Tag Archives: Topography

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.


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.

Modeling the shape of a planetary body

Hi there! Do you know the shape of the Moon? You say yes of course! But up to which accuracy? The surface of the Moon has many irregularities, which prompted Christian Hirt and Michael Kuhn to study the limits of the mathematics, in modeling the shape of the Moon. Their study, entitled Convergence and divergence in spherical harmonic series of the gravitational field generated by high-resolution planetary topography — A case study for the Moon, has recently been accepted for publication in Journal of Geophysical Research: Planets.

The shape of planetary bodies

If you look at a planetary body from far away (look at a star, look at Jupiter,…), you just see a point mass. If you get closer, you would see a sphere, if the body is not too small. Small bodies, let us say smaller than 100 km, can have any shape (may I call them potatoids?) If they are larger, the material almost arranges as a sphere, which gives the same gravity field as the point mass, provided you are out of the body. But if you look closer, you would see some polar flattening, due to the rotation of the body. And for planetary satellites, you also have an equatorial ellipticity, the longest axis pointing to the parent planet. Well, in that case, you have a triaxial ellipsoid. You can say that the sphere is a degree 0 approximation of the shape, and that the triaxial ellipsoid is a degree 2 approximation… but still an approximation.

A planetary body has some relief, mountains, basins… there are explanations for that, you can have, or have had, tectonic activity, basins may have been created by impacts, you can have mass anomalies in the interior, etc. This means that the planetary body you consider (in our example, the Moon), is not exactly a triaxial ellipsoid. Being more accurate than that becomes complicated. A way to do it is with successive approximations, in the same way I presented you: first a sphere, then a triaxial ellipsoid, then something else… but when do you stop? And can you stop, i.e. does your approximation converge? This study addresses this problem.

The Brillouin sphere

This problem is pretty easy when you are far enough from the body. You just see it as a sphere, or an ellipsoid, since you do not have enough resolution to consider the irregularities in the topography… by the way, I am tempted to make a confusion between topography and gravity. The gravity field is the way the mass of your body will affect the trajectory of the body with which it interacts, i.e. the Earth, Lunar spacecrafts… If you are close enough, you will be sensitive to the mass distribution in the body, which is of course linked to the topography. So, the two notions are correlated, but not fully, since the gravity is more sensitive to the interior.

But let us go back to this problem of distance. If you are far enough, no problem. The Moon is either a sphere, or a triaxial ellipsoid. If you get closer, you should be more accurate. And if you are too close, then you cannot be accurate enough.

This limit is given by the radius of the Brillouin sphere. Named after the French-born American physicist Léon Brillouin, this is the circumscribing sphere of the body. If your planetary body is spherical, then it exactly fills its Brillouin sphere, and this problem is trivial… If you are a potatoidal asteroid, then your volume will be only a fraction of this sphere, and you can imagine having a spacecraft inside this sphere.

The asteroid Itokawa in its Brillouin-sphere. Credit: JAXA.
The asteroid Itokawa in its Brillouin-sphere. Credit: JAXA.

The Moon is actually pretty close to a sphere, of radius 1737.4±1 km. But many mass anomalies have been detected, which makes its gravity field not that close to the one of the sphere, and you can be inside the equivalent Brillouin sphere (if we translate gravity into topography), in flying over the surface at low altitude.

Why modeling it?

Why trying to be that accurate on the gravity field / topography of a planetary object? I see at least two good reasons, please pick the ones you prefer:

  • to be able to detect the time variations of the topography and / or the gravity field. This would give you the tidal response (see here) of the body, or the evolution of its polar caps,
  • because it’s fun,
  • to be able to control the motion of low-altitude spacecrafts. This is particularly relevant for asteroids, which are somehow potatoidal (am I coining this word?)

You can object that the Moon may be not the best body to test the gravity inside the Brillouin sphere. Actually we have an invaluable amount of data on the Moon, thanks to the various missions, the Lunar Laser Ranging, which accurately measures the Earth-Moon distance… Difficult to be more accurate than on the Moon…

The goal of the paper is actually not to find something new on the Moon, but to test different models of topography and gravity fields, before using them on other bodies.

