Cost Effect of Launch Site Location on Multistage Rocket Design to Be Used in Geostationary Satellite Launch Missions

This paper aims to present the effect of launch site location on multistage rockets, which are used for geostationary satellite launch missions. Geostationary orbit has a zero-degree inclination angle circular geosynchronous orbit whose period equals one complete earth rotation. In other words, the period of the geostationary orbit is equal to one sidereal day of the Earth. Due to geometric constraints, a direct launch cannot be made into orbit with an inclination angle lower than the launch site latitude. To launch into such an orbit with a low inclination angle, it is necessary to make a plane change maneuver with another rocket engine ignition. The fuel required to perform this plane change maneuver varies significantly with the latitude of the launch site. The conceptual design of the rocket suitable for this mission should consider how much $\Delta V$ will be required for the plane change maneuver of the rocket in the final stage and how much fuel will be needed for this maneuver. Also, other maneuvers must be performed to place a satellite in a geostationary orbit, such as entering the transfer ellipse from the parking orbit and circularization. After all these maneuvers and velocity increment requirements are planned, stage optimization can be made in the conceptual rocket design, and the maximum payload can be placed in a geostationary orbit with minimum liff-of-weight. Stage optimization will be done in this study using the Lagrange Multipliers method. Unlike the classical stage optimizations made with the Lagrange Multipliers method, not only the total velocity change of all stages but also the velocity changes required for each stage will be determined separately as constraints and optimization will be done. Since there is more than one constraint, the Newton-Raphson method will be used numerically to calculate more than one Lagrange multiplier.