Comparison of uniform to non-uniform gravitational equations with variable density for an aero-gravity assist maneuver

For inter-planetary trajectory design, a planets gravitational force on a spacecraft can be used to provide course alterations to the spacecraft\u27s trajectory. The course alterations are often expressed as delta-V maneuvers. By changing the velocity; i.e. delta-V, either in direction or magnitude, the spacecraft\u27s trajectory can be controlled. These delta-V maneuvers come at no expense in terms of fuel required. However, for these gravity-assist maneuvers, the maximum change in velocity direction, i.e. the turning angle, is limited. If a planet has an atmosphere, then an aero-gravity assist maneuver can be used in which the spacecraft uses atmospheric forces in addition to the gravitational forces to increase the turning angle, thus providing more control over the trajectory design process. Typically for analysis, planets are modeled as spherical, resulting in a uniform gravitational model, and the atmosphere is modeled as having a constant temperature. Because of the large distances involved between planets, the terminal conditions of an interplanetary trajectory phase of the mission are highly sensitive to perturbations in initial conditions. The initial conditions of the interplanetary phase are the terminal conditions of the aero-gravity assist phase of the spacecraft\u27s trajectory. Hence, perturbations in the terminal conditions of the aero-gravity assist phase can lead to significant perturbations in the arrival conditions at another planet. The specific perturbations to the aero-gravity assist phase to be considered arise from the non-spherical planet shape, leading to a non-uniform gravitational model, and temperature variations in the atmosphere corresponding to Day and Night atmospheric temperatures. Through numerical simulations it will be demonstrated that perturbations resulting from the use of different environmental models; i.e., planet shape and temperature variation, leads to significant perturbations in the terminal conditions of the aero-gravity assist phase of the spacecraft\u27s trajectory. These results are provided in tabulated form for use by trajectory designers in order to quickly assess the level of environmental model fidelity required in order to meet trajectory design specifications