Abstract
One of the objectives of mission design is selecting an optimum orbital transfer which often translated as a transfer which requires minimum propellant consumption. In order to assure the selected trajectory meets the requirement, the optimality of transfer should first be analyzed either by directly calculating the ∆V of the candidate trajectories and select the one that gives a minimum value or by evaluating the trajectory according to certain criteria of optimality. The second method is performed by analyzing the profile of the modulus of the thrust direction vector which is known as primer vector. Both methods come with their own advantages and disadvantages. However, it is possible to use the primer vector method to verify if the result from the direct method is truly optimal or if the ∆V can be reduced further by implementing correction maneuver to the reference trajectory. In addition to its capability to evaluate the transfer optimality without the need to calculate the transfer ∆V, primer vector also enables us to identify the time and position to apply correction maneuver in order to optimize a non-optimum transfer. This paper will present the analytical approach to the fuel optimal impulsive transfer using primer vector method. The validity of the method is confirmed by comparing the result to those from the numerical method. The investigation of the optimality of direct transfer is used to give an example of the application of the method. The case under study is the prograde elliptic transfers from Earth to Mars. The study enables us to identify the optimality of all the possible transfers.
Highlights
In an interplanetary mission, one of the mission analysis objectives is designing a trajectory with minimum propellant to allow the spacecraft brings more useful mass [1]
Mission designers often include corrective maneuver(s) to further reduce the amount of required propellant which is known as Deep Space Maneuver (DSM)
In order to validate the analytical solution of the in-plane primer vector components expressed in equations 5 and 6, the propagation results are compared to the result from numerical integration using state transition matrix
Summary
One of the mission analysis objectives is designing a trajectory with minimum propellant to allow the spacecraft brings more useful mass [1]. The interplanetary flight requires the spacecraft to leave the orbit of one celestial body to enter the orbit of another planet or performing rendezvous with another planet or object in space. It is possible to design a more complex transfer involving other celestial bodies passed by the spacecraft during the transfer, commonly known as gravity assist trajectory. The latter is much more complicated than a conic arc, it is widely used by a mission designer due to its advantage of significantly reducing the amount of required propellant for the transfer. Mission designers often include corrective maneuver(s) to further reduce the amount of required propellant which is known as Deep Space Maneuver (DSM). Such trajectory, which combines gravity assist and deep space maneuver, is referred to as Multiple Gravity Assist - Deep Space Maneuver (MGA-DSM) trajectory [2]
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