Abstract
We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.
Highlights
In the past decades, valuable insight about celestial bodies in our Solar System has been gained using spacecraft, such as Jupiter visited by Galileo [1]
We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR)
A model of the Gravity Assist Mapping was proposed based on a machine-learning method called Gaussian Process Regression
Summary
Valuable insight about celestial bodies in our Solar System has been gained using spacecraft, such as Jupiter visited by Galileo [1]. In Section Gravity Assist Mapping, it is described how the GPR model is to learn the features of flybys from training samples generated by PCR3BP equations of motion. This is used in a multi-start approach to avoid being trapped in local minima (more precisely: the gradient procedure is initiated at 10 different initial combinations of hyper-parameter values); (6) Determine the optimal size of the set of training data This is done by adding training samples gradually until a stable error, i.e. the difference between the outputs of the numerical PCR3BP and the GPR models on the test dataset, is observed. The random seed number for generating training dataset is a negligible influence factor for the performance of GPR models
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