   Chapter 7, Problem 42P

Chapter
Section
Textbook Problem

An artificial satellite circling the Earth completes each orbit in 110 minutes, (a) Find the altitude of the satellite, (b) What is the value of g at the location of this satellite?

(a)

To determine

The altitude of the satellite.

Explanation

Given Info:

The time taken by artificial satellite for each orbit around the earth is 110min.

According to Kepler’s third law,

T2=(4π2GM)r3

Here, G is the gravitational constant, M is the mass of Earth, r is the radius and T is the time period.

On re-arranging,

Re-arrange to calculate the radius of the artificial satellite is,

r=(T2GM4π2)13

Substitute 110min for T, 6.67×1011Nm2kg2 for G and 5.98×1024kg for M to find the radius of the orbit,

r=((110min(60.0s1.0min))2(6.67×1011Nm2kg2)(5

(b)

To determine

The value of acceleration due to gravity at the location of satellite.

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