Tag Archives: Impacts

The lowlands of Mars

Hi there! Today I will give you the composition of the subsurface of the lowlands of Mars. This is the opportunity for me to present you The stratigraphy and history of Mars’ northern lowlands through mineralogy of impact craters: A comprehensive survey, by Lu Pan, Bethany L. Ehlmann, John Carter & Carolyn M. Ernst, which has recently been accepted for publication in Journal of Geophysical Research: Planets.

Low- and Highlands

Topography of Mars. We can see lowlands in the North, and highlands in the South. © USGS
Topography of Mars. We can see lowlands in the North, and highlands in the South. © USGS

As you can see on this image, the topography of Mars can be divided into the Northern and the Southern hemispheres, the Northern one (actually about one third of the surface) being essentially constituted of plains, while the Southern one is made of mountains. The difference of elevation between these two hemispheres is between 1 to 3 km. Another difference is the fact that the Southern hemisphere is heavily cratered, even if craters exist in the lowlands. This Martian dichotomy is very difficult to explain, some explanations have been proposed, e.g., the lowlands could result from a single, giant impact, or the difference could be due to internal (tectonic) processes, which would have acted differentially, renewing the Northern hemisphere only… Anyway, whatever the cause, there is a dichotomy in the Martian topography. This study examines the lowlands.

The lowlands are separated into: Acidalia Planitia (for plain), Arcadia Planitia, Amazonis Planitia, Chryse Planitia, Isidis Planitia, Scandia Cavi (the polar region), Utopia Planitia, Vatistas Borealis,…

Plains also exist in the Southern hemisphere, like the Hellas and the Argyre Planitiae, which are probably impact basins. But this region is mostly known for Olympus Mons, which is the highest known mountain is the Solar System (altitude: 22 km), and the Tharsis Montes, which are 3 volcanoes in the Tharsis region.

To know the subsurface of a region, and its chemical composition, the easiest way is to dig… at least on Earth. On Mars, you are not supposed to affect the nature… Fortunately, the nature did the job for us, in bombarding the surface. This bombardment was particularly intense during the Noachian era, which correspond to the Late Heavy Bombardment, between 4.1 to 3.7 Gyr ago. The impacts excavated some material, that you just have to analyze with a spectrometer, provided the crater is preserved enough. This should then give you clues on the past of the region. Some say the lowlands might have supported a global ocean once.

The past ocean hypothesis

Liquid water seems to have existed at the surface of Mars, until some 3.5 Gyr ago. There are evidences of gullies and channels in the lowlands. This would have required the atmosphere of Mars to be much hotter, and probably thicker, than it is now. The hypothesis that the lowlands were entirely covered by an ocean has been proposed in 1987, and been supported by several data and studies since then, even if it is still controversial. Some features seem to be former shorelines, and evidences of two past tsunamis have been published in 2016. These evidences are channels created by former rivers, which flowed from down to the top. These tsunamis would have been the consequences of impacts, one of them being responsible for the crater Lomonosov.

The fate of this ocean is not clear. Part of it would have been evaporated in the atmosphere, and then lost in the space, part of it would have hydrated the subsurface, before freezing… This is how the study of this subsurface may participate in the debate.

The CRISM instrument

To study the chemical composition of the material excavated by the impacts, the authors used CRISM data. CRISM, for Compact Reconnaissance Imaging Spectrometer for Mars, is an instrument of Mars Reconnaissance Orbiter (MRO). MRO is a NASA spacecraft, which orbits Mars since 2006.
CRISM is an imaging spectrometer, which can observe both in the visible and in the infrared ranges, which requires a rigorous cooling of the instrument. These multi-wavelengths observations permit to identify the different chemical elements composing the surface. The CRISM team summarizes its scientific goals by follow the water. Studying the chemical composition would permit to characterize the geology of Mars, and give clues on the past presence of liquid water, on the evolution of the Martian climate,…

In this study, the authors used CRISM data of 1,045 craters larger than 1 km, in the lowlands. They particularly focused on wavelengths between 1 and 2.6μm, which is convenient to identify hydrated minerals.

