Chapter 2: Space Curves
Section 2.9: Applications to Dynamics
A satellite is traveling at a constant speed in a circular orbit 400 miles above the surface of the earth where the acceleration of gravity is 30 ft per sec2. If the radius of the earth is taken as 4000 miles, what is the speed (in miles per hour) of the satellite?
For uniform circular motion, v is constant, so v.=0. The satellite traverses a circle of radius 4400 miles, with the center at the center of the earth. Hence, κ=1/4400. From
m g N=m aN N=m κ v2N
working in the units determined by g, obtain the equation 30=v24400⋅5280, and hence,
v=26400 ft/s = 264005280=5 m/s = 5⋅3600=18000 m/h
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