Show that `V_(0) =sqrt(gr)`

Explanation

For a satellite its orbit, gravitational force = centripetal force
`("GM"cancelm)/(r^(cancel(2)))=(cancelmv_(0)^(2))/(cancelr), " i.e., "v_(0)^(2)=(GM)/(r)`
i.e., `v_(0)=sqrt((GM)/(r))` where r = R + h but `g=(GM)/(R^(2))` for close orbits
`:. " for " h lt lt R,r ~~R`
`v_(0)=sqrt((GM)/(R)xx(R)/(R))=sqrt(gR)" ":.v_(0)=sqrt(gR)`
Hence orbital velocity is independent of mass and location of projection.