`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`
`implies F= (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)`
