Pluto on the brink of chaos Goldilocks zone for orbits

(ORDO NEWS) — The existence of another planet – “The Ninth Planet”, or “Planet X” – scientists began to talk at the end of the 19th century, when they studied the perturbations of the orbit of Neptune.

It was possible to detect a hypothetical object in 1930. After much discussion, the new planet was named Pluto. In 2006, he was deprived of the status of a planet in the solar system and transferred to the category of dwarf planets, although they did not stop exploring.

Scientists were especially interested in the unusually elongated orbit. The orbit of a dwarf planet is relatively stable on a scale of billions of years, but is subject to chaotic perturbations and changes over short periods of time, a new study has shown.

The planets of the solar system fly in almost circular orbits in approximately the same plane. Against their background, Pluto stands out strongly: its orbit is elongated and inclined to the ecliptic plane (the plane of the Earth‘s orbit around the Sun) by 17.14 °.

The orbital period of the dwarf planet is 248 years, of which it spends 20 years closer to the Sun than Neptune. Many attempts have been made to calculate how Pluto got into such a strange trajectory and how it changed over time.

Scientists have identified two important features of Pluto’s orbit that help the dwarf planet avoid colliding with Neptune – “mean motion resonance” and “vZLK wobble.” Due to the “mean motion resonance”, when Pluto and Neptune are at the same distance from the Sun, the difference between their longitudes reaches almost 90 °.

Pluto’s perihelion passes high above the plane of Neptune’s orbit. Such a resonance was called the “vZLK oscillation” – in honor of the Swedish astronomer Hugo von Zeipel, the Soviet scientist M. L. Lidov and the Japanese astronomer Yoshihide Kozai, who studied this phenomenon as part of the “three-body problem”.

And in the late 1980s, with the help of more powerful computers and numerical simulations, scientists discovered another feature of Pluto’s orbit: it is chaotic, but this chaos is limited.

Small deviations from the initial values ​​lead to an exponential discrepancy between the results of calculating the orbit after tens of millions of years. And yet, thanks to the first two features, over a span of billions of years, the orbit remains stable, despite all the signs of chaos.

As part of a new study, astronomers decided to use numerical simulations to test the behavior of Pluto’s orbit over the next five billion years. They hoped that this would help explain how Pluto got into such a trajectory.

According to the “planet migration hypothesis”, Neptune provoked the appearance of the “resonance of the mean motion” during the migration. The hypothesis made it possible to assume that other trans-Neptunian objects are in “mean motion resonance”. Observations have confirmed this. But how did it happen?

“The inclination of Pluto’s orbit is associated with the vZLK wobble. Therefore, we assumed that if we deal with the conditions for the fluctuation of vZLK in Pluto, then maybe we will unravel the reason for the appearance of the tilt.

We started by studying the influence of each of the giant planets (Jupiter, Saturn and Uranus) on the orbit of Pluto,” explains planetary scientist Renu Malhotra, who has long been studying the orbits of Pluto and Neptune.

Pluto on the brink of chaos Goldilocks zone for orbits 2
Comparative size of the largest trans-Neptunian objects since Pluto. Below – Moon and Earth

Together with astronomer Takashi Ito, they modeled the evolution of Pluto’s orbit over the next five billion years under various perturbations of the orbits of the giant planets. It turned out that all three giants are necessary for the stability of the “vZLK oscillation”. But why are these planets so important?

The gravitational influence of Jupiter, Saturn and Uranus on Pluto is described by 21 parameters. To simplify the calculations, Malhorta and Ito combined them into one parameter (J2), which, in fact, is tantamount to the “flattened Sun” effect.

Then they picked up the masses and orbits of the giant planets, which provided the value of the J2 parameter necessary for the occurrence of the vZLK resonance.

This window of parameters of masses and orbits turned out to be quite narrow: a step to the side – and there will be chaos. Malhorta likened it to “Goldilocks conditions”, only for the orbits.

It turns out that during the era of planetary migration, conditions in the outer regions of the solar system changed so that many of the trans-Neptunian objects – and Pluto among them – were in the vZLK resonance necessary for long-term stability.

Another curious conclusion: Jupiter has mainly a stabilizing effect on the orbit of Pluto, and Uranus – a destabilizing one. But most importantly, the orbit of Pluto is really close to the zone of strong chaos.

The results of the new work will greatly influence the study of the evolution of the motion of bodies in our system. It imposes numerical restrictions on the dynamics of the development of the solar system.

Renu Malhorta is confident that further study of the migration of giant planets will allow us to finally understand how Pluto and other bodies ended up in their orbits.


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