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

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.


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


Don’t forget to leave comments!

A new ringlet around Saturn

Hi there! Today I will tell you about the detection of a ringlet in the rings of Saturn, by Matthew Hedman and Brian Carter, at the University of Idaho (USA). This ringlet presents an interesting dynamics, this is why it caught my attention. Such a discovery is made possible thanks to the Cassini-Huygens space mission, which orbits Saturn since 2004.

The mission Cassini-Huygens

Cassini-Huygens is a joint mission of the NASA, the ESA, and the Italian Space Agency ISA. It consists of a spacecraft, Cassini, which orbits Saturn since 2004, and a probe, Huygens, which landed and died on Titan in January 2005.
This mission Cassini-Huygens is one of the most ambitious ever made, this is why it required an American-European collaboration. It has given us, and is still giving, invaluable information on the system of Saturn. For instance, it permitted the expected discovery of a global subsurface ocean for Titan, and a more surprising one for Enceladus,. Mimas may also have one, from the measurements of its rotation, and that would be even more surprising. Before Cassini-Huygens, we thought that the system of Saturn was a kind of old, frozen and boring world, while it is actually pretty recent, and even the mid-sized icy satellites may present complex interiors. As a consequence, this pushed some of our colleagues to propose new scenarios of formation of the satellites of Saturn, either as droplets composed of ring material which would have migrated outward, or as remnants of larger progenitors, which were impacted.
These are just examples, and I cannot give an exhaustive list of discoveries due to Cassini-Huygens. We have now images of the surface of Titan, we have in situ measurements of its winds, we know the satellites and the planet Saturn much better… Let us focus on the rings.

Rings of Saturn facts

The rings of Saturn are known since Galileo Galilei, and the evolution of Earth telescopes made possible the discoveries of structures in them. The most famous of them is the Cassini Division, which is a 4,000 km wide gap between the two densest of Saturn’s rings, i.e. the A and the B rings. To have a quick overview:

  • 186,000 km: Orbit of Mimas, the closest of the major satellites of Saturn
  • 141,800 km: Orbit of Pandora
  • 140,200 km: The F ring (pretty faint)
  • 139,500 km: Orbit of Prometheus
  • 139,350 km: The new ringlet
  • 122,000 to 137,000 km: The A ring (dense)
  • 133,600 km: the Encke gap, i.e. a lack of material in the A ring
  • 117,500 to 122,000 km: The Cassini Division (still some material, but pretty few)
  • 92,000 to 117,500 km: The B ring (the densest one)
  • 74,600 to 92,000 km: The C Ring (faint)
  • 67,000 to 74,500 km: The D Ring (faint)
  • 58,200 km: Radius of Saturn, where its atmospheric pressure reaches 1 bar

It is known whether a ring is faint or dense from its optical density, which is then associated with an estimated surface density of the ring, seen as a flat structure. Here, I have mixed the main structures of the rings with fainter ones, which are more relevant in this study. I have particularly emphasized the new ringlet, which discovery is presented in this study.

Beside this, you can notice the presence of some small satellites embedded in the rings. I mention Prometheus and Pandora since they are close to the new ringlet, but there are actually more, e.g. Janus, Epimetheus, Atlas, Pan,…

Discovering this new ringlet

A ringlet is a kind of narrow ring of dusty material, i.e. small particles, their radius being something between the centimeter and the meter. Discovering a new ring is challenging because it is very faint. Here, it was discovered on images of the Narrow Angle Camera (NAC) of the Imaging Science Subsystem of the Cassini spacecraft. To make its presence obvious, it is necessary to use images which are not saturated, to remove the background luminosity, and to equalize the response of the different pixels constituting the image (flat-fielding). For this study, the authors used mostly images taken between 2012 and 2014, but some in 2006 as well.

An interesting dynamics

The authors find that this ring is an ellipse with a small eccentricity (0.0012), which precesses. This means that this ellipse is not fixed, but moves around Saturn, while the particles constituting the ringlet move much faster, on the ellipse. Their orbital period is pretty the same as Prometheus’, i.e. some 15 hours, but surprisingly the precession period of the ellipse is longer, i.e. 133 days, against 130 for Prometheus, and is very close to the one of the F Ring.
This is pretty unexpected for the following reason: in an ideal (keplerian) problem, i.e. a point-mass planet around which orbits a particle, the orbit does not precess. The precession is due to departures from this problem, mostly the polar flattening of Saturn, but also the gravitational perturbation of the other satellites. It can be easily shown that, if you get closer to Saturn, you precess faster. Here, the ringlet precesses slower than Prometheus while its orbit is inside. The authors have an elegant explanation, in showing convincingly that the collisions between the particles can synchronize the precession of this ringlet with the one of the F ring, providing that this ringlet is faint enough. I admit that I had not heard of this mechanism before, but the authors convince me. I would have a priori suspected the gravitational interaction of Pandora, but its precession is even slower than the measured one. There is at least one another example of synchronization of the precessions in the system of Saturn: Titan is so massive that it forces the precession of the orbit of Rhea.
The authors also mention the possibility that the particles of this new ringlet are affected by a co-orbital mean-motion resonance with Prometheus. I choose to focus on the synchronization of the precession with the F Ring, since I consider this is the most exciting result of the study. This would be the first accurate measurement of this collision-assisted synchronization, and we can expect in the future many other examples of this mechanism.

Some links

  • The webpage of Matt Hedman
  • The study, accepted for publication in Icarus, and made freely available on arXiV by the authors, many thanks for sharing!
  • The space mission Cassini-Huygens

That’s all folks! Please, don’t hesitate to leave a comment!