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Neural networks have provided powerful approaches to solve various scientificproblems. Many of them are even difficult for human experts who are good ataccessing the physical laws from experimental data. We investigate whetherneural networks can assist us in exploring the fundamental laws of classicalmechanics from data of planetary motion. Firstly, we predict the orbits ofplanets in the geocentric system using the gate recurrent unit, one of thecommon neural networks. We find that the precision of the prediction isobviously improved when the information of the Sun is included in the trainingset. This result implies that the Sun is particularly important in thegeocentric system without any prior knowledge, which inspires us to gainCopernicus' heliocentric theory. Secondly, we turn to the heliocentric systemand make successfully mutual predictions between the position and velocity ofplanets. We hold that the successful prediction is due to the existence ofenough conserved quantities (such as conservations of mechanical energy andangular momentum) in the system. Our research provides a new way to explore theexistence of conserved quantities in mechanics system based on neural networks.

Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks