Worksheet
Universal Gravitation and Satellites
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Some formulas you might like to reference as your complete this worksheet:
Refer to the following information for the next four questions.
On average, the distance from the earth to the sun (from center to center) is 150 x 10
^{9}
meters and it takes the earth 365 days to make one complete revolution.
What is the earth's average tangential velocity as it circles the sun?
What is the strength of the sun's gravitational field at the earth's orbital radius?
What is the mass of the sun?
What is the magnitude of the gravitational force of attraction between the earth and the sun? That is, how much does the earth "weigh" in the sun's gravitational field?
Refer to the following information for the next two questions.
An imaginary planet has a mass twice as great as the earth's, but the same radius.
What is the acceleration due to gravity on the surface of the planet?
At what height above the surface of the planet would the planet's acceleration due to gravity equal that on the earth's surface?
Refer to the following information for the next six questions.
A GPS satellite is in orbit about the earth at a height of 20,000 km above the earth's surface.
What is the strength of the earth's gravitational field at this altitude?
If the satellite has a mass of 1350 kg, how much would it "weigh" while it is in orbit?
What is the magnitude of the centripetal acceleration experienced by the satellite?
What is the satellite's tangential velocity?
How many seconds does it take the satellite to make one revolution around the earth?
How would the height of a satellite that has been placed in geosynchronous orbit about the earth's equator compare to the height of this GPS satellite?
Refer to the following information for the next three questions.
The earth-to-moon distance (from center to center) is 3.84 x 10
^{5}
km.
What is the strength of the earth's gravitational field at the moon's location?
What is the moon's tangential velocity about the earth?
What is the period of the moon in seconds?
Refer to the following information for the next three questions.
During one of the Apollo missions the command module orbited the moon at a height of 100 km above the moon's surface.
What was its orbital period?
To have a period twice as long, at what height should it have gone into orbit?
How would the command module's tangential velocity at 100 km compare to its velocity at this new, higher orbit?
Refer to the following information for the next three questions.
The rings of Saturn are composed of chunks of methane ice orbiting the planet. The innermost ring has a radius of 73,000 km while the outermost ring has a radius of 170,000 km.
If a chunk of ice in the innermost ring takes only 5.58 hours to complete one orbit around Saturn, what is Saturn's mass?
What is the tangential velocity of this piece of ice?
How long does it take a chunk of ice chunk in the outermost ring to complete one orbit?
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