   Chapter 7, Problem 41P

Chapter
Section
Textbook Problem

A satellite is in a circular orbit around the Earth at an altitude of 2.80 × 106 m. Find (a) the period of the orbit, (b) the speed of the satellite, and (c) the acceleration of the satellite. Hint: Modify Equation 7.23 so it is suitable for objects orbiting the Earth rather than the Sun.

(a)

To determine
The period of the orbit.

Explanation

Given Info:

The altitude of the satellite is 2.80×106m .

Explanation:

The radius of the satellite’s orbit is,

r=h+R

• r is the radius of the satellite’s orbit
• h is the altitude of the satellite
• R is the radius of the earth

After modifying the Kepler’s third law about earth for an orbital motion,

T2=(4π2GM)r3

• G is the gravitational constant
• M is the mass of earth

Formula to calculate the period of the orbit is,

T=(4π2GM)(h+R)3

Substitute 6.67×1011Nm2kg2 for G , 5.98×1024kg for M, 2.80×106m for h and 6

(b)

To determine
The speed of the satellite.

(c)

To determine
The acceleration of the satellite.

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