Irodov Problem 1.226

The satellite is moving very close to the Earth's surface, so we can assume that the radius of its orbit is almost equal to R - the radius of the Earth. Let the mass of Earth be M and its time period of rotation about its own axis be T. As already solved in problem 1.225, the angular velocity of the satellite w with respect to a stationary observer is given by irrespective of the direction (East to West or West to East) it moves. It absolute velocity is given by . The absolute velocity of an observer on Earth is given by . The velocity of the satellite as measured by an observer on Earth for the two satellites (moving East to West and West to East) will be v+vE and v-vE respectively. So the ratio of kinetic energies of the satellite (of mass m ) as perceived by an observer on Earth will be,









The exact numerical value can be computed by putting the values,



given by approximately 1.27.