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Obtain an expression for the critical velocity of a satellite orbiting around the Earth. |
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Answer» Solution :Suppose a satellite of mass is taken above the Earth 's atmosphere to an altitude H and then projected horizontally with the critical velocity `v_(c )`. This PUTS the satellite into a circular orbit of RADIUS R = R + h, where R is the radius of theEarth. Let M be the mass of the Earth. For the satellite to perform UCM with orbital radius r, the centripetal force necessary is `mv_(c)^(2)//r`. In this case, it is the gravitational force `GmM//r^(2)` exerted on the satellite by the Earth. `therefore (mv_(c)^(2))/(r) = (GmM)/(r^(2))""...(1)` `therefore v_(c)^(2) = (GM)/(r)` `therefore v_(c)=sqrt((GM)/(R+H))""...(2)` `vec(v_(c))` is along the tangent to the path of the satellite as shown in the figure. 
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