is 1.5*108 km.

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If you weighed 100 lbs on Earth, what would you weigh at the upper atmosphere of Jupiter? For reference, Jupiter has a mass that is about 300 times the Earth's mass and a radius that is 10 times the Earth's radius.

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Mercury orbits the Sun with an average distance of 0.4 AU, and its mass is 0.06 times that of the Earth. The gravitational force that the Sun exerts on Mercury is _______________ times the force of gravity that the Sun exerts on the Earth.

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