This thesis presents a neural network, that solves the three-body problem numerically. The three-body problem, a fundamental challenge in classical mechanics and astronomy, involves predicting the dynamic behavior of three celestial bodies under mutual gravitational influences. This thesis builds upon the n-body solver of G. Gonçalves Ferrari, T. Boekholt, and S. F. Portegies Zwart and introduces a novel methodology that conceptualizes solvers for the two-body problem as neurons within a neural network. Combining these solvers, the network predicts the complex gravitational interactions among celestial bodies. Unlike conventional neural networks, which often act as "black boxes", this approach maintains interpretability by integrating physical calculations directly into the network's architecture. This enables the learning of arbitrary calculational components of the underlying physical formulas, including the masses of celestial bodies. The thesis is structured to guide the reader from foundational concepts to the specific TensorFlow implementation of the n-body simulator, transforming the simulator written in Python into a neural network. To show the potential of this approach, learning algorithms for this unique model are developed, and the masses of celestial objects are accurately approximated using synthetic data, marking the beginning of further investigation, potentially leading to an improvement in the estimation of the planet's masses in our solar system.