Radial action ($J_r$)

For radial motion between turning radii $r_{-}$ and $r_{+}$ in a central potential, the radial action per unit mass isIt vanishes on a circular orbit and is canonically conjugate to the radial angle.

For a bound Kepler orbit of semimajor axis $a$ around mass $M$,Adiabatic central-mass change therefore preserves $Ma$ and orbital eccentricity.