Concept explainers
(a)
The
(a)
Answer to Problem 92P
The angular displacement of Earth in one day is
Explanation of Solution
Write an expression to calculate the angular displacement of Earth in one day.
Here, the angular displacement of Earth in one day is
Conclusion:
Substitute
Thus, the angular displacement of Earth in one day is
(b)
The change in Earth’s velocity.
(b)
Answer to Problem 92P
The change in Earth’s velocity is
Explanation of Solution
Write an expression to calculate the change in Earth’s velocity.
Here, the change in Earth’s velocity is
Conclusion:
Substitute
Thus, the change in Earth’s velocity is
(c)
The average acceleration during one day.
(c)
Answer to Problem 92P
The average acceleration during one day is
Explanation of Solution
Write an expression to calculate the average acceleration during one day.
Here, the average acceleration during one day is
Conclusion:
Substitute
Thus, the average acceleration during one day is
(d)
Compare the average acceleration with Earth’s instantaneous radial acceleration.
(d)
Answer to Problem 92P
The average acceleration with Earth’s is equal to the instantaneous radial acceleration.
Explanation of Solution
Write an expression to calculate the radial acceleration.
Here, the radial acceleration is
Conclusion:
Substitute
Thus, Earth’s motion for one day tends to make small angle at the Sun, thus, the arc length and the chord length along the Earth's orbit are very nearly equal.
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