NT23: Exact Relation Between the Orbital Invariant and Eccentricity

This note derives the functional relation (quadratic), inverted as , between the orbital invariant and the eccentricity , closing the Advanced result of NT6 that established without an explicit formula. The derivation uses the elliptic orbit equation from P15 to relate the bulk displacement to , then substitutes into the definition of . The coefficient is expressed in terms of fundamental bulk parameters. The result is Closed* for under the subcritical regime and the concavity condition . The observational chain provides a path to measuring from the second harmonic once detected by eROSITA.