  Neural networks have provided powerful approaches to solve various scientific
problems. Many of them are even difficult for human experts who are good at
accessing the physical laws from experimental data. We investigate whether
neural networks can assist us in exploring the fundamental laws of classical
mechanics from data of planetary motion. Firstly, we predict the orbits of
planets in the geocentric system using the gate recurrent unit, one of the
common neural networks. We find that the precision of the prediction is
obviously improved when the information of the Sun is included in the training
set. This result implies that the Sun is particularly important in the
geocentric system without any prior knowledge, which inspires us to gain
Copernicus' heliocentric theory. Secondly, we turn to the heliocentric system
and make successfully mutual predictions between the position and velocity of
planets. We hold that the successful prediction is due to the existence of
enough conserved quantities (such as conservations of mechanical energy and
angular momentum) in the system. Our research provides a new way to explore the
existence of conserved quantities in mechanics system based on neural networks.
