Tag Archives: Planet Nine

Asteroids: Trans-Neptunian Objects

Weighing the Kuiper Belt

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Hi there! Today, we are back to the Solar System, and more especially the Kuiper Belt. You know, all these small bodies, which orbit beyond Neptune. Instead of speaking of specific cases, like Pluto, Haumea or Sedna, we will see the Kuiper Belt as a whole.
The study I present, Mass of the Kuiper Belt, by E.V. Pitjeva and N.P. Pitjev, constrains its total mass with planetary ephemerides. This study has been recently published in Celestial Mechanics and Dynamical Astronomy.

Outline

The Kuiper Belt
Planetary ephemerides
The Kuiper Belt as a ring
As many data as possible
Observed and fitted parameters
A light Kuiper Belt
The Planet Nine would have a limited influence
The study and its authors

The Kuiper Belt

I have presented the Kuiper Belt many times. These are objects, orbiting beyond the orbit of Neptune. This zone is named after the Dutch-American astronomer Gerard Kuiper, who hypothesized that it could have been a reservoir of comets, even if he thought that it would be almost clear. At that time, the only known Kepler Belt Object was Pluto. Now, more than 2,000 of them are known, and many more are probably to be discovered.
Most of these objects orbit between 30 and 50 AU (astronomical units) from the Sun.

This study wants to constrain the total mass of the Kuiper Belt, from the motion of the planets. For that, the authors built and used planetary ephemerides.

Planetary ephemerides

Planetary ephemerides give the location of the Solar System objects, especially the planets, at given dates. They have been of strategical importance during centuries for celestial navigation. Now, we still need them, for instance to identify potentially hazardous objects, to guide spacecraft, to detect new objects,…

I can cite 3 institutions, which provide ephemerides:

  • NASA’s JPL,
  • IMCCE, Paris Observatory, France,
  • Institute of Applied Astronomy, Russian Academy of Sciences.

JPL stands for Jet Propulsion Laboratory. It is located near Pasadena, CA, and is associated with the Californian Institute of Technology (CalTech). As part of NASA, it is associated with the American spacecraft.
The IMCCE, for Institute of Celestial Mechanics, is responsible for the French ephemerides. It has been founded in 1795 as the Bureau des Longitudes, in a context of rivalry between France and England. Its goal was then to assist France, to regain control of the seas.
And the Institute of Applied Astronomy, in Russia, is the place where this study has been conducted.

These 3 institutions provide their own ephemerides, i.e. solutions for the orbital motion of the planets, their satellites, the asteroids,… Now, let us see how to include the Kuiper Belt.

The Kuiper Belt as a ring

The orbital motion of planetary bodies come from the numerical integration of the gravitational equations, in which each body is perturbed by all the other ones… this makes many of them. So many that a common computer cannot handle that, when it comes to 2,000 of them. Moreover, there are probably many more Kuiper Belt Objects, which are not discovered yet, but which perturb the motion of the planets…

The authors by-passed this problem in modeling the Kuiper Belt as a ring. Not the whole Kuiper Belt actually. The 31 most massive of these objects are modeled as point masses, ans the remaining ones are embedded into a fictitious rotating ring, which mass perturbs the planets.

If you know the perturbation, you know the mass… Easy, isn’t it? Well, not that easy, actually…

As many data as possible

The authors maintain their ephemerides since many years, and each new version is enriched with new data. The current version, EPM2017, uses about 800,000 positional observations of planets and spacecraft, ranging from 1913 to 2015. Many of the observations of planets are Earth-based astrometric observations, while spacecraft observations include MESSENGER (mission to Mercury), Venus Express (to Venus), Cassini (to Saturn), and the Martian missions Viking-1 & 2, Pathfinder, Mars Global Surveyor, Odyssey, Mars Reconnaissance Orbiter, and Mars Express.

Very small objects like spacecraft are very sensitive to planetary perturbations, this is why their navigation data may be invaluable.

