The Rosetta Cycle: Venus, Earth, and the Prime Pulse of Planetary Identity

This paper identifies a precise numerical structure embedded in the 8-year Venus–Earth orbital cycle. While the fivefold geometric pattern traced by their conjunctions is well known, we show that its duration and spacing align through an exact factorization—one involving a prime number with unique binary properties. These values arise naturally from planetary motion and repeat with consistent fidelity, revealing a hidden layer of numerical order beneath celestial geometry. The result is a measurable resonance across time, symmetry, and number—a possible Rosetta Stone for understanding how planetary motion may encode arithmetic structure within the solar system