(a) Show that if a satellite orbits very near the surface of a planet with period T, the density (=mass per unit volume) of the planet is
Part (a)
To Show:If a satellite orbits very near to the surface of a planet with period
Answer to Problem 55P
Solution:
The density of the planet in terms of period and gravitational constant is obtained as
Explanation of Solution
When a satellite orbits, the centripetal acceleration will be equal to the gravitational acceleration.
Mathematically,
Rearranging the above,
Where,
The density is the ratio of mass and unit volume. Mathematically,
Equating the above two:
On rearrangement:
Hence, the density of the planet in terms of time period and gravitational constant is obtained.
Conclusion:
Therefore, the density of the planet in terms of time period and gravitational constant is obtained as
Part (b)
The density of the Earth.
Answer to Problem 55P
Solution:
The density of the planet is
Explanation of Solution
Given:
Period,
Formula used:
From the previous part, the density of the planet can be obtained by:
Calculation:
Substituting the values of
Conclusion:
Therefore, the density of the planet is
Chapter 5 Solutions
Physics: Principles with Applications
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