Hydrated vs. mafic minerals

The authors investigated different parts of the craters: the central peak, which might be constituted of the deepest material, the wall, the floor… The CRISM images should be treated, i.e. denoised before analysis. This requires to perform a photometric, then an atmospheric correction, to remove spikes, to eliminate dead pixels…

And after this treatment, the authors identified two kinds of minerals: mafic and hydrated ones. Mafic minerals are silicate minerals, in particular olivine and pyroxenes, which are rich in magnesium and iron, while hydrated minerals contain water. They in particular found a correlation between the size of the crater and the ratio mafic / hydrated, in the sense that mafic detections are less dependent on crater size. Which means that mafic minerals seem to be ubiquitous, while the larger the crater, the likelier the detection of hydrated minerals. Since larger craters result from more violent impacts, this suggests that hydrated minerals have a deeper origin. Moreover, no hydrated material has been found in the Arcadia Planitia, despite the analysis of 85 craters. They also noticed that less degraded craters have a higher probability of mineral detection, whatever the mineral.

However, the authors did not find evidence of concentrated salt deposits, which would have supported the past ocean hypothesis.

The study and the authors

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.

Avalanches on the Moon

Hi there! Did you know that there could be avalanches on the Moon? Why not? You have slopes, you have boulders, so you can have avalanches! Not snow avalanches of course. This is the topic of Granular avalanches on the Moon: Mass-wasting conditions, processes and features, by B.P. Kokelaar, R.S. Bahia, K.H. Joy, S. Viroulet and J.M.N.T. Gray, which has recently been accepted for publication in Journal of Geophysical Research: Planets.

The Moon vs. the Earth

On the Moon we have

  • No atmosphere: The wind cannot trigger an avalanche. Moreover, the erosion is much slower than on Earth, since it is only due to micrometeorites bombardment. The erosion tends to flatten the terrains. When you have no erosion, an steep terrain may remain steep for ages/
  • No liquid water: This means no snow! This is why you have no snow avalanche. Another consequence of this absence of fluid is that no rain can trigger an avalanche, and the regolith involved is necessarily dry. Wet sand does not behave like dry sand.
  • Less gravity: The gravity on the Moon is about one sixth of the gravity of the Earth, and as you can imagine, gravity assists the avalanches. It appears that a smaller gravity results in slower avalanches, but the final result remains pretty the same, i.e. you cannot infer the gravity from the final result of an avalanche.

The irregularity of the Moon’s topography is mainly due to the numerous impact craters. The steep edges of the craters are where avalanches happen.

Causes of the avalanches

For an avalanche to happen, you need a favorable terrain, and a triggering event.

A favorable terrain is first a slope. If you are flat enough, then the boulders would not be inclined to roll. The required limit inclination is called the dynamic angle of repose. On Earth, the dry sand has a dynamic angle of repose of 34°, while the wet sand remains stable up to 45°. This illustrates pretty well the influence of the water.

Triggering an avalanche requires to shake the terrain enough. A way is an impact occurring far enough to not alter the slope, but close enough to shake the terrain. Another way is a seismic phenomenon, due to geophysical activity of the Moon.

Datasets

The authors focused their efforts on the Kepler crater, before investigating 6 other ones. The impact craters have to be preserved enough, in particular from micrometeorite impacts. These craters are:

Crater Diameter Slope
Kepler 31 km ~32°
Gambart B 11 km ~30°
Bessel 16 km 31.5°
Censorinus 3.8 km 32°
Riccioli CA 14.2 km 34°
Virtanen F 11.8 km 32°
Tralles A 18 km 32°

The first 4 of these craters are situated in maria, while the last three are in highlands. These means that we have different types of regolith.