Observed and fitted parameters

Making ephemerides consists in fitting a dynamical model to data, i.e. observed positions. The dynamical model is mainly composed of the gravitational interactions between the planetary bodies, with some relativistic corrections (Einstein-Infeld-Hoffmann equations). These interactions use the masses of the objects as parameters.

When you want to fit the model to the data, you fit the initial conditions, i.e. the location of the objects at the beginning of the simulation, and some of the parameters. Why only some of them? It depends on how well you know them.

For instance, in this case, the mass of (1)Ceres is assumed to be accurately known, thanks to the Dawn mission (just finished, by the way). This means that fitting this mass would be counterproductive.

So, the authors have to make critical choices between what they fit and what they don’t, and also how they ponder the observations between each other.

A light Kuiper Belt

From formation models of the Solar System, the initial Kuiper Belt should be as massive as ten times our Earth. However,
fitting the ephemerides gives much smaller numbers. You can find below the outcomes of the previous studies and this last one, by the same team.

Year Kuiper Belt mass (in Earth mass)
2010 0.0258
2013 0.0263
2014 0.0197
2017 0.0228 ± 0.0046
2018 0.0197 ± 0.0035

As you can see

  • the current Kuiper Belt is by far much lighter than the original one. This means that this region of the Solar System has probably been depleted by the gravitational action of the main planets, only few objects remaining,
  • the numbers do not converge very fast, but they converge. In particular, each new measurement is consistent with the previous one, and the uncertainty tends to shrink. Slowly, but it shrinks.

This number of 0.02 Earth mass makes the Kuiper Belt about 2 orders of magnitudes (i.e. between 10 and 1,000) heavier than the Asteroid Main Belt, but some 3 orders of magnitude lighter than the proposed Planet Nine.

The Planet Nine would have a limited influence

You remember the Planet Nine? It is a yet undiscovered body, which is supposed to exist anyway. It should orbit far behind the orbit of Neptune, should be as massive as 10 Earth masses, and would be responsible for the clustering of the pericentres of the Trans-Neptunian Objects (the Kuiper Belt), and for the obliquity of the Sun.

In this study, the authors benefited from the very accurate navigation data of the space mission Cassini, which orbited Saturn until September 2017. And for Cassini, the Kuiper Belt has a much stronger influence than the hypothetical Planet Nine. This makes me think that the author believe that using such ephemerides is not a good strategy for constraining the Planet Nine.

Actually, the planetologists looking for the Planet Nine focus on the individual trajectories of the Kuiper Belt Objects, because these are the most sensitive to it.

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

Asteroids: Extreme Trans-Neptunian Objects

How the Planet Nine would affect the furthest asteroids

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Hi there! You have heard of the hypothetical Planet Nine, which could be the explanation for an observed clustering of the pericentres of the furthest asteroids, known as eTNOS for extreme Trans-Neptunian Objects. I present you today a theoretical study investigating in-depth this mechanism, in being focused on the influence of the inclination of this Planet Nine. I present you Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth by Melaine Saillenfest, Marc Fouchard, Giacomo Tommei and Giovanni B. Valsecchi. This study has recently been accepted for publication in Celestial Mechanics and Dynamical Astronomy.

Outline

Is there a Planet Nine?
The secular dynamics of an asteroid
The Kozai-Lidov mechanism
Methodology
Results
To know more…

Is there a Planet Nine?

An still undiscovered Solar System planet has always been dreamed, and sometimes even hinted. We called it Tyche, Thelisto, Planet X (“X” for mystery, unknown, but also for 10, Pluto having been the ninth planet until 2006). Since 2015, this quest has been renewed after the observation of clustering in the pericentres of extreme TNOS. Further investigations concluded that at least 5 observed dynamical features of the Solar System could be explained by an additional planet, now called Planet Nine:

  1. the clustering of the pericentres of the eTNOs,
  2. the significant presence of retrograde orbits among the TNOs,
  3. the 6° obliquity of the Sun,
  4. the presence of highly inclined Centaurs,
  5. the dynamical detachment of the pericentres of TNOs from Neptune.

