Practice Problems
Satellites
Directions:
On this worksheet you will practice using the basic formulas for satellites in uniform circular motion.
omit
Question 1
If the mass of the moon equals 7.36 x 10
^{22}
kg and a lunar day lasts for 27.3 'Earth days', how far from the center of the moon would a lunar satellite need to be placed to remain in a seleno-synchronous orbit?
8.6 x 10
^{7}
m
1.24 x 10
^{7}
m
1.44 x 10
^{7}
m
9.04 x 10
^{7}
m
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Question 2
Based on
Question #1
, at what average distance from the center of the moon did Apollo 11's lunar command module orbit if it completed 30 revolutions in roughly 11712 minutes?
2.93 x 10
^{6}
meters
4.07 x 10
^{6}
meters
1.09 x 10
^{6}
meters
2.33 x 10
^{6}
meters
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Question 3
What was the average tangential velocity of the command module in
Question #2
?
1.09 x 10
^{3}
m/sec
6.86 x 10
^{3}
m/sec
6.26 x 10
^{3}
m/sec
1.74 x 10
^{3}
m/sec
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Question 4
Mars takes approximately 687 'Earth days' to complete one orbit of our Sun. What is its average orbital radius from the center of the Sun? Correspondingly, the Earth takes 365 days to complete one orbit at an average radius of 1.5 x 10
^{11}
meters.?
3.39 x 10
^{11}
m
1.5 x 10
^{11}
m
2.28 x 10
^{11}
m
8.42 x 10
^{11}
m
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Question 5
What is the strength of the Sun's gravitational field at Mars' orbital radius found in
Question #4
?
5.9 x 10
^{-3}
m/sec
^{2}
2.55 x 10
^{-3}
m/sec
^{2}
6.54 x 10
^{-3}
m/sec
^{2}
7.67 x 10
^{-3}
m/sec
^{2}
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Question 6
What is Mars' tangential velocity while traversing its orbit around the Sun?
4.54 x 10
^{4}
m/sec
3.84 x 10
^{4}
m/sec
2.41 x 10
^{4}
m/sec
2.99 x 10
^{4}
m/sec
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Question 7
Astronomical data shows that one of the two natural moons orbiting Mars, Phobos, takes 7.66 hours to complete one orbit . Since Phobos orbits faster than Mars rotates, it rises and sets twice each 'Martian day.' Phobos orbits at an extremely low height of only 6.00 x 10
^{6}
meters above the Martian surface. If the average planetary radius of Mars is 3.39 x 10
^{6}
meters, then what is the anticipated mass of Mars based on these observations?
4.87 x 10
^{23}
kg
2.14 x 10
^{23}
kg
7.31 x 10
^{23}
2kg
6.44 x 10
^{23}
kg
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Question 8
The Mars Reconnaissance Orbiter (MRO) has a near circular orbit at a height of approximately 3.14 x 10
^{5}
meters above the surface of Mars. What is its average orbital velocity?
8.13 x 10
^{3}
m/sec
3.41 x 10
^{3}
m/sec
3.13 x 10
^{3}
m/sec
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