Category Archives: Planets

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.

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.

Measuring the tides of Mercury

Hi there! I have already told you about the tides. If you follow me, you know that the tides are the deformations of a planet from the gravitational action of its parent star (the Sun for Mercury), and that a good way to detect them is to measure the variations of the gravity field of a planet from the deviations of a spacecraft orbiting it. From periodic variations we should infer a coefficient k2, known as the potential Love number, which represents the response of the planet to the tides…

That’s all for today! Please feel free to comment… blablabla…

Just kidding!

Today, I will tell you about another way to measure the tides, from the rotation of Mercury. For this, I will present you a study entitled Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque, which was recently published in The Monthly Notices of the Royal Astronomical Society. This is a collaboration between English and Italian mathematicians, i.e. Michele Bartuccelli, Jonathan Deane, and Guido Gentile. In planetary sciences mathematics can lead to new discoveries. In this case, the idea is: tides slow down the rotation of a planetary body, which eventually reaches an equilibrium rotation (or spin). For the Moon, the equilibrium is the synchronous rotation, while for Mercury it is the 3:2 spin-orbit resonance. Very well. A very good way to describe this final state is to describe the equilibrium rotation, i.e. in considering that the tides do not affect the spin anymore. But this is just an approximation. The tides are actually still active, and they affect the final state. In considering it, the authors show that the variations of the spin rate of Mercury should be composed of at least two sinusoids, i.e. two periodic effects, the superimposition of these two periods being quasi-periodic… you now understand the title.

The rotation of Mercury

I have already presented you Mercