Pluto’s Resonant Orbit Visualized in 4D

Orbital resonances are notoriously difficult to explain due to the complex dynamical processes that govern such orbital motion. One of the most famous examples is Pluto’s 3:2 mean motion resonance (MMR) with Neptune. Owing to this MMR, there are two direct effects on Pluto’s orbit: its semimajor axis librates around a value of 1.31 times Neptune’s, its eccentricity librates about a central value of 0.25, and its alternate perihelion passages librate about a point 90 degrees leading (trailing) the longitudinal position of Neptune these librations have a period of about 20,000 years. A less well known aspect of Pluto’s resonant orbital dynamics is related to the property that Pluto’s orbit plane is inclined about 17 degrees to Neptune’s orbit plane. A secular resonance (independent of the MMR) enforces a libration of Pluto’s argument of perihelion around a central value of 90 degrees the period of this libration is about four megayears. The physical manifestation of this secular resonance is that Pluto’s perihelion passage does not drift greatly in its z-location: it occurs repeatedly near its largest excursion above Neptune’s orbital plane. We have developed a software tool (in Python) to visualize these properties of Pluto’s resonant orbit in two and three dimensions. By projecting the orbital motions in a frame rotating with an angular velocity equal to Neptune’s mean motion, and with an appropriate choice of viewing angle, the tool allows visualization of the time variation of the resonant librations in three dimensions. With choice of nearby initial orbital elements, the tool can be used to visually distinguish resonant from non-resonant orbital motion. And with choice of input parameters, the tool can be extended to other MMR systems. This tool can be useful for education and research in orbital dynamics.