Tag Archives: Hydrodynamics

Forming the satellites of Uranus

Merry Christmas! Today we discuss how the satellites of Uranus were formed. It is usually thought the satellites of a giant planets formed from a protoplanetary nebula. Originally there was a cloud of gas and dust, mass accumulated in the center to form the planet, and protosatellites were created from the accretion of mass as well. This was well understood for the gas giants like Jupiter, but Uranus is much smaller (23 times lighter). The Swiss study I present today, In situ formation of icy moons of Uranus and Neptune, by Judit Szulágyi, Marco Cilibrasi and Lucio Mayer, solves this problem. This study has recently been published in The Astrophysical Journal Letters.

The satellites of Uranus

Uranus has 27 known satellites, which can be classified into 3 groups:

  • the inner moons, which are small satellites embedded in the rings,
  • the main moons, which are mid-sized icy bodies. These are the ones we are interested in today,
  • and the irregular moons, which orbit very far from the planet, and on significantly eccentric and inclined orbits. These bodies are probably former asteroids, which were trapped by the gravitational field of Uranus.

As I said, we are interested in the main 5 satellites, which are listed below. Their semimajor axes are given with respect to the mean equatorial radius of Uranus, which is 25,559 km.

U-5 Miranda U-1 Ariel U-2 Umbriel U-3 Titania U-4 Oberon
Discovery 1948 1851 1851 1787 1787
Semimajor axis 5.062 RU 7.474 RU 10.408 RU 17.055 RU 21.070 RU
Eccentricity 0.0013 0.0012 0.0039 0.0011 0.0014
Inclination 4.232° 0.260° 0.205° 0.340° 0.058°
Orbital period 1.413 d 2.520 d 4.144 d 8.706 d 13.463 d
Diameter 471.6 ± 1.4 km 1157.8 ± 1.2 km 1169.4 ± 5.6 km 1576.8 ± 1.2 km 1522.8 ± 5.2 km
Density 1.20 g/cm3 1.66 g/cm3 1.40 g/cm3 1.72 g/cm3 1.63 g/cm3

As you can see, these 5 bodies are

  • A small one (Miranda), which is pretty close to the planet,
  • two larger ones, Ariel and Umbriel, which orbit further from the planet,
  • and two even larger ones, Titania and Oberon, which orbit even further from the planet.


Titania and Oberon have been discovered in 1787 by the German-British astronomer William Herschel, only 6 years after the same William Herschel discovered Uranus. Actually, Uranus was (and still is) visible to the naked eye, and had been observed many times before. But how to know it was a planet, and not a star? Well, a star does not move in the sky (actually, it does a very little…), while a planet moves. But since Uranus orbits very far from the Sun, its motion is pretty slow. Herschel detected such motion, but he thought at that time that Uranus was a comet. The computation of its motion showed a pretty circular orbit, proving it was a planet.
After that, Uranus has been observed many times, and Herschel noticed two dots following Uranus. Since they followed Uranus, it meant they were gravitationally bound to it, hence satellites. These two dots were the two largest of them, i.e. Titania and Oberon.

Seventy years after the discovery of Uranus, the British merchant and astronomer William Lassell, who by the way made his fortune as a beer brewer, built his own telescope. He polished himself the mirror, and pioneered the use of the equatorial mount, which facilitated the tracking of objects with respect to the rotation of the Earth. His telescope permitted him to discover the satellite of Neptune Triton, to co-discover the satellite of Saturn Hyperion, and to discover the satellites of Uranus Ariel and Umbriel.

For Miranda, we had to wait for the Dutch-American astronomer Gerard (Gerrit) Peter (Pieter) Kuiper. He discovered Miranda in 1948 and the satellite of Neptune Nereid in 1949, at McDonald Observatory (TX, USA). Kuiper is mostly known for having proposed the existence of the so-called Kuiper Belt, i.e. a belt of asteroids orbiting beyond the orbit of Neptune. He has also been the thesis advisor of Carl Sagan.


Let us go back to the table, and have a look at their properties. We can see that these bodies have small eccentricities and inclinations, i.e. they orbit in the equatorial plane of Uranus, on pretty circular orbits. There is anyway an exception to this rule, which is the significant inclination of Miranda (4.2°). This inclination has probably been excited by a past 3:1 mean motion resonance with Umbriel.

Another interesting point is the density of these bodies. 1g/cm3 means a composition close to water. Pure water ice would be a little less dense. Here we have densities between 1 and 2, which means that these bodies are mixtures of ice and silicates.

This property they share is a clue, which suggests a common formation process. Let us investigate the formation from the protoplanetary disk.

From the disk to the satellites

Let us figure out how a giant planet is formed. First you have a protoplanetary nebula, made of gas and dust. Matter accumulates and aggregates at its center, creating a star (if the nebula is massive enough). To compensate this accumulation at the center (conservation of the total angular momentum), the matter which is still outside the star accelerates, and the nebula becomes a disk, which orbits the star.
Then (may be a little meanwhile, actually), you have local accretions of matter, which create the planets. And sometimes, if you have enough matter, then you have a circumplanetary disk around some of the planets, in which matter aggregates… and creates the satellites! Well, this way, it seems to be easy.
One question is: how massive need the protoplanetary disk to be, to create the satellites. It was known that it works for Jupiter. This study wonders whether it works for Uranus.

Hydrodynamic simulations

To answer this question, the authors ran intensive numerical simulations, using the hydrocode JUPITER. By hydrocode I mean that it simulates a hydrodynamic system.

Actually, a disk is made of particles of gas and dust. It is highly challenging, even if it is sometimes tried, to consider all the particles constituting it, and model their motion and their interactions. Instead, you can consider that the whole disk acts as a gas, and model the collisions between the particles as a viscosity.

Simulating this motion requires to split the disk into cells, use the method of finite elements, i.e. the state of a given part of the disk depends on the state of its neighbors… This requires intensive computing facilities. In JUPITER, you can focus on a given region, for instance where a planet is created.

The authors ran 25,000 simulations, depending on the following parameters:

  • the disk dispersion timescale,
  • the dust-to-gas ratio,
  • the dust refilling timescale: when dust accumulates at the center to create the planet, the disk needs to reach a new equilibrium. This parameter controls the velocity of this process,
  • the distance from the planet where the first proto-satellites are created,
  • the initial temperature of the central planet.

It appeared that this temperature, set to 1000K, 500K and 100K, plays a critical role in the possibility to create the satellites. Consider this effect is possible in JUPITER since 2016 and the implementation of a module, which models the radiative transfer in the disk. As a consequence, it models the effects of the heating and cooling of the gas.

Yes, it is possible!

The simulations show that the circumplanetary gaseous disk was formed when the temperature dropped below 500K (227°C, or 441°F). In that case, icy moons were formed in most of the simulations, which strongly suggests that the present satellites of Uranus were formed that way.

What about Neptune?

Neptune is somehow like Uranus, by its size. This is why the authors ran similar simulations, which showed similar results, i.e. formation of icy, mid-sized satellites. But wait, this is not what we see.

When we observe the system of Neptune, we see a large satellite, Triton, which is highly inclined, on a retrograde orbit. As we discussed here, Triton behaved like a cuckoo.

The satellite of Neptune Triton seen by Voyager 2 in 1989. © NASA
The satellite of Neptune Triton seen by Voyager 2 in 1989. © NASA

Triton was an asteroid, which has been trapped in the gravity field of Neptune. Then it was so massive than it ejected the satellites, which were present… if they existed. What this study tells us is that they probably existed. Nereid was probably one of them. Where are the others now? In my opinion, they could be almost anywhere, since the Solar System is a mess.

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.