Asatellite orbits the earth in the same direction it rotates in a circular orbit above the equator a distance of 250 km from the surface. by how many seconds per day will a clock on such a satellite run slow compared to a clock on the earth? (compute just the special relativistic effects.)

Clock on the satellite is slower than the one present on the earth = 29.376 s

Given:

Distance of satellite from the surface, d = 250 km

Explanation:

Here, the satellite orbits the earth in circular motion, thus the necessary centripetal force is provided by the gravitation force and is given by:

where

v =  velocity of the satellite

R = radius of the earth = 6350 km = 6350000 m

G = gravitational constant =

M = mass of earth =

Therefore, the above eqn can be written as:

Now, for relativistic effects:

Now,

r = R + 250

Ratio of rate of satellite clock to surface clock:

Clock on the satellite is slower than the one present on the earth: