Satellite moves in a circular orbit around the Earth at a speed of 5.1 km/s.Determine the satellite's altitude above the surface of the Earth....

We can assume that the altitude of the satellite is x from earth and so it is earths radius R +x  meter distant from the centre of the earth.

The satellites speed is v . We also assume that the gravitational force F is given by:

F = GMm/(r+x)^2 and this is equal to the centrepetal force of the satellite, mv^2/(R+x), where G is the gravitational constant, M =mass of the earth and m is the mass of the satellite. Using the known values, we would detrmine the value of x, the altitude of the satellite.

GMm/(R+x)^2=mv^2/(R+x). Reducinf by m/(R+x) , we get:

GM/(R+x) = v^2 or

R+x = GM/v^2 or

x = GM/v^2 - R

=6.67259*10^-11*5.98*10^24/5100^2  - (6370000)

= 8971056.594 m

=8971.056594 Km.