(Figure 1) A satellite that goes around the earth once every 24 hours is called
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Question
(Figure 1) A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite. Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants: The universal gravitational constant G is 6.67 times 10-11 N m2/kg2. The mass of the earth is 5.98 times 1024 kg. The radius of the earth is 6.38 times 106 m. Give the orbital radius in meters to three significant figures.Explanation / Answer
mv^2/r=GmM/r^2, where M is the mass of the earth. v^2=GM/r r=GM/v^2 To find v, we have w=v/r So v=w*r. w=2*pi/Period. Period is 24 hours=3600*24seconds Period= 86400s w=7.27e-5 v=7.27e-5*r r=GM/(7.27e-5*r)^2 r^3=GM/(7.27e-5)^2 r=(GM)^1/3*1/(7.27e-5)^2/3 r=4.22e7m=42211.85km
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