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What is the condition for setting up an artificial satellite at a height h from the earth's surface ? (Radius of the earth=R , mass of the earth =M) |
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Answer» Solution :Suppose height of the artificial satellite from the EARTH.s surface is h . Hence, the radius of the ORBIT is (R+h) . If V is the orbital SPEED, the centripetal force necessary to keep the satellite in that orbit is `(mv^2)/((R+h))` ( m= mass of the stellite ). if the mutual force of gravitation between the earth and the satellite can supplythis centripetal force, the satellite WOULD be in the orbit. Gravitational force between the satellite and the earth is `(GMm)/((R+h)^2)`. Hence, the necessary condition is `(mv^2)/(R+h)=(GMm)/((R+h)^2) or, v=sqrt((GM)/(R+h))` |
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