The combination of all of these elements tends to rule out a random process. It appears that this Planet Nine would be pretty like Neptune, i.e. 10 times heavier than our Earth, that its pericentre would be at 200 AU (while Neptune is at 30 AU only!), and its apocentre between 500 AU and 1200 AU. This would indeed be a very distant object, which would orbit the Sun in several thousands of years!

Astronomers (Konstantin Batygin and Michael Brown) are currently trying to detect this Planet Nine, unsuccessfully up to now. You can follow their blog here, from which I took some inspiration. The study I present today investigates the secular dynamics that this Planet Nine would induce.

The secular dynamics of an asteroid

The secular dynamics is the one involving the pericentre and the ascending node of an object, without involving its longitude. To make things clear, you know that a planetary object orbiting the Sun wanders on an eccentric, inclined orbit, which is an ellipse. When you are interested in the secular dynamics, you care of the orientation of this ellipse, but not of where the object is on this ellipse. The clustering of pericentres of eTNOs is a feature of the secular dynamics.

This is a different aspect from the dynamics due to mean-motion resonances, in which you are interested in objects, which orbital periods around the Sun are commensurate with the one of the Planet Nine. Some studies address this issue, since many small objects are in mean-motion resonance with a planet. Not this study.

The Kozai-Lidov mechanism

A notable secular effect is the Kozai-Lidov resonance. Discovered in 1961 by Michael Lidov in USSR and Yoshihide Kozai in Japan, this mechanism says that there exists a dynamical equilibrium at high inclination (63°) for eccentric orbits, in the presence of a perturber. So, you have the central body (the Sun), a perturber (the planet), and your asteroid, which could have its inclination pushed by this effect. This induces a libration of the orientation of its orbit, i.e. the difference between its pericentre and its ascending node would librate around 90° or 270°.

This process is even more interesting when the perturber has a significant eccentricity, since the so-called eccentric Kozai-Lidov mechanism generates retrograde orbits, i.e. orbits with an inclination larger than 90°. At 117°, you have another equilibrium.

Now, when you observe a small body which dynamics suggests to be affected by Kozai-Lidov, this means you should have a perturber… you see what I mean?

Of course, this perturber can be Neptune, but only sometimes. Other times, the dynamics would rather be explained by an outer perturber… which could be the Planet Nine, or a passing star (who knows?)

Methodology

Before mentioning the results of this study I must briefly mention the methodology. The authors made what I would call a semi-analytical study, i.e. they manipulated equations, but with the assistance of a computer. They wrote down the Hamiltonian of the restricted 3-body problem, i.e. the expression of the whole energy of the problem with respect to the orbital elements of the perturber and the TNO. This energy should be constant, since no dissipation is involved, and the way this Hamiltonian is written has convenient mathematical properties, which allow to derive the whole dynamics. Then this Hamiltonian is averaged over the mean longitudes, since we are not interested in them, we want only the secular dynamics.

A common way to do this is to expand the Hamiltonian following small parameters, i.e. the eccentricity, the inclination… But not here! You cannot do this since the eccentricity of the Planet Nine (0.6) and its inclination are not supposed to be small. So, the authors average the Hamiltonian numerically. This permits them to keep the whole secular dynamics due to the eccentricity and the inclination.

Once they did this, they looked for equilibriums, which would be preferential dynamical states for the TNOs. They also detected chaotic zones in the phase space, i.e. ranges of orbital elements, for which the trajectory of the TNOs would be difficult to predict, and thus potentially unstable. They detected these zones in plotting so-called Poincaré sections, which give a picture of the trajectories in a two-dimensional plane that reduces the number of degrees-of-freedom.

Results

And the authors find that the two Kozai-Lidov mechanisms, i.e. the one due to Neptune, and the one due to the Planet Nine, conflict for a semimajor axis larger than 150 AU, where orbital flips become possible. The equilibriums due to Neptune would disappear beyond 200 AU, being submerged by chaos. However, other equilibriums appear.

For the future, I see two ways to better constrain the Planet Nine:

  1. observe it,
  2. discover more eTNOs, which would provide more accurate constraints.

Will Gaia be useful for that? Anyway, this is a very exciting quest. My advice: stay tuned!

