a. At what height above the earth is the free-fall

Chapter 13, Problem 32P

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QUESTION:

Problem 32P

a. At what height above the earth is the free-fall acceleration 10% of its value at the surface?

b. What is the speed of a satellite orbiting at that height?

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QUESTION:

Problem 32P

a. At what height above the earth is the free-fall acceleration 10% of its value at the surface?

b. What is the speed of a satellite orbiting at that height?

ANSWER:

Step 1 of 5

Part (a)

We are going to find the altitude where the acceleration due to gravity is 10 % of its original value \(\mathrm{g}\).

The radius of the Earth \(\mathrm{R}=6.37 \times 10^{6} \mathrm{~m}\)

The mass of the Earth \(\mathrm{M}=5.98 \times 10^{24} \mathrm{~kg}\)

The gravitational constant \(mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)

 

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