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DYNAMICS - EXAMPLE


Moon Satellite
  Example

 

The moon orbits the earth with an eccentricity of 0.0549. The maximum distance between the moon and earth centers is 407,000 km. A small satellite also orbits the moon in a circular orbit with a velocity of 5 km/s at an elevation of 50,000 km. What is the minimum distance between the earth center and the satellite? Neglect any effect the earth has on the satellite. Both the moon and satellite move in the same plane.

   
    Solution


Moon and Satellite Orbits

  First, find the perigee distance, ro.
   
   407,000 = ro (1.0549 / 0.9451)
   ro = 364,600 km

Minimum distance
   dmin = ro - 50,000 =364,600 - 50,000

dmin= 314,600 km