To know more…

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Asteroids: Extreme Trans-Neptunian Objects

Discovery of 6 new Extreme Trans-Neptunian Objects

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Hi there! You know the Trans-Neptunian Objects, these bodies which orbit beyond the orbit of Neptune… There are the furthest known objects in the Solar System. Today I will particularly tell you on the most distant of them, which have a semimajor axis larger than 150 AU, while Neptune is at 30 AU… Yes, we can observe some of them. 6 have been recently discovered by the OSSOS survey, in OSSOS. VI. Striking biases in the detection of large semimajor axis Trans-Neptunian Objects, by Cory Shankman and 11 collaborators (full list at the end). This paper has recently been published in The Astronomical Journal. In this study, the authors particularly focus on the possible observational biases, and discuss the Planet Nine hypothesis.

Outline

The OSSOS survey
The Canada-France-Hawaii Telescope
Observational biases
Statistical tests
This study
What about the Planet Nine?
To know more…

The OSSOS survey

I should probably write OSSOSurvey instead, since it stands for Outer Solar System Origins Survey. It is a systematic observation program that ran on the Canada-France-Hawaii Telescope (CFHT) between 2013 and 2017, devoted to the discovery and orbit determination of Trans-Neptunian Objects. For that, the program used an imager with a field of 1×1 degree, to image 21 square degree fields, in different parts of the sky. During the 4 years, these fields were regularly re-observed to follow the motion of the discovered objects. 16 months of astrometric observations are required to obtain an accurate orbit.
The authors announce that OSSOS permitted the detection of more than 830 TNOs, with a “40% detection efficiency at r(ed)-band magnitude 24.4-24.5”. OSSOS followed another survey, CFEPS, for Canada-France-Hawaii Ecliptic Plane Survey, which discovered some 200 Kuiper Belt Objects, i.e. Trans-Neptunian Objects, which are not as far as the objects we discuss today. This makes more than 1,000 small objects discovered by the CFHT.

Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.
Some TNOs detected by CFEPD and OSSOS. Replotted from the public data. Copyright: The Planetary Mechanics Blog.

The Canada-France-Hawaii Telescope

The Canada-France-Hawaii Telescope is a joint facility of the University of Hawaii, the French Centre National de la Recherche Scientifique, and the Canadian National Research Council. It has also partnerships with institutions based in the two Chinas, South Korea, and Brazil. It has a 3.58-m telescope, which is functional since 1979.
It is ideally situated, close to the summit of the Mauna Kea mountain, Hawaii (altitude: 4,204 m). It is equipped of different instruments, to observe in the visible to infrared bands. One of them, the wide field imager MegaCam, was used for OSSOSurvey.

Observational biases

If you are looking for stars to the West, you will find some. But only on the West, and brighter than a given magnitude. Does that mean that there are no fainter stars, and no stars in the opposite direction? Of course not. You have found only those stars because your observation means and protocol precluded from discovering other stars. This is an observational bias.

This is a very important issue for understanding surveys, i.e. how to extrapolate the catalog of discovered objects to the existing but unknown ones? Observational biases can be due to:

  • The direction in which you observe. Since our sky is moving, this is strongly correlated to the observation date.
  • The weather. Hard to see something behind a cloud.
  • Your field of view. Is there something behind this tree?
  • The limitations of your instrument.
  • The albedo of your object. How efficiently does it reflect the incident Solar light?
  • …

There is something very significant in the name of CFEPS… E stands for ecliptic, which is the orbital plane of the Earth. The Solar System is roughly planar (with many exceptions of course), and it made sense to look for objects with a small orbital inclination. Consequence: most of the objects discovered by CFEPS have a low inclination… observational bias, which was in fact a way to optimize the chances to discover objects. But it would be wrong to conclude from these discoveries a lack of objects with a small inclination.

OSSOS had observational biases as well, mostly due to the absence of observations in the direction of the Galactic Plane, and to the allocated observation time. The Galactic Plane is full of stars, which complicates the observations of faint objects. This is why the authors maximized their chances in avoiding that part of the sky. As a consequence, OSSOS could not detect objects with an ascending node (the point where the orbit of the object crosses the ecliptic) between -120° and -20°, and had a poor sensitivity between 115° and 165°.

