Concept explainers
(a)
The time taken by the satellite to complete one orbit.
(a)
Answer to Problem 29P
The time taken by the satellite to complete one orbit is
Explanation of Solution
Write the expression for the
Here,
Write the expression for the gravitational force.
Here,
Equate equation (I) and (II) to solve for
Write the expression for
Here,
Write the expression for the period of revolution.
Here,
Use equation (IV) and (III) in (V) to solve for
Conclusion:
Substitute
Therefore, the time taken by the satellite to complete one orbit is
(b)
The speed of the satellite.
(b)
Answer to Problem 29P
The speed of the satellite is
Explanation of Solution
Use equation (IV) in (III) to solve for
Conclusion:
Substitute
Therefore, the speed of the satellite is
(c)
The minimum input energy needed to place the satellite in the orbit.
(c)
Answer to Problem 29P
The minimum input energy needed to place the satellite in the orbit is
Explanation of Solution
Write the expression for minimum energy needed to place the satellite in the orbit.
Here,
Write the expression for
Here,
Write the expression for
Use equation (X) in (IX) to solve for
Write the expression for the
Write the expression for
Write the expression for
Use equation (IV) in (XIII) to solve for
Use equation (XV), (XIII), (XII), (XI) in (VIII) to solve for
Conclusion:
Substitute
Therefore, the minimum input energy needed to place the satellite in the orbit is
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Chapter 11 Solutions
Principles of Physics: A Calculus-Based Text
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