The Solar System is a mess: Using Big Data to clear it up

Hi there! When you look at our Solar System, you wonder how it came to be that way. I mean, it formed from a nebula, in which grain accreted to create the Sun, the planets,… and all these small bodies. Most of them have disappeared since the origin, they were either ejected, or accreted on a planet, or on the Sun… anyway still many of them remain. You have the Asteroid Main Belt, the Centaurs, the Kuiper Belt, the Oort cloud, the comets… Several studies have tried to determine connections between them, i.e. where does this comet come from? Was it originally a Centaur, a Kuiper Belt Object, something else? And how did it change its orbit? A close approach with a giant planet, maybe?
And to address this question, you simulate the trajectories… which is not straightforward to do. It is pretty classical to simulate a trajectory from given initial conditions, but to answer such a question, you need more.
You need more because you do not know how reliable are your initial conditions. Your comet was there that day… very well. How sure are you of that? You observe a position and a velocity, fine, but you have uncertainties on your measurements, don’t you?
Yes, you have. So, you simulate the trajectories of many comets, which initial conditions are consistent with your observations. That’s better. And you hope that the outcome of the trajectories (trajectories simulated backward, if you want to know the origin) will be pretty much the same, since the initial conditions are very close to each other…
But they are not! This is what we call sensitivity to the initial conditions. This often means chaos, but I do not want to detail this specific notion. But basically, when a comet swings by a giant planet, its trajectory is dramatically deviated. And the deviation is highly sensitive to the location of the comet. So sensitive that at some point, you lose the information given by your initial conditions. C’est la vie.
As a result, there are in the literature many studies presenting their simulations, and which conclusions are sometimes inconsistent with each other.
The study we discuss today, It’s Complicated: A Big Data Approach to Exploring Planetesimal Evolution in the Presence of Jovian Planets, by Kevin R. Grazier, Julie C. Castillo-Rogez, and Jonathan Horner, suggests another approach to clear up this mess. It considers that all of these possible trajectories constitute a reservoir of Big Data. This study has recently been published in The Astronomical Journal.

Architecture of the Solar System

You know the 8 planets of our Solar System, from the closest to the outermost one:

  • Mercury,
  • Venus,
  • Earth,
  • Mars,
  • Jupiter,
  • Saturn,
  • Uranus,
  • Neptune.

And these planets are accompanied by many small bodies, which constitute

  • the Near-Earth Asteroids, which orbit among the 4 terrestrial planets (from Mercury to Mars),
  • the Main Belt Asteroids, which orbit between Mars and Jupiter,
  • the Centaurs, which orbit between Jupiter and Neptune,
  • the Kuiper Belt, which extends between 30 and 50 AU (astronomical units) from the Sun. So, its inner limit is the orbit of Neptune,
  • the scattered disc, which extends to 150 AU from the Sun. These objects are highly inclined. Eris is the largest known of them.
  • the detached objects, like Sedna. This population is very poorly known, and we do not even know if it is truly a population, or just some objects,
  • the hypothetical Oort cloud, which could be as far as one light-year, or 50,000 AU.

Of course, this list is not exhaustive. For instance, I did not mention the comets, which could originate from any of those populations of small objects.

In this study, the authors limit themselves to the orbit of Neptune. They consider 3 populations of objects between the orbits of Jupiter and Saturn, between Saturn and Uranus, and between Uranus and Neptune. And the question is: how do these populations evolve, to the current state? For that, planetary encounters appear to be of crucial importance.

Planetary encounters

Imagine a small body flying by Jupiter. It approaches Jupiter so closely that it enters its sphere of influence, in which the gravity of Jupter dominates the one of the Sun. Virtually, the object orbits Jupiter, but usually this orbit cannot be stable, since the approach is too fast. Locally, its orbit around Jupiter is hyperbolic, and the object does not stay there. Jupiter ejects it, and you do not know where, because the direction of the ejection is highly sensitive to the velocity of the object during its approach. It also depends on the mass of Jupiter, but this mass is very well known. Sometimes, the action of Jupiter is so strong that it fragments the object, as it did for the comet Shoemaker-Levy 9, in July 1994. And you can have this kind of phenomenon for any of the giant planets of the Solar System.