In the specific case of extreme TNOs, there is another bias due to their dynamics: a small object orbiting at a distance of 150 AU has no chance to be detected from the Earth. So, the only detected objects came close enough, which means that their orbits is highly elongated, i.e. highly eccentric. The 8 objects considered in this study, i.e. 6 newly discovered and 2 already known, have a pericentric distance between 31 and 50 AU, which involves an eccentricity between 0.727 and 0.932 (the eccentricity of the Earth is some 0.016). Among the extreme TNOs, only the highly eccentric ones can be detected. This does not mean that they are all highly eccentric.

The reason why the scientific community became excited about the Planet Nine is that a clustering of the orbits of the extreme TNOs was identified in other data, in particular a clustering of the pericentres of the objects. It was then concluded that this clustering was the dynamical signature of the Planet Nine, proving its existence. OSSOS gives independent data, are they clustered?

Answering such a question is not straightforward when the data are scattered. Looking at them with the naked eye is not enough, there are mathematical tools which can measure the statistical relevance of an hypothesis. In particular, the Planet Nine hypothesis should be compared with the null hypothesis, i.e. an equal distribution of the pericentres of the extreme TNOs.

Statistical tests

A common tool is the Kolmogorov-Smirnov test, or KS-test. The idea is to determine a distance between your sample and the one that a given law would give you. If the distance is small enough, then it makes sense to conclude that your sample obeys the law you tested.
This test has been refined as Kuiper’s test, which is insensitive to cyclic transformations of the variables. Cyclic phenomena are everywhere in orbital dynamics.

This study

The following table presents you the 8 eTNOs presented in this study.

Name Semimajor axis Eccentricity Inclination Magnitude
2013 GP136 150.2 AU 0.727 33.5° 23.1
2013 SY99 735 AU 0.932 4.2° 24.8
2013 UT15 200 AU 0.780 10.7° 24.1
2015 KH163 153 AU 0.739 27.1° 24.7
2015 RY245 226 AU 0.861 6° 24.6
2015 GT50 312 AU 0.877 8.8° 24.5
2015 RX245 430 AU 0.894 12.1° 24.1
2015 KG163 680 AU 0.940 14° 24.3

All of them have been discovered by OSSOS, the first two ones being known before that study. The 6 other ones are the 6 newly discovered. We can see that all have huge semimajor axes and eccentricities. You can see the high relative magnitudes in the red band during their discoveries. Their discoveries were made possible by their high eccentricities, which reduce significantly the minimal distances to the Sun and to the Earth.

And now their orbits are drawn!

Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.
Projection of the orbits of the 8 eTNOs on the ecliptic. The orbit of Neptune is embedded into the small circle delimited by the orbits. Copyright: The Planetary Mechanics Blog, after inspiration from OSSOS.

Do they look clustered?

What about the Planet Nine?

The Kuiper’s test used by the authors say that the orbital elements of the detected eTNOS are statistically consistent with a uniform repartition. We must be careful with words. This means that there is no evidence of clustering in this sample. That does not mean that there is no Planet Nine. We should keep in mind that 8 objects do not constitute a statistically relevant sample.

My feeling is that if you were skeptical about the existence of the Planet Nine, you remain skeptical. However, if you believed in it, there is still room for belief. The fact is that this study does not comfort the existence of the Planet Nine.

To know more…

  • The study, made freely available by the authors on arXiv. You can also find a presentation of the study by the authors themselves here.
  • A presentation by Nature.
  • The website of the OSSOS survey, and its Twitter.
  • The quest for the Planet Nine.

And the authors of the study:

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Planets

Hinting for Planet Nine in the orbits of Trans-Neptunian Objects

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Hi There! Today I will present you a paper by Matthew Holman and Matthew Payne, entitled Observational constraints on Planet Nine: Astrometry of Pluto and other Trans-Neptunian Objects, which aims to derive constraints on the hypothetical Planet Nine from the orbits of small bodies, which orbit beyond the orbit of Neptune. For that, the authors investigate how an unknown, distant and massive planet, could improve the ephemerides of the known Trans-Neptunian Objects (TNOs). This study has recently been accepted for publication in The Astronomical Journal.

