On the dynamics in planetary systems, globular clusters and galactic nuclei

N-body simulations are used to investigate the dynamics of planetary systems based on the observed period-radius distribution by Kepler. The stability of the distri- bution is tested using integrations of 2,000 systems and with the addition of a Jupiter-like perturber in an aligned and inclined configuration sufficient for Lidov- Kozai (LK) oscillations. ∼ 67% of planetary systems are found stable, falling to ∼ 62% and ∼ 48% with an aligned or inclined giant perturber. Planet ejections are rare. Instability timescales of systems are predicted by spacing and multiplicity of planets, but exceptions are common. Evolution of select individual systems are investigated and classified. The dynamics of stellar binaries on eccentric orbits around a massive black hole (MBH) in the empty loss cone (LC) are also explored. The LK mechanism is sup- pressed by two-body relaxation from stars in galactic nuclei whilst tidal perturba- tions from the MBH excite the eccentricity of the binary to produce mergers in ∼ 75% of simulations. Stellar tides circularise the binaries and produce low velocity mergers. Enhanced magnetic fields in merger products could explain relativistic jet formation in tidal disruption events (TDEs). A method is presented for rapidly calculating the stellar evolution of stars with masses \[m=8.0-300.0M_\odot\] and metallicities \[-4.0\leq [Z/H]\leq 0.5\] that can be incorporated into future n-body simulations