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if the satellite is stopped suddenly …

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if the satellite is stopped suddenly in its orbit and allowed to fell freely on to the earth. Find the speed with which it hits the surface of the earth.
  • 6 answers

Nishita Tomar 6 years, 11 months ago

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Ʌɐpɐʎ Ɐuɐɥsɹɐp . 6 years, 11 months ago

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Aman Kumar 6 years, 11 months ago

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Aman Kumar 6 years, 11 months ago

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Gaurav Seth 6 years, 11 months ago

The question is incomplete.

Q. A satellite is moving Only a circular orbit around the earth Again a height 6400km if the satellite Is suddelny stopped in its orbit and allowed to fall freely towards earth find the speed with which it hits the surface of the earth.

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Ans.

Height of the satellite from the surface of Earth = H = 6400 km.
Radius of Earth = R = 6400 km.
Mass of Earth = M.
G = Universal Gravitational constant.

Initial KE = 0.  Speed = 0.    
Gravitational potential energy of the satellite at height 6400 km 
   PE1 = - G M m/(H+R) = - G M m/ (2R) 
           = - (G M/R²) * (mR/2)
          = - m g R / 2         ,    as gravity g on Earth's surface = GM/R²

This potential energy on the surface of Earth:
     PE2 = - GMm/R = - (GM/R²) × (mR)
             = - m g R

Potential Energy lost = PE1 - PE2
       ΔPE  = m g R/2

Kinetic energy gained = ΔKE = 1/2 m v²
              1/2 m v² = m g R/2
               v² = g R
                v = √[g R] 
                   = √[9.81 × 6400,000]   m/s
                v = 7923.64 m/s. = 28, 525 km/hr

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