The quest for Planet Nine

Here is a longstanding pending question: is there a ninth planet on the Solar System? Some will answer: Yes, and its name is Pluto. But as you may know, Pluto has been reclassified in 2006 as a dwarf planet by the International Astronomical Union. So, is there another ninth planet, still to be discovered? In January 2016, Konstantin Batygin and Michael Brown, answered “probably yes” to this question, from the orbits of TNOs. They discovered that the clustering of their orbits could hardly be due to chance, and so there should be a cause, which has a gravity action. Since this study, several groups try to constrain its orbit and mass, while observers try to detect it.

The purpose of this post is to discuss the study of one of these groups. Let me briefly cite other ones (sorry for oblivion):

  • In 2014, Chad Trujillo and Scott Sheppard discovered a TNO, 2012VP113, whose apparent orbit seemed to be too difficult to explain with the known planets only. This made a case for the existence of the Planet Nine.
  • In 2015, a team led by the Brazilian astronomer Rodney Gomes, showed that a Planet Nine could explain an excess of bright object in the population of the most distant TNOs.
  • In January 2016, Batygin and Brown published their result, which triggered a bunch of other studies.
  • Hervé Beust, from Grenoble (France), showed from a statistical analysis that resonant effects with Neptune could explain the observed clustering,
  • Renu Malhotra, Kat Volk and Xianyu Wang, from the University of Arizona, considered that the largest TNOs could be in mean-motion resonance with the Planet Nine, i.e. that their orbital periods could be commensurate with the one of the Planet Nine. Such a configuration has a dynamical implication on the stability of these bodies. In such a case, the TNO Sedna would be in a 3:2 resonance with the Planet Nine.
  • A team led by Agnès Fienga, from the Observatoire de la Côte d’Azur (France), has suggested that a signature of the Planet Nine could be found in the deviation of the Cassini spacecraft, which currently orbits Saturn. The JPL (Jet Propulsion Laboratory, NASA) does not seem to believe in this option, and indicates that the spacecraft does not present any anomaly in its motion.
  • Gongjie Li and Fred Adams, based respectively at the Harvard-Smithsonian Center for Astrophysics, and at the University of Michigan, show that the orbit of the Planet Nine is pretty unlikely to be stable, because of passing stars close to the outer Solar System, which should have ejected it.
  • de la Fuente Marcos and de la Fuente Marcos, from Spain, reexamined the statistics, and concluded that there should be at least two massive perturbers beyond the orbit of Pluto
  • Matthew Holman and Matthew Payne, from the Harvard-Smithsonian Center for Astrophysics, tried to constrain the orbit of the Planet Nine from the orbits of the TNOs.

All this should result in the present architecture for the Solar System (AU stand for Astronomical Unit, i.e. ≈150 million km:

  • 1 AU: the Earth,
  • 5.2 AU: Jupiter,
  • 9.55 AU: Saturn,
  • 19.2 AU: Uranus,
  • 30.1 AU: Neptune,
  • 39.5 – 48 AU: the Kuiper Belt,
  • 39.5 AU: Pluto,
  • >50 AU: the scattered disk,
  • 67.8 AU: Eris
  • 259.3 AU: 2012VP113
  • 526.2 AU: Sedna,
  • 300 – 1500 AU: the Planet Nine,
  • 50,000 AU: the Oort Cloud,
  • 268,000 AU: Proxima Centauri, which is the closest known star beside the Sun.

Astrometry

The astrometry consists to measure the position of an object in the sky. Seen by a terrestrial observer, the sky is a spherical surface. You can determine two angles which will give the direction of the object, but no distance. These two angles are the right ascension and the declination.

