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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth?
Verified Answer
An artificial satellite is moving in a circular orbit around the earth...
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/R)2 * (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/R)2 * (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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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth?
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An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the Earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth?.
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