A companion paper establishes, from the standard 0—30 Ma geomagnetic polarity timescale, a clear periodicity in Earth's prevailing magnetic polarity near 1.1101 million years. This paper sets that figure aside and asks an independent question: does a period of similar length appear anywhere in the dynamics of the solar system itself, arrived at without any reference to Earth's magnetic field? Two such periods are identified, from two distinct physical mechanisms. The Uranus—Neptune orbital energy exchange, established via numerical integration of the outer planets (the LONGSTOP project), gives 1.119 Myr — a drifting, near-resonant beat. The Jupiter—Uranus perihelion anti-alignment, a stable secular frequency difference computable directly from measured planetary precession rates, gives 1.107 Myr — a fixed period. Both sit within a fraction of a percent of the geomagnetic figure. The paper also records the recovery, after a decades-long search, of the original source for a long-held personal note of "1.108 Myr" for this cycle. The explanation for why these independent timescales agree so closely is left for a future paper.