Determining the right ascension and the declination of an object you observe is not that easy. It involves for example to have good reference points on the sky, whose positions are accurately known, with respect to which you will position your object. These reference points are usually stars, and their positions are gathered in catalogs. You should also consider the fact that an object is more than a dot, it appears on your image as a kind of a circle. To be accurate, you should determine the location of the center of the object from its light circle, due to light diffraction. You should in particular consider the fact that the center of the light is not necessarily the center of this object.

When all this is done, you have a right ascension and a declination with uncertainties, at a given date. This date is corrected from the light travel time, i.e. the position of an object we observe was the position of the object when the Solar light was refracted on its surface, not when we observe it. Gathering several observations permits to fit ephemerides of the considered body, i.e. a theory which gives its orbit at any time. These ephemerides are very convenient to re-observe this object, and to send a spacecraft to it…

Fitting an orbit

Ephemerides give you the orbit of a given body. Basically, the orbit of a Solar System body is an ellipse, on which the body is moving. For that, a set of 6 independent orbital elements shall be defined. The following set is an example:

  1. the semimajor axis,
  2. the eccentricity (a null eccentricity means that the orbit is circular; an elliptical orbit means that the eccentricity is smaller than 1),
  3. the inclination, usually with respect to the ecliptic, i.e. the orbital plane of the Earth,
  4. the pericentre, at which the distance Sun-body is the smallest,
  5. the ascending node, locating the intersection between the orbital plane and the ecliptic,
  6. the longitude, which locates the body on its orbit.

The first 5 of these elements are constant if you have only the Sun and an asteroid; in practice they have a time dependence due to the gravitational perturbations of the other bodies, in particular the giant planets, i.e. Jupiter, Saturn, Uranus and Neptune. This study aims at identifying the gravitational influence of the Planet Nine.

A numerical simulation gives you the orbit of an asteroid perturbed by the Sun and the giant planets. But for that, you need to know initial conditions, i.e. the location of the body at a given date. The initial conditions are derived from astrometric positions. Since the astrometry does not give exact positions but positions with some uncertainty, you may have many solutions to the problem. The best fit is the solution which minimizes what we call the residuals, or the O-C, for Observed Minus Calculated. All the O-C are gathered under a statistical quantity known as χ2. The best fit minimizes the χ2.

This study

The purpose of this study is to use 42,323 astrometric positions of TNOs with a semimajor axis larger than 30 AU, 6,677 of them involving Pluto. For that, the fitting algorithm not only includes the gravitational influence of the giant planets, but also of 10 large TNOs, and of the hypothetical Planet Nine, in considering two models: either the Planet Nine is moving on a circular orbit, or it is a fixed point-mass. Its expected orbital period, i.e. several thousands of years, is so large that no significant difference between the two models is expected, given the time span covered by the observations.

Indeed, the two models give pretty the same result. The authors split the sky into several tiles, to check the preferred locations for the Planet Nine, and it appears that for some locations the fit is better, while it is worse for some others.

They also find that if the Planet Nine has a mass of 10 Earth masses, then the distance of the Planet Nine to the Sun should be between 300 and 1,000 AU, while Batygin and Brown found it to be between 400 and 1,500 AU. This discrepancy could be explained by the presence of an another planet at a distance of 60 to 100 AU. In addition to that, the node of the Planet Nine seems to be aligned with the one of Pluto, which had already been noticed by other authors. This could reveal an enhanced dynamical interaction between them.

Finally the authors acknowledge that the astrometric positions have some inaccuracy, and that further observations could affect the results.

The quest for Planet Nine is very exciting, and I am pretty sure that new results will come in a next future!

To know more…

  • The study, made freely available by the authors here, thanks to them for sharing!
  • The webpage of Matthew Holman
  • The profile of Matthew Payne on ResearchGate
  • The press release relating the likely existence of the Planet Nine
  • The study by Trujillo and Sheppard
  • The study by Gomes et al.
  • The study by Batygin and Brown, freely available here
  • The study by Beust, also freely available here
  • The study by Malhotra et al., also freely available here
  • The study by Fienga et al., also freely available here
  • The study by de la Fuente Marcos and de la Fuente Marcos, also freely available here

 

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