Resonance in the perturbations of a synchronous satellite due to angular rate of the earth-moon system around the sun and the earth’s rotation rate

This paper investigates resonances in the perturbations of a synchronous satellite including its latitude, angular rate of the earth-moon system around the sun and the earth’s rotation rate about its axis. This is found that resonances occur due to the commensurability between (i) angular velocity of the satellite and angular rate of earth’s rotation about its axis and (ii) angular rate of the earth-moon system around the sun and angular rate of the rotation of the earth. Amplitude and time-period of the oscillation at the resonance points are determined using the procedure of Brown and Shook [3]. Effect of (orbital angle of the mass-centre of the earth-moon system around the sun) on amplitude and time period is also analyzed. It is found that for increasing the values of from to amplitude decreases and time period also decreases. Effect of time on the latitude of the satellite including earth oblateness is also studied. It is seen that for increasing the value of , there is a small change in , the latitude of the synchronous satellite.