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A satellite in uniform circular orbit around earth (radius of orbit = 4.6x10^7 m )...

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tayaah | Student | (Level 1) eNoter

Posted May 7, 2013 at 5:38 AM via web

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A satellite in uniform circular orbit around earth (radius of orbit = 4.6x10^7 m ) experiences a gravitational fore of 228N.
     a) determine the mass of the satellite.

     b) determine the speed of the satellite.

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted May 7, 2013 at 7:17 AM (Answer #1)

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(a) Given radius of the orbit (r)=4.6x10^7 m

              Gravitational force(F)=228 N.

Let mass of the earth be M and mass of the satellite be m. Then by the Newton's law of gravitation force F of pull by earth is given by

          F=GMm/r^2``

Here G is the Universal gravitational constant. Value of G is =6.67x10^-11 N(m/Kg)^2. And

Mass of the Earth(M)=5.97x10^24 Kg.

So      228=(6.67x10^-11)(5.97x10^24)m/(4.6x10^7)^2

  or,   m=228(4.6x10^7)^2 (10^11)/{(6.67)(5.97x10^24)}

            =1211.575 Kg.    Answer.

        

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