   Chapter 7, Problem 44P

Chapter
Section
Textbook Problem

A 600-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth’s mean radius. Find (a) the satellite’s orbital speed, (b) the period of its revolution, and (c) the gravitational force acting on it.

(a)

To determine
The orbit speed of the satellite.

Explanation

Given info: The gravitational constant is 6.67×1011Nm2/kg2 , mass of Earth is 5.98×1024kg , and the mean radius of Earth is 6.38×106m .

Explanation: The satellite revolves the earth with radius of the orbit r=2RE and the gravitational force gives the centripetal acceleration of the satellite. The centripetal force and the gravitational force between the satellite and Earth is related as follows msv2/2RE=GmEms/(2RE)2 and this expression is rearranged to the orbit speed of the satellite.

The formula for the orbit speed of the satellite is,

v=GmE2RE

• G is gravitational constant.
• mE is mass of Earth.
• RE is mean radius of Earth.

Substitute 6.67×1011Nm2/kg2 for G , 5

(b)

To determine
The period of the satellite’s revolution.

(c)

To determine
The gravitational force acting on the satellite.

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