Spherical harmonics expansion

Usually the gravity field (and the topography) is described as a spherical harmonics expansion, i.e. you model your body as a sum of waves with increasing frequencies, over two angles, which are the latitude and the longitude. This is why the order 0 is the exact sphere, the order 2 is the triaxial ellipsoid… and in raising the order, you introduce more and more peaks and depressions in your shape… In summing them, you should have the gravity field of your body… if your series converge. It is usually assume that you converge outside the Brillouin sphere… It is not that clear inside.

To test the convergence, you need to measure a distance between your series and something else, that you judge relevant. It could be an alternative gravitational model, or just the next approximation of the series. And to measure the distance, a common unit is the gal, which is an acceleration of 1 cm/s2 (you agree that gravity gives acceleration?). In this paper, the authors checked differences at the level of the μgal, i.e. 1 gal divided by 1 million.


In this study, the authors used data from two sources:

  • high-resolution shape maps from the Lunar Orbiter Laser Altimeter (LOLA),
  • gravity data from the mission GRAIL (Gravity Recovery And Interior Laboratory),

and they modeled 4 gravity fields:

  1. Topography of the surface,
  2. Positive topographic heights, i.e. for basins the mean radius was considered, while the exact topography was considered for mountains,
  3. “Brillouin-sphere”, at a mean altitude of 11 km,
  4. “GRAIL-sphere”, at a mean altitude of 23 km.

In each of these cases, the authors used series of spherical harmonics of orders between 90 (required spatial resolution: 60.6 km) and 2,160 (resolution: 2.5 km). In each case, the solution with spherical harmonics was compared with a direct integration of the potential of the body, for which the topography is discretized through an ensemble of regularly-shaped elements.


And here are the results:

Not surprisingly, everything converges in the last two cases, i.e. altitudes of 11 and 23 km. However, closer to the surface the expansion in spherical harmonics fails from orders 720 (case 1) and 1,080 (case 2), respectively. This means that adding higher-order harmonics does not stabilize the global solution, which can be called divergence. The authors see from their calculations that this can be predicted from the evolution of the amplitude of the terms of the expansion, with respect to their orders. To be specific, their conclusion is summarized as follows:

A minimum in the degree variances of an external potential model foreshadows divergence of the spherical harmonic series expansions at points inside the Brillouin-sphere.


My feeling is that this study should be seen as a laboratory test of a mathematical method, i.e. testing the convergence of the spherical harmonics expansion, not on a piece of paper, but in modeling a real body, with real data. I wonder how the consideration of time variations of the potential would affect these calculations.

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.

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.


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.

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.

The contraction of Mercury

Hi there! Today’s post deals with the early evolution of Mercury, in particular its cooling. At the beginning of its life, a planet experiences variations of temperature, and then cooling, and while cooling, it contracts. The surface may present some signature of this contraction, and this is the object of the paper I present you today. It is entitled Timing and rate of global contraction of Mercury, by Kelsey T. Crane and Christian Klimczak, from the University of Georgia, and it has been recently accepted for publication in Geophysical Research Letters. The idea is to infer the history of the contraction from the observation of the craters and the faults.

Mercury’s facts

Mercury is the innermost planet of the Solar System, with a mean distance to the Sun which is about one third of the Sun-Earth distance. It has an eccentric orbit, with an eccentricity of 0.206, and orbits the Sun in 88 days while the planet rotates around itself in 58 days. This is very long when compared to the terrestrial day, but it also means that there is a ratio 1.5 between the spin and the orbital frequencies. This is called a 3:2 spin-orbit resonance, which is a dynamical equilibrium favored by the proximity of the Sun and the orbital eccentricity.

Mercury seen by MESSENGER (Credit: NASA)

An interesting fact is the high density of Mercury, i.e. Mercury is too dense for a terrestrial planet. Usually, a large enough body is expected to have a stratified structure, in which the heaviest elements are concentrated in the core. Mercury is so dense than it is thought to be the core of a former and larger proto-Mercury.

Mercury’s early life

There is no agreement on the way Mercury lost its mantle of lighter elements. You can find the following scenarios in the literature:

  1. Slow volatilization of the mantle by the solar wind,
  2. Very large impact,
  3. Loss of the light elements by photophoresis,
  4. Magnetic erosion.

The scenario of the large impact was very popular until the arrival of MESSENGER, in particular because the models of formation of the Solar System and the observation of the surface of Mercury suggest that Mercury has been heavily impacted in its early life. However, the detection of volatiles elements, in particular potassium, on the surface of Mercury, is interpreted by some planetary scientists as inconsistent with the large impact scenario. The large impact would have induced extreme heating of the planet, and for some scientists the potassium would not have survived this episode. The other scenarios involve much slower processes, and less heating.

This raises the question: how hot was the early Mercury? We still do not know, but this is related to the study I present here.

The exploration of Mercury

The proximity of Mercury to the Sun makes it difficult to explore, because of the large gravitational action of the Sun which significantly perturbs the orbit of a spacecraft, and more importantly because of the large temperatures in this area of the Solar System.

Contrarily to Venus and Mars, which regularly host space programs, Mercury has been and will be the target of only 3 space missions so far:

  1. Mariner 10 (NASA): It has been launched in November 1973 to make flybys of Venus and Mercury. Three flybys of Mercury have been realized between March 1974 and March 1975. This mission gave us the first images of the surface of the planet, covering some 45% of it. It also discovered the magnetic field of Mercury.
  2. MESSENGER (Mercury Surface, Space Environment, Geochemistry, and Ranging) (NASA): This was the first human-made object to orbit Mercury. It was launched in August 2004 from Cape Canaveral and has been inserted around Mercury in March 2011, after one flyby of the Earth, two flybys of Venus, and three flybys of Mercury. These flybys permitted to use the gravity of the planets to reduce the velocity of the spacecraft, which was necessary for the orbital insertion. MESSENGER gave us invaluable data, like the gravity field of Mercury, a complete cartography with topographical features (craters, plains, faults,…), new information on the gravity field, it supplemented Earth-based radar measurements of the rotation, it revealed the chemical composition of the surface… The mission stopped in April 2015.
  3. Bepi-Colombo (ESA / JAXA): This is a joint mission of the European and Japanese space agencies, which is composed of two elements: the Mercury Magnetospheric Orbiter (MMO, JAXA), and the Mercury Planetary Orbiter (MPO, ESA). It should be launched in October 2018 and inserted into orbit in December 2025, after one flyby of the Earth, two flybys of Venus, and 6 flybys of Mercury. Beside the acquisition of new data on the planet with a better accuracy than MESSENGER, it will also perform a test of the theory of the general relativity, in giving new measurements of the post-newtonian parameters β and γ. β is associated with the non-linearities of the gravity field, while γ is related with the curvature of the spacetime. In the theory of the general relativity, these two parameters should be strictly equal to 1.

This paper

The idea of the paper is based on the competition between two processes for altering the surface of Mercury:

  1. Impacts, which are violent, rapid phenomena, creating craters,
  2. Tides, which is a much slower process that creates faults, appearing while the planet is contracting. The local stress tensor can be inferred from the direction of the faults.

Dating a crater is possible, from its preservation. And when a crater and a fault are located at the same place, there are two possibilities:

  1. either the fault cuts the crater (see Enheduanna, just below), or
  2. the crater interrupts the fault.

In the first case, the fault appeared after the impact, while in the second case, the fault was already present before Mercury was impacted. So, if you can constrain the age of the crater, you can constrain the apparition of the fault, and the contraction of the planet. From a global analysis of the age of the faults, the authors deduced the variation of the contraction rate over the ages.

A close up of Enheduanna Crater. Credit: IAU

The authors used a database of 3,112 craters ranging from 20 to 2,000 km, which were classified into 5 classes, depending on their degree of preservation. And the result are given below.

Class Name Age Craters Cut Superpose
1+2 Pre-Tolstojan + Tolstojan >3.9 Gy 2,310 1,192 4
3 Calorian 3.9 – 3.5 Gy 536 266 104
4 Mansurian 3.5 – 1 Gy 244 49 55
5 Kuiperian < 1 Gy 22 0 3

We can see that the eldest craters are very unlikely to superpose a fault, while the bombardment was very intense at that time. However, the authors have detected more superposition after. They deduced the following contraction rates:

Time Contraction (radius)
Pre-Tolstojan + Tolstojan 4.0 ± 1.6 km
Calorian 0.90 ± 0.35 km
Mansurian 0.17 ± 0.07 km
Kuiperian 0

This means that the contraction rate has decreased over the ages, which is not surprising, since the temperature of Mercury has slowly reached an equilibrium.

A perspective : constraining the early days of Mercury

In my opinion, such a study could permit to constrain the evolution of the temperature of Mercury over the ages, and thus date its stratification. Maybe this would also give new clues on the way Mercury lost its light elements (impact or not?).

To know more

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