This is how planetary encounters could move, disperse, eject,… entire populations in the Solar System.

The Big Data approach

With so many objects (the authors considered 3 ensembles of 10,000 test particles, the ensembles being the 3 zones between two consecutive giant planets) and so many potential planetary encounters (the trajectories were simulated over 100 Myr), you generate a database of planetary encounters… how to deal with that? This is where the Big Data approach enters the game.

The authors performed it into two stages. The first one consisted to determine close encounter statistics and correlations, for instance with changes of semimajor axis, i.e. how a planetary encounter displaces an object in the Solar System. And the second stage aimed at reconstituting the path of the particles.

And now, the results.

Random walk from one belt to another

It appears that the particles could easily move from one belt to another. Eventually, they can be ejected. As the authors say, the classification of a particle into a population or another is ephemeral. It depends on when you observe it. In other words, a small object you observe in the Solar System could have been formed almost anywhere else. Even in situ. Now let us talk about specific examples.

The origin of Ceres

For instance, Ceres. You know, this is the largest of the Main Belt Asteroids, and the first to have been discovered, in 1801. It has recently been the target of the mission Dawn, which completed in October 2018.

Ceres seen by Dawn. © NASA
Ceres seen by Dawn. © NASA

Ceres is rich in volatiles like ammonia and carbon dioxides, as are other asteroids like Hygeia. Hygeia is itself a large Main Belt Asteroid. Knowing the origin of Ceres could give you the origin of these volatiles… but they could have been partly accreted after the migration… You see, it is difficult to be 100% sure.

Ceres could have formed in situ, i.e. between Mars and Jupiter, but this study shows that it could have originated from much further in the Solar System, and migrated inward.

The origin of trapped satellites

Most of the main satellites of the giant planets are thought to have been formed with the planet, in the protoplanetary nebula.
But in some cases, you have satellites, which orbit far from the parent planet, on an irregular orbit, i.e. a significantly inclined and eccentric one. In such a case, the body has probably not been formed in situ, but has been trapped by the planet. Among them are Saturn’s Phoebe and Neptune’s Triton, which are large satellite. I have discussed the case of Triton here. The trapping of Triton probably ejected mid-sized satellites of Neptune, which are now lost.

Phoebe seen by <i>Cassini</i> in August 2017 © NASA/ESA/JPL/SSI
Phoebe seen by Cassini in August 2017 © NASA/ESA/JPL/SSI
Mosaic of Triton taken by Voyager 2 in 1989. © NASA
Mosaic of Triton taken by Voyager 2 in 1989. © NASA

Phoebe and Triton entered the sphere of influence of their parent planet, but did not leave it. And where did they come from?

It seems probable that Triton was a Trans-Neptunian Object (TNO) before. In that part of the Solar System, the velocities are pretty low, which facilitate the captures. However, several scenarios are possible for Phoebe. The study show that it could have originated from an inner or from an outer orbit, and have jumped to Saturn from close encounters with Jupiter / Uranus / Neptune.

Something frustrating with such a study, which goes back to the origins, is that you lose some information. As a consequence, you can only conclude by “it is possible that”, but you cannot be certain. You have to admit it.

A way to secure some probabilities is to cross the dynamics with the physical properties, i.e. if you see that element on that body, and if that element is thought to have formed there, then you can infer something on the body, and the authors discuss these possibilities as well. But once more, you cannot be 100% sure. How do you know that this element has been formed there? Well, from the dynamics… which is chaotic… And when you see an element at the surface of a planetary body, does it mean that it is rich in it, or just coated by it, which means it could have accreted after the migration?

You see, you cannot be certain…

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.

Weighing the Kuiper Belt

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.

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.