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I describe new tools and techniques I've built to solve different problems in gravitational dynamics. First, I describe our popular Rebound code, MERCURIUS, designed to solve for the evolution, including formation and long-term dynamics, of planetary systems. Unlike its predecessor, MERCURY, it is numerically symplectic and time-reversible. I also describe current work on a code, TRACE, which significantly improves on the accuracy and speed of MERCURIUS.

I then tackle the problem of the stability of the Solar System. Although great progress has been made in the last decades towards an understanding of chaos and stability of the Solar System due to the development of modern computers, I show that all studies I found are affected by numerical chaos, which causes artificial Solar System chaos and instability. The physical mechanism behind Mercury's orbital instability has been traditionally described by a diffusive process in a secular frequency, but our current work shows a subdiffusive process fits simulated data far better.

I describe new tools for the potential discovery of interstellar objects (IOs). The tools solve the linking problem, in which independent observations are linked together as a potential object of interest, using crude approximations. These objects are then validated using state of the art orbit fitters. I describe the validation tests I've done with this pipeline, which promises to be able to exploit the vast Solar System data expected from Rubin/LSST.

I next describe a suite of tools, including powerful new Kepler solvers and new symplectic integrators and their tangent equations, called NBODYGRADIENT. Unlike other popular methods, we can solve planetary systems with arbitrary geometries and orbits including moons. We have implemented these tools to solve the transit timing variation problem, and derive the properties and possible compositions of TRAPPIST-1 planets.