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DYNAMICS - CASE STUDY SOLUTION

    Solution of a)


Circular Orbit, ε = 0
 

The initial velocity required to give the satellite a circular orbit can be found from,

    
where   g = 32.2 ft/s2
            RE = 3.960 mi = 20.9 x 106 ft
            ro = 10,000 mi = 52.8 x 106 ft

     

          = 16,300 ft/s

     
    Solution of b)


Parabolic Orbit, ε =1
 

The minimum initial velocity required to escape the earth's gravitational pull can be found from:

     

           = 23.1 x 103 ft/s

     
    Solution of c)


Elliptical Orbit, 0 < ε < 1

 

To find the maximum radius, the eccentricity of the orbit must be determined when the initial velocity of the satellite is 20,000 ft/sec.

     

       = 0.500

Because 0 < ε < 1, the orbit must be elliptical, and thus the maximum radius occurs at apogee.

     

           = 158 x 106 ft = 29,900 miles

     
   
 
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