Hi there! Did you know that an asteroid could be resonant and in polar orbit? Yes? No? Anyway, one of them has been confirmed as such, i.e. this body was already discovered, known to be on a polar orbit, but it was not known to be in mean-motion resonance with Neptune until now. This is the opportunity for me to present you First transneptunian object in polar resonance with Neptune, by M.H.M. Morais and F. Namouni. This study has recently been accepted for publication in *The Monthly Notices of the Royal Astronomical Society*.

###### Outline

Polar asteroids

Behavior of the resonant asteroids

Numerical and analytical study

Results

To know more…

## Polar asteroids

The planets of the Solar System orbit roughly in the same plane. In other words, they have small mutual inclinations. However, asteroids are much more scattered, and can have any inclination with respect to the ecliptic, i.e. the orbital plane of the Earth, even if low inclinations are favored.

Two angles are needed to orientate an orbit:

- the ascending node, which varies between 0 and 360°, and which is the angle between a reference and the intersection between the ecliptic and the orbital plane,
- the inclination, which is the angle between the ecliptic and the orbital plane. It varies between 0° and 180°.

So, an almost planar orbit means an inclination close to 0° or close to 180°. Orbits close to 0° are prograde, while orbits close to 180° are retrograde. However, when your inclination is close to 90°, then you have a polar orbit. There are prograde and retrograde polar orbits, whether the inclination is smaller (prograde) or larger (retrograde) than 90°.

There are 7 known Trans-Neptunian Objects with an eccentricity smaller than 0.86 and inclination between 65 and 115°, hence 7 known polar TNOs. You can find them below:

Semimajor axis | Eccentricity | Inclination | Ascending node | Period | |
---|---|---|---|---|---|

(471325) 2011 KT_{19} (Niku) |
35.58 AU | 0.33 | 110.12° | 243.76° | 212.25 y |

2008 KV_{42} (Drac) |
41.44 AU | 0.49 | 103.41° | 260.89° | 266.75 y |

2014 TZ_{33} |
38.32 AU | 0.75 | 86.00° | 171.79° | 237.20 y |

2015 KZ_{120} |
46.07 AU | 0.82 | 85.55° | 249.98° | 312.70 y |

(127546)2002 XU_{93} |
67.47 AU | 0.69 | 77.95° | 90.39° | 554.18 y |

2010 WG_{9} |
52.90 AU | 0.65 | 70.33° | 92.07° | 384.77 y |

2017 CX_{33} |
73.97 AU | 0.86 | 72.01° | 315.88° | 636.21 y |

These bodies carry in their names their year of discovery. As you can see, the first of them has been discovered only 15 years ago. We should keep in mind that TNOs orbit very far from the Earth, this is why they are so difficult to discover, polar or not.

The last of them, 2017 CX_{33}, is so recent that the authors did not study it. A recent discovery induces a pretty large uncertainty on the orbital elements, so waiting permits to stay on the safe side. Among the 6 remaining, 4 (Niku, Drac, 2002 XU_{93} and 2010 WG_{9}) share (very) roughly the same orbit, 2 of them being prograde, while the others two are retrograde. This happened very unlikely by chance, but the reason for this rough alignment is still a mystery.

The study I present you today investigated the current dynamics of these bodies, and found a resonant behavior for one of them (Niku).

## Behavior of the resonant asteroids

By resonant behavior, I mean that an asteroid is affected by a mean-motion resonance with a planet. This means that it makes a given (integer) number of revolutions around the Sun, while the planet makes another number of revolutions. Many outcomes are possible. It can slowly enhance the eccentricity and / or the inclination, which could eventually lead to a chaotic behavior, instability, collision… it could also protect the body from close encounters…

It usually translates into an integer combination of the fundamental frequencies of the system (orbital frequencies, frequencies of precession of the nodes and pericentres), which is null, and this results in an integer combination of angles positioning the asteroid of the planet, which oscillates around a given number instead of circulating. In other words, this angle is bounded.

Another point of interest is how the asteroid has been trapped into the resonance. A resonance is between two interacting bodies, but the mass ratio between an asteroid and a planet implies that the planet is insensitive to the gravitational action of the asteroid, and so the asteroid is trapped by the planet. The fundamental frequencies of the orbital motion are controlled by the semimajor axes of the two bodies, so a trapping into a resonance results from a variation of the semimajor axes. Models of formation of the Solar System suggest that the planets have migrated, this could be a cause. Another cause is close encounters between planets and asteroids, which result in abrupt changes in the trajectory of the asteroid. And this is probably the case here: Niku got trapped after a close encounter.

## Numerical and analytical study

The authors used both numerical and analytical methods to get, understand, and secure their results.

#### Numerical study

The authors ran long-term numerical simulations of the orbital motion of the 6 relevant asteroids, perturbed by the planets. They ran 3 kinds of simulations: 2 with different integrators (algorithms) over 400 kyr and 100 Myr and 8 planets, and one over 400 Myr and the four giant planets. With less planets, you go faster. Moreover, since the inner planets have shorter orbital periods, removing them allows you to increase the time-step, and thus go further in time, inward and backward. In each of these simulations, the authors cloned the asteroids to take into consideration the uncertainty on the orbital elements. They used for that a well-known devoted code, MERCURY.

#### Analytical study

Numerical studies give you an idea of the possible dynamical states of a system, but you need to write down equations to fully understand it. Beside these numerical simulations, the authors wrote a dynamical theory of resonant polar orbits, in another paper (or here).

This consists in reducing the equations to the only terms, which are useful to reproduce the resonant dynamics. For that, you keep the secular variations, i.e. precessions of the nodes and pericentres, and the term involving the resonant argument. This is a kind of averaged dynamics, in which all of the small oscillations of the orbital elements have been dropped. To improve the relevance of the model, the authors used orbital elements which are based on the barycenter (center of mass) of the whole Solar System instead on the Sun only. This is a small correction, since the barycenter is at the edge of the Sun, but the authors mention that it improves their results.

## Results

Niku, i.e. (471325) 2011 KT_{19}, is trapped into a 7:9 mean-motion resonance with Neptune. In other words, it makes 7 revolutions around the Sun (sorry: the barycenter of the Solar System) while Neptune makes 9. More precisely, its resonant argument is φ=9λ-7λ_{N}-4ϖ+2Ω, where λ and λ_{N} are the mean longitudes of the asteroid and of Neptune, respectively, ϖ is the longitude of its pericenter, and Ω is the one of its ascending node. Plotting this argument shows a libration around 180°. Niku has been trapped in this resonance after a close encounter with Neptune, and should leave this resonance in 16±11 Myr. This means that all of the numerical simulations involving Niku show a resonant object, however they disagree on the duration of the resonance.

Their might be another resonant object: a few simulations suggest that Drac, i.e. 2008 KV_{42} is in a 8:13 mean-motion resonance with Neptune.

## To know more

- The study, made freely available by the authors on arXiv, thanks to them for sharing!
- Another study on the orbits of the polar asteroids (or here).
- The web page of Maria Helena Moreira Morais,
- The IAU page of Fathi Namouni.

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