Kepler seen by LROC (© NASA/GSFC/Arizona State University)
Kepler seen by LROC (© NASA/GSFC/Arizona State University)

We need high-precision data to determine the shape of the avalanches. The space mission Lunar Reconnaissance Orbiter (LRO) furnishes such data. In particular the authors used:

  • Images from the LROC, for LRO Camera. This instrument is equipped of 3 cameras, two Narrow Angle Cameras (NACs), with a resolution between 0.42 and 1.3 meter per pixel, and a WAC, for Wide Angle Camera, with a resolution of 100 m /pixel, but with a much wider field. The NAC data permitted to characterize the type of flow, while the WAC data gave their extent.
  • Digital Elevation Models (DEM), obtained from the Lunar Orbiter Laser Altimeter (LOLA), mentioned here, and from the Terrain Camera of the Japanese mission SELENE / Kaguya. Knowing the variations of the topography permitted to estimate the slopes of the craters and the volume of flowing material.

Three flow types

And from the images, the authors determined 3 types of flows:

  • Multiple Channel and Lobe (MCL): these are accumulations of multiple small-volume flows. These flows are the most common in the study, and can be found on Earth too,
  • Single-Surge Polylobate (SSP): the flows have the structure of fingers,
  • Multiple Ribbon (MR): these are very elongated flows with respect to their widths, i.e. they are typically kilometer-long and meter-wide. These flows have been predicted by lab experiments, but this is their first observation on a planetary body. In particular, they are not present on the Earth. Lab experiments suggest that they are extremely sensitive to slope changes.
Debris flows observed on the northeast inner wall Kepler. This is NOT water! © NASA/GSFC/Arizona State University
Debris flows observed on the northeast inner wall Kepler. This is NOT water! © NASA/GSFC/Arizona State University

The word flow evokes a fluid phenomenon. Of course, there is no fluid at the surface of the Moon, but granular regolith may have a kind of fluid behavior. A true fluid would have a dynamic angle of repose of 0°. Regolith has a higher angle of repose because of friction, that prevents it from flowing. But it of course depends on the nature of the regolith. In particular, fine-grained material tends to reduce friction, and consequently increases the mobility of the material. This results in extended flows.

But this extension has some limitation. On Earth, we observe flows on adverse slopes, which are thought to be facilitated by the presence of liquid water. This statement is enforced by the fact that no such flow has been observed on the Moon.

The accuracy of data we dispose on the Moon has permitted the first observations of granular flows in dry and atmosphereless conditions. Such results could probably be extrapolated to other similar bodies (Mercury? Ceres? Pluto?).

Laboratory experiments

The multiple ribbon have been predicted by lab experiments. It is fascinating to realize that we can reproduce lunar condition in a room, and with accelerated timescales. This is made possible by the normalization of physical quantities.
If we write down the equations ruling the granular flows, we have a set of 3 partial derivative equations, involving the avalanche thickness, and the concentration and velocity of the particles. Mathematical manipulations on these equations permit to emphasize quantities, which have no physical dimension. For instance, the height of a mountain divided by the radius of the planet, or the time you need to read this article divided by the time I need to write it… In acting on all the quantities involved in such adimensional numbers, we can reduce an impact crater of the Moon evolving during millions of years, to a room evolving during a few days…
In this problem, a critical number is the Froude number, which depends on the gravity, the avalanche thickness, the velocity, and the slope.

The study and the authors

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.

How rough is Mercury?

Hi there! Today I will tell you on the smoothness of the surface of Mercury. This is the opportunity for me to present The surface roughness of Mercury from the Mercury Laser Altimeter: Investigating the effects of volcanism, tectonism, and impact cratering by H.C.M. Susorney, O.S. Barnouin, C.M. Ernst and P.K. Byrne, which has recently been published in Journal of Geophysical Research: Planets. This paper uses laser altimeter data provided by the MESSENGER spacecraft, to measure the regularity of the surface in the northern hemisphere.

