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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

After docking with the Soyuz, the Apollo must re-enter the earth's atmosphere from perigee (the closest point of the orbital path to the earth). If the Apollo is traveling too fast, it will burn up during re-entry.

What is known:

  • The mass of the Apollo is mA = 18.0 Mg.
  • At apogee (the furthest point of the orbital path from the earth), the speed of the Apollo is vA = 4,373 m/s.
  • At apogee, the Apollo's distance from the center of the earth is rA = 16,000 km.
  • The radius of the earth is RE = 6,370 km.
   
  Question

 

At perigee, what is the Apollo's angular momentum, distance from the center of the earth, and speed?

   
    Approach

   
  • Use the equations of angular momentum to determine the angular momentum at apogee, then at perigee.
  • Use equations involving the distance from the center of the earth and the transverse velocity (derived from angular momentum) to find the velocity at perigee.
     
   
 
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