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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 Earthâs 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 Earthâs orbit around the Sun is 3.156 Ã 107 s and its distance from the Sun is 1.496 Ã 1011 m. SOLUTION Conceptualize Based on the mathematical representation of Keplerâs 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 4ï° 2 r 3 Ms ï½ GT 2 the Sun: Substitute the known values: Ms ï½ 4ï° 2 ï¨1.496 ï´1011 m ï© ï¨ 6.674 ï´10 ï11 3 N ï m 2 kg 2 ï©ï¨ 3.156 ï´107 s ï© 2 ï½ 1.99 ï´ 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 Ï and at an altitude h above the Earthâs 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