The surface of Mercury

I already had the opportunity to present Mercury on this blog. This is the innermost planet of the Solar System, about 3 times closer to the Sun than our Earth. This proximity makes space missions difficult, since they have to comply with the gravitational action of the Sun and with the heat of the environment. This is why Mercury has been visited only by 2 space missions: Mariner 10, which made 3 fly-bys in 1974-1975, and MESSENGER, which orbited Mercury during 4 years, between 2011 and 2015. The study of MESSENGER data is still on-going, the paper I present you today is part of this process.

Very few was known from Mercury before Mariner 10, in particular we just had no image of its surface. The 3 fly-bys of Mariner 10 gave us almost a full hemisphere, as you can see below. Only a small stripe was unknown.

Mercury seen by Mariner 10. © NASA.
Mercury seen by Mariner 10. © NASA.

And we see on this image many craters! The details have different resolutions, since this depends on the distance between Mercury and the spacecraft when a given image was taken. This map is actually a mosaic.
MESSENGER gave us full maps of Mercury (see below).

Mercury seen by MESSENGER. © USGS
Mercury seen by MESSENGER. © USGS

Something that may be not obvious on the image is a non-uniform distribution of the craters. So, Mercury is composed of cratered terrains and smooth plains, which have different roughnesses (you will understand before the end of this article).
Craters permit to date a terrain (see here), i.e. when you see an impact basin, this means that the surface has not been renewed since the impact. You can even be more accurate in dating the impact from the relaxation of the crater. However, volcanism brings new material at the surface, which covers and hides the craters.

This study focuses on the North Pole, i.e. latitudes between 45 and 90°N. This is enough to have the two kinds of terrains.

Three major geological processes

Three processes affect the surface of Mercury:

  1. Impact cratering: The early Solar System was very dangerous from this point of view, having several episodes of intense bombardments in its history. Mercury was particularly impacted because the Sun, as a big mass, tends to focus the impactors in its vicinity. It tends to rough the surface.
  2. Volcanism: In bringing new and hot material, it smoothes the surface,
  3. Tectonism: Deformation of the crust.

If Mercury had an atmosphere, then erosion would have tended to smooth the surface, as on Earth. Irrelevant here.

To measure the roughness, the authors used data from the Mercury Laser Altimeter (MLA), one of the instruments of MESSENGER.

The Mercury Laser Altimeter (MLA) instrument

This instrument measured the distance between the spacecraft and the surface of Mercury from the travel time of light emitted by MLA and reflected by the surface. Data acquired on the whole surface permitted to provide a complete topographic map of Mercury, i.e. to know the variations of its radius, detect basins and mountains,… The accuracy and the resolution of the measurements depend on the distance between the spacecraft and the surface, which had large variations, i.e. between 200 and 10,300 km. The most accurate altimeter data were for the North Pole, this is why the authors focused on it.

Roughness indicators

You need at least an indicator to quantify the roughness, i.e. a number. For that, the authors work on a given baseline on which they had data, removed a slope, and calculated the RMS (root mean square) deviation, i.e. the average squared deviation to a constant altitude, after removal of a slope. When you are on an inclined plane, then your altitude is not constant, but the plane is smooth anyway. This is why you remove the slope.

But wait a minute: if you are climbing a hill, and you calculate the slope over 10 meters, you have the slope you are climbing… But if you calculate it over 10 km, then you will go past the summit, and the slope will not be the same, while the summit will affect the RMS deviation, i.e. the roughness. This means that the roughness depends on the length of your baseline.

This is something interesting, which should be quantified as well. For this, the authors used the Hurst exponent H, such that ν(L) = ν0LH, where L is the length of the baseline, and ν the standard deviation. Of course, the data show that this relation is not exact, but we can say it works pretty well. H is determined in fitting the relation to the data.

Results

To summarize the results:

  • Smooth plains: H = 0.88±0.01,
  • Cratered terrains: H = 0.95±0.01.

