Concept explainers
(a)
Find the total energy of the satellite-Earth system.
(a)
Answer to Problem 79CP
The total energy of the satellite-Earth system is
Explanation of Solution
Write the equation for total energy,
Here,
Conclusion:
Substitute
Therefore, the total energy of the satellite-Earth system is
(b)
Find the magnitude of the
(b)
Answer to Problem 79CP
The magnitude of the angular momentum of the satellite is
Explanation of Solution
Write the equation for angular momentum.
Conclusion:
Substitute
Therefore, the magnitude of the angular momentum of the satellite is
(c)
Find the satellite speed and distance from the center of Earth from the apogee.
(c)
Answer to Problem 79CP
The satellite speed and distance from the center of Earth from the apogee are
Explanation of Solution
As the energy of the satellite-Earth system and angular momentum of the Earth are conserved then at apogee,
Conclusion:
Substitute the known values in equation III.
Solving the above equations simultaneously and suppressing units.
This further reduces to,
The above equation is the quadric equation then the solution is,
The above equation gives two values such as,
Then the distance between satellite and Earth center is,
Therefore, satellite speed and distance from the center of Earth from the apogee are
(d)
Find the semi major axis of the satellite orbit.
(d)
Answer to Problem 79CP
The semi major axis of the satellite orbit is
Explanation of Solution
Write the equation for the major axis,
Here,
Conclusion:
Substitute
Therefore, the semi major axis of the satellite orbit is
(e)
Find the period of satellite.
(e)
Answer to Problem 79CP
The period of satellite is
Explanation of Solution
Write the equation for the period,
Here,
Conclusion:
Substitute
Therefore, the period of satellite is
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Chapter 13 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
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