   Chapter 7, Problem 53AP

Chapter
Section
Textbook Problem

The Solar Maximum Mission Satellite was placed in a circular orbit about 150 mi above Earth. Determine (a) the orbital speed of the satellite and (b) the time required for one complete revolution.

(a)

To determine
The orbital speed of the satellite.

Explanation

Given info: The circular orbit of the satellite is 150mi above Earth.

Explanation:

The radius of the satellite orbit will be,

r=Re+h       (1)

• Re is the radius of earth
• h is the distance of the satellite from earth

The centripetal force required for the circular motion of the satellite will be provided by the gravitational force. Hence,

mvt2r=GMemr2

• Me is the mass of earth
• m is the mass of the satellite
• G is the universal gravitational constant
• r is the distance between the centre of earth to the satellite
• vt is the tangential speed

On re-arrangement for the tangential speed,

vt=GMer       (2)

Combining (1) and (2), the tangential speed of the satellite will be,

vt=GMeRe+h

Substitute 6.67×1011Nm2kg-2 for G , 5.98×1024kg for Me , 6.38×106m for Re , 150mi for h to determine the orbital speed of the satellite,

vt=(6

(b)

To determine
The time taken by the satellite to complete one complete revolution.

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