Calculation of the Best Stability Orbit of the Satellite around the Earth before Transferring to Orbit around Mars

In this research, the eccentricity will be calculated as well as the best height of satellite orbit that can used to transfer from that orbit around the Earth to construct an interplanetary trajectory, for example Mars, when the transfer can be accomplished by a simple impulse, that means the transfer consists of an elliptical orbit from the inner orbit (at a perigee point) to the outer orbit (at apogee point). We will determine Keplerian equation to find the value of a mean anomaly(M) by Rung-Cutta method. There are several types of satellites orbits around the Earth, but by this study, we find that the best stable orbit to the satellite that is used to inter its orbit around Mars is the Medium Earth Orbit (MEO) at a height about 3500km above the Earth surface. (MEO) comprises a wide range of orbits anywhere between LEO and GEO, its height above the Earth surface is about 2000-35700 km, and it is very commonly used by navigation satellites. The values ​​of Euler angles (i=23.45°, Ω=20°, w=60°) were installed and the values ​​of each of the height of the perigee point were changed by controlling the height from the ground surface (hp=500, 3500, 35800) km and the eccentricity of the orbit from e=0.1 to 0.9. We found that the best stable orbit of the satellite around the Earth in preparation for its transition to another orbit around Mars is at an altitude of 3500 km, with eccentricity of approximately 0.6, because this orbit was the most stable according to the program results shown in the graphs (no.10) because at the perigee of the orbit we obtained the highest escape speed was approximately 8 km/sec, which means the possibility of transfer with the lowest possible energy.