  Nearly all known extreme trans-Neptunian objects (ETNOs) have argument of
perihelion close to 0 degrees. An existing observational bias strongly favours
the detection of ETNOs with arguments of perihelion close to 0 degrees and 180
degrees yet no objects have been found at 180 degrees. No plausible explanation
has been offered so far to account for this unusual pattern. Here, we study the
dynamical evolution of comet 96P/Machholz 1, a bizarre near-Earth object (NEO)
that may provide the key to explain the puzzling clustering of orbits around
argument of perihelion close to 0 degrees recently found for the population of
ETNOs. Comet 96P/Machholz 1 is currently locked in a Kozai resonance with
Jupiter such that the value of its argument of perihelion is always close to 0
degrees at its shortest possible perihelion (highest eccentricity and lowest
inclination) and about 180 degrees near its shortest aphelion (longest
perihelion distance, lowest eccentricity and highest inclination). If this
object is a dynamical analogue (albeit limited) of the known ETNOs, this
implies that massive perturbers must keep them confined in orbital parameter
space. Besides, its future dynamical evolution displays orbital flips when its
eccentricity is excited to a high value and its orbit turns over by nearly 180
degrees, rolling over its major axis. This unusual behaviour, that is preserved
when post-Newtonian terms are included in the numerical integrations, may also
help understand the production of NEOs on retrograde orbits.
