A brief guide to the Mojo n-body example

Since August 2023, the Mojo repository has included the nbody.mojo benchmark, based on the N-body simulation from The Computer Language Benchmarks Game. This simulation models the orbits of Jovian planets using a simple symplectic integrator to test single-core numeric performance. Although not easily parallelizable, the benchmark allows for basic vectorization and addresses the complexities of numerically integrating orbital dynamics, which can lead to exponential errors over time. The implementation in Mojo uses SIMD data types for optimization, representing planets with a structure that includes position, velocity, and mass, and utilizes a symplectic integrator to maintain system energy stability. The simulation, designed to run 50 million steps, demonstrates the performance benefits of Mojo's built-in support for SIMD operations, achieving around 46% faster execution than a similar C implementation. Additionally, the post highlights the importance of choosing appropriate units to simplify calculations and reduce numerical instability, using a mass unit of the Sun divided by 4π² and a distance unit of one Astronomical Unit. The post invites the community to explore further optimizations and contribute to the project, offering a glimpse into the potential of Mojo for writing efficient code.