Concept explainers
(a)
The height of the satellite’s orbit if its total energy were
(a)
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Answer to Problem 73PQ
The height of the satellite’s orbit if its total energy were
Explanation of Solution
Write the equation total energy for a satellite in a circular orbit.
Here,
Write the expression for the energy difference of the satellite in two positions.
Here,
Rearrange above equation to get
Initial position of the satellite is
Write the expression for
Here,
Conclusion:
Radius of earth is
Substitute
Substitute
Substitute
Substitute
Rearrange above equation to
Therefore, the height of the satellite’s orbit if its total energy were
(b)
The difference in the system’s kinetic energy.
(b)
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Answer to Problem 73PQ
The kinetic energy of the system decreases by
Explanation of Solution
Total energy of an object in bound orbit is always negative. Therefore, for higher and lower orbits, the total energy of the satellite is negative. Its absolute value is equal to kinetic energy. For a circular orbit, total energy and potential energy can be related as
For a circular orbit, kinetic energy and potential energy can be related as
Therefore, change in kinetic energy is equal to negative change in total energy. In this problem, total energy of the satellite is increased by
Conclusion:
Therefore, kinetic energy of the system decreases by
(c)
The difference in the system’s potential energy.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 73PQ
The potential energy of the system increases by
Explanation of Solution
For an object in bound orbit, its total energy is always negative. Therefore, for higher and lower orbits, the total energy of the satellite is negative. Its absolute value is equal to kinetic energy.
For a circular orbit, total energy and potential energy can be related as
In this problem, total energy of the satellite is increased by
Conclusion:
Therefore, potential energy of the system increases by
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Chapter 8 Solutions
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