This paper aims to study, the process of satellite transition between different orbits and evaluate the characteristics of the turbulent transitional orbit of transferring a satellite from Low Earth Orbit (LEO) to geostationary orbit (GEO) (hp=35790km). The measurements in this research involve considering different LEO characteristics of perigee heights (h_p=200, 400, 600,800) and eccentricities (e=0.01, 0.05 and 0.1), whereas the inclination is fixed to be (i= 23.445 degree).Also, the transfer of the satellite was studied in two stages. The first stage was from the perigee of the first orbit at height 200 km, to the apogee of the second orbit at height 945 km with eccentricity (0.01). the second stage, was the transition the satellite from the perigee of the second orbit at height 800 km to the final orbit (GEO) with the same eccentricity. Two types of turbulence were considered which are atmospheric drag and perturbation (Geopotential acceleration The perturbing acceleration effects on satellite due to the Earth’s gravity potential represent as function of J2 parameter). A program in MATLAB was designed to calculate the speed that for the transition, time and the ratio mass change, which represents the percentage of fuel as well as the extent of the effect of turbulence on the orbital elements of the transitional orbit.
The perturbed equation of motion was solved using Runge–Kutta method. The results showed that the increase altitude, the lower ΔV(velocity required to transition), where the ΔV at altitude of 800 km was the best results, reaching (2.244 km/sec). As for the transition in two stage, it may need a higher energy for the transition, as the difference between it and the direct phase in (ΔV= 0.011 km/sec). As the height of the initial orbit increases, the effect of the disturbance on the orbital elements of the transitional orbit decreases, and since the transition time is less than half a day (0.44 day), the effect of the disturbance is clear, so it cannot be neglected.