The authors allowed the baseline to vary between 500 m and 250 km. The definition of the Hurst exponent works well for baselines up to 1.5 km. But for any baseline, the results show a bimodal distribution, i.e. two kinds of terrains, which are smooth plains and cratered terrains.

It is tempting to compare Mercury to the Moon, and actually the results are consistent for cratered terrains. However, the lunar Maria seem to have a slightly smaller Hurst exponent.

To know more

That’s it for today! The next mission to Mercury will be Bepi-Colombo, scheduled for launch in 2018 and for orbital insertion in 2025. Meanwhile, please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Tilting and retilting our Moon

Hi there! The Moon is so close and so familiar to us, but I realize this is my first post on it. Today I present you a paper entitled South Pole Aitken Basin magnetic anomalies: Evidence for the true polar wander of Moon and a lunar dynamo reversal, by Jafar Arkani-Hamed and Daniel Boutin, which will be published soon in Journal of Geophysical Research: Planets. The idea is to track the variations of the magnetic field of the Moon along its history, as a signature of the motion of its rotation pole, i.e. of a polar wander.

Our Moon’s facts

The Moon is a fascinating object, as it is the only known natural satellite of the Earth, and we see it as large as the Sun in our sky. It orbits around the Earth at a distance of almost 400,000 km in 27.3 days. It shows us always the same face, as a result of a tidal locking of its rotation, making it synchronous, i.e. its spin period is equal to its orbital period.

Moonset over Paris, France. Copyright: Josselin Desmars.

Something interesting is its pretty large size, i.e. its radius is one fourth of the one of the Earth. It is widely admitted that the Moon and the Earth have a common origin, i.e. either a proto-Earth has been impacted by a Mars-sized impactor, which split it between the Earth and the Moon, or the Earth-Moon system results from the collision of two objects of almost the same size. In both cases, the Earth and the Moon would have been pretty hot just after the impact, which also means active… and this has implications for the magnetic field.

A very weak magnetic field has been detected for the Moon, but which is very different from the Earth’s. The magnetic field of the Earth, or geomagnetic field, has the signature of a dipolar one, in the sense that it has a clear orientation. This happens when the rotating core acts as a dynamo. The north magnetic pole is some 10° shifted from the spin pole of the Earth, and has an amplitude between 25 and 65 μT (micro-teslas). However, the magnetic field of the Moon, measured at its surface, does not present a clear orientation, and never reaches 1 μT. Its origin is thus not obvious, even if we could imagine that the early Moon was active enough to harbor a dynamo, from which the measured magnetic field would be a signature… But the absence of preferred orientation is confusing.

The core dynamo

The core of the Earth spins, it is surrounded by liquid iron, which is conductive, and there is convection in this fluid layer, which is driven by the heat flux diffusing from the core to the surface of the Earth. This process creates and maintains a magnetic field.

For the Earth, the core dynamo is assumed to account for 80 to 90% of the total magnetic field. This results in a preferred orientation. Other processes that could create a magnetic field are a global asymmetry of the electric charges of the planet, or the presence of an external magnetic field, for instance due to a star.

A dynamo could be expected for many planetary objects, which would be large enough to harbor a global fluid layer. It is usually thought that the detection of a magnetic field is a clue for the presence of a global ocean. Such a magnetic field has been detected for Jupiter’s moon Ganymede, which is probably due to an outer liquid layer coating its iron core.

The Moon has probably no dynamo, but could have had one in the past. The measured magnetic field could be its signature. A question is: what could have driven this dynamo? The early Moon was hotter than the current one, so a magnetic field existed at that time. And after that, the Moon experienced intense episodes of bombardment, like the Late Heavy Bombardment. The resulting impacts affected the orientation of the Moon, its shape, and also its temperature. This could have itself triggered a revival of the magnetic field, particularly for the biggest impact.

The study I present today deals with measurements of the magnetic field in the South Pole-Aitken Basin, not to be confused with the Aitken crater, which is present in its region. The South Pole-Aitken Basin is one of the largest known impact crater in the Solar System, with a diameter of 2,500 km and a depth of 13 km. This basin contains other craters, which means that it is older than all of them, its age is estimated to be 4.1 Gyr (gigayears, i.e. billions of years). Measurements of the magnetic field in each of these craters could give its evolution over the ages. But why is it possible?

The magnetic field as a signature of the history

When a material is surrounded by a magnetic field, it can become magnetic itself. This phenomenon is known as induced magnetization, and depends on the magnetic susceptibility of the material, i.e. the efficiency of this process depends on the material. Once the surrounding magnetic field has disappeared, the material might remain magnetic anyway, i.e. have its remanent magnetic field. This is what has been measured by the Lunar Prospector mission, whose data originated this study.
An issue is the temperature. The impact should be hot enough to trigger the magnetic field, which implies that the material would be hot, but it cannot be magnetized if it is too hot. Below a Curie temperature, the process of induced magnetization just does not work. You can even demagnetize a material in heating it. For the magnetite, which is a mineral containing iron and present on the Moon, the Curie temperature is 860 K, i.e. 587°C, or 1089°F.

Lunar Prospector

This study uses data of the Lunar Prospector mission. This NASA mission has been launched in January 1998 from Cape Canaveral and has orbited the Moon on a polar orbit during 18 months, until July 1999. It made a full orbit in a little less than 2 hours, at a mean altitude of 100 km (60 miles). This allowed to cover the whole surface of the Moon, and to make measurements with 6 instruments, related to gamma rays, electrons, neutrons, gravity… and the magnetic field.

Results of this study

This study essentially consists of two parts: a theoretical study of the temperature evolution of the Moon over its early ages, including after impacts, and the interpretation of the magnetic field data. These data are 14 magnetic anomalies in the South Pole-Aitken Basin, which the theoretical study helps to date. And the data show two orientations of the magnetic field in the magnetic in the past, giving an excursion of more than 100° over the ages.

Now, if we consider that in the presence of a core dynamo, the magnetic field should be nearly aligned with the spin pole, this means that the Moon has experienced a polar wander of more than 100° in its early life. More precisely, the two orientations are temporally separated by the creation of the Imbrium basin, 3.9 Gyr ago. In other words, the Moon has been tilted. This is not the only case in the Solar System, see e.g. Enceladus.

To know more

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 and Facebook.

Enceladus lost its balance

Hi there! Today I will present you True polar wander of Enceladus from topographic data, by Tajeddine et al., which has recently been published in Icarus. The idea is this: Enceladus is a satellite of Saturn which has a pretty stable rotation axis. In the past, its rotation axis was already stable, but with a dramatically different orientation, i.e. 55° shifted from the present one! The authors proposed this scenario after having observed the distribution of impact basins at its surface.

Enceladus’s facts

Enceladus is one of the mid-sized satellites of Saturn, it is actually the second innermost of them. It has a mean radius of some 250 km, and orbits around Saturn in 1.37 day, at a distance of ~238,000 km. It is particularly interesting since it presents evidence of past and present geophysical activity. In particular, geysers have been observed by the Cassini spacecraft at its South Pole, and its southern hemisphere presents four pretty linear features known as tiger stripes, which are fractures.

Enceladus seen by Cassini (Credit: NASA / JPL / Space Science Institute).
Enceladus seen by Cassini (Credit: NASA / JPL / Space Science Institute).

Moreover, analyses of the gravity field of Enceladus, which is a signature of its interior, strongly suggest a global, subsurfacic ocean, and a North-South asymmetry. This asymmetry is consistent with a diapir of water at its South Pole, which would be the origin of the geysers. The presence of the global ocean has been confirmed by measurements of the amplitude of the longitudinal librations of its surface, which are consistent with a a crust, that a global ocean would have partially decoupled from the interior.

The rotation of a planetary satellite

Planetary satellites have a particularly interesting rotational dynamics. Alike our Moon, they show on average always the same face to a fictitious observer, which would observe the satellite from the surface of the parent planet (our Earth for the Moon, Saturn for Enceladus). This means that they have a synchronous rotation, i.e. a rotation which is synchronous with their orbit, but also that the orientation of their spin axis is pretty stable.
And this is the key point here: the spin axis is pretty orthogonal to the orbit (this orientation is called Cassini State 1), and it is very close to the polar axis, which is the axis of largest moment of inertia. This means that we have a condition on the orientation of the spin axis with respect to the orbit, AND with respect to the surface. The mass distribution in the satellite is not exactly spherical, actually masses tend to accumulate in the equatorial plane, more particularly in the satellite-planet direction, because of the combined actions of the rotation of the satellites and the tides raised by the parent planet. This implies a shorter polar axis. And the study I present today proposes that the polar axis has been tilted of 55° in the past. This tilt is called polar wander. This result is suggested by the distribution of the craters at the surface of Enceladus.

Relaxing a crater

The Solar System bodies are always impacted, this was especially true during the early ages of the Solar System. And the inner satellites of Saturn were more impacted than the outer ones, because the mass of Saturn tends to attract the impactors, focusing their trajectories.
As a consequence, Enceladus got heavily impacted, probably pretty homogeneously, i.e. craters were everywhere. And then, over the ages, the crust slowly went back to its original shape, relaxing the craters. The craters became then basins, and eventually some of them disappeared. Some of them, but not all of them.
The process of relaxation is all the more efficient when the material is hot. For material which properties strongly depend on the temperature, a stagnant lid can form below the surface, which would partly preserve it from the heating by convection, and could preserve the craters. This phenomenon appears preferably at equatorial latitudes.
This motivates the quest for basins. A way for that is to measure the topography of the surface.

Modeling the topography

The surface of planetary body can be written as a sum of trigonometric series, known as spherical harmonics, in which the radius would depend on 2 parameters, i.e. the latitude and the longitude. This way, you have the radius at any point of the surface. Classically, two terms are kept, which allow to represent the surface as a triaxial ellipsoid. This is the expected shape from the rotational and tidal deformations. If you want to look at mass anomalies, then you have to go further in the expansion of the formula. But to do that, you need data, i.e. measurements of the radius at given coordinates. And for that, the planetologists dispose of the Cassini spacecraft, which made several flybys of Enceladus, since 2005.
Two kinds of data have been used in this study: limb profiles, and control points.
Limb profiles are observations of the bright edge of an illuminated object, they result in very accurate measurements of limited areas. Control points are features on the surface, detected from images. They can be anywhere of the surface, and permit a global coverage. In this study, the authors used 41,780 points derived from 54 limb profiles, and 6,245 control points.
Measuring the shape is only one example of use of such data. They can also be used to measure the rotation of the body, in comparing several orientations of given features at different dates.
These data permitted the authors to model the topography up to the order 16.

The result

The authors identified a set of pretty aligned basins, which would happen for equatorial basins protected from relaxation by stagnant lid convection. But the problem is this: the orientation of this alignment would need a tilt of 55° of Enceladus to be equatorial! This is why the authors suggest that Enceladus has been tilted in the past.

The observations do not tell us anything on the cause of this tilt. Some blogs emphasize that it could be due to an impact. Why not? But less us be cautious.
Anyway, the orientation of the rotation axis is consistent with the current mass distribution, i.e. the polar axis has the largest moment of inertia. Actually, mid-sized planetary satellites like Enceladus are close to sphericity, in the sense that there is no huge difference between the moments of inertia of its principal axes. So, a redistribution of mass after a violent tilt seems to be possible.

To know more

And now the 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 and Facebook.