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Transcript
Finalize Notice that the weight of the Space Station is less when it is in orbit, as we
expected. It has about 10% less weight than it has when on the Earth’s surface,
representing a 10% decrease in the magnitude of the gravitational field.
Example 13.4 The Mass of the Sun
Calculate the mass of the Sun, noting that the period of the Earth’s orbit around the
Sun is 3.156 × 107 s and its distance from the Sun is 1.496 × 1011 m.
SOLUTION
Conceptualize Based on the mathematical representation of Kepler’s third law
expressed in Equation 13.11, we realize that the mass of the central object in a
gravitational system is related to the orbital size and period of objects in orbit around
the central object.
Categorize This example is a relatively simple substitution problem.
Solve Equation
13.11 for the mass of
4 2 r 3
Ms 
GT 2
the Sun:
Substitute the known
values:
Ms 
4 2 1.496 1011 m 
 6.674 10
11
3
N  m 2 kg 2  3.156 107 s 
2
 1.99  1030 kg
Example 13.5 A Geosynchronous Satellite
Consider a satellite of mass m moving in a circular orbit around the Earth at a constant
speed υ and at an altitude h above the Earth’s surface as illustrated in Figure 13.9.
(A) Determine the speed of satellite in terms of G, h, RE (the radius of the Earth), and
ME (the mass of the Earth).
SOLUTION
Conceptualize Imagine the satellite moving around the Earth in a circular orbit under
the influence of the gravitational force. This motion is similar to that of the