Given
#T->"time period of revolution"= 90min=5400s#
#h-> " height of the orbit"=280km#
#R->"radius of the earth is at the equator" =6400 km#
Let
#m-> " mass of the satellite"#
#M-> " mass of the earth"#
#G-> " Gravitational constant"#
#g-> " acceleration due to gravity"=9.8ms^-2#
#v-> " speed of the satellite at height h"#
Considering the gravitational pull on satellite when it is on the surface of the earth we can write
#G(mM)/R^2=mg#
#=>GM=gR^2.........(1)#
Again considering the gravitational pull on satellite when it is revolving round the earth in an an orbit at height h in the equatorial plane with speed v , we can write
#G(mM)/(R+h)^2=(mv^2)/(R+h)#
#=>(GM)/(R+h)=v^2#
Now replacing #GM=gR^2 #
#=>(gR^2)/(R+h)=v^2#
#=>v=Rxxsqrt(g/(R+h))=6400kmxxsqrt((9.8xx10^-3kms^-2)/((6400+280)km))#
#=>v=(64xx7)/sqrt3340kms^-1~~7.75kms^-1#
