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What is the orbital velocity of satellite ? Derive its equation. |
Answer» Solution :`implies` The velocity of satellite to revolve it around EARTH in a given orbit is known as orbital velocity of satellite.  `implies` A satellite of mass m at height from the surface of earth revolving around the earth as shown in figure. Its distance from the centre of earth `r = R_(E) +h` `implies ` The orbital velocity of satellite is `v_0` `impliesF= (GM_(E) m)/(r^2) ""...(1)` `implies`The centripetal force on satellite is , `F = (mv_0)/r^2 "" ....(2)` `implies` The necessary centripetal force for this circular MOTION of satellite is provided by the earth.s gravitational force on it. `implies :.` Centripetal force of satellite `implies` = Gravitational force exerted by earth on Satellite. `:. (mv_0^2)/(r)=(GM_(E)m)/r` `implies :. v_(0)^2=(GM_(E))/r""...(3)` but `r = R_(E) +h` `:. v_(0) = sqrt((GM_(E))/(R_E+h))""....(4)` `implies` Equation indicates that as h INCREASES Vo decreases. `implies`Gravitational acceleration on earth.s surface, `implies g = (GM_(E))/(R_E^2)` `:. GM_(E) = gR_(E) ^(2) ""...(5)` `implies` Substituting the VALUE of equation (5) in equation (4), `:. v_0=sqrt((gR_E^2)/((R_(E)+h)))` `:. v_(0) =R_(E) sqrt((g)/(R_(E)+h))""...(6)` `implies` For a satellite very close to the surface of earth h can be neglected in COMPARISON to RE Equations (4) and (6) written as below , `v_(0) =sqrt((GM_(E))/R_E)""..(7)` `v_(0) =sqrt(gR_E)""...(8)` |
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