A satellite moves in a circular orbit around the earth at a speed of 6.8 km/s. determine the satellites altitude above the surface.assume the earth...

The gravitational force of attraction between two bodies
of mass M1 and M2 and separated by a distance r is given
by:

F = G*M1*M2 / r^2

The
satellite is revolving around the Earth with a velocity equal to v and at a height of r;
the centripetal force is equal to mv^2 / r.

As the height
of the satellite above the Earth has been taken to be r and its speed is 6.8 km/s, this
gives us:

G*Me*Ms / (r + 6370000)^2 = Ms * (6800)^2/ (r +
6370000)

( the distances have been converted to m and r +
6370000 is the distance from the center of the Earth which is required, Ms is the mass
of the satellite and gets cancelled)

=> r + 6370000
= G* Me / (6800)^2

=> r = [6.67*10^-11 * 5.98 *
10^24 / (6800)^2] – 6370000

=> r = [6.67*10^-11 *
5.98 * 10^24 / (6800)^2] - 6370000

=> r = 2255994.8
m

=> r = 2255.99
km

The height of the satellite is 2255.99
km