It is estimated that artificial earth satellites have produced approximately 40,

Question

It is estimated that artificial earth satellites have produced approximately 40,000 pieces of debris larger than a pea. Suppose that one of the larger pieces of debris of mass 518 kg is in a circular orbit at two earth radii from the center of the earth and that the mass strikes a satellite in the same orbit, traveling in the opposite direction. Calculate the kinetic energy of the mass relative to the satellite. For comparison, the energy released by 1 million tons of TNT (or a 1 megaton nuclear bomb) equals 4.18 109 J.

Explanation / Answer

orbital speed of sattelite and the debris:

F = ma    >>>>   GmM/r2 = m(v2/r)   >>>>   v2 = GM/r   >>>>> v = (GM/r)0.5

M = Mass of the earth

 

the speed of the debris relative to the satellite is 2v >>>>> v' = 2*v = 2 * (GM/r)0.5

 

the kinetic energy of the mass relative to the satellite = (1/2)* m * (v')2

         = 0.5*518*4*(GM/r)

         = 0.5*518*4*(6.67*10-11*5.97*1024/(2*6.37*106))

         = 3238.1 * 107 J

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