TNO2024

Pluto's argument of perihelion is known to librate around ${90}^{\circ }$. This libration happens due to Pluto's relatively small value of the parameter $k^2=(1-e^2){\cos }^{2}I$ where $e$ is eccentricity and $I$ is inclination measured with respect to Neptune's orbit plane or the solar system's invariable plane. When $k^2$ is larger than a certain critical value, Pluto's libration of perihelion would not occur. The critical value is substantially influenced by the 3:2 mean motion resonance between Pluto and Neptune. The secular effects of other disturbing planets (Jupiter, Saturn, Uranus) also play a significant role in determining Pluto's critical $k^2$. Here we present our estimate of the critical value of $k^2$ for the Pluto-like 3:2 resonant objects using numerical quadrature with several approximations. We also show that the presently known Plutinos whose argument of perihelion librates can be well confined on the parameter plane composed by their $k^2$ and the amplitude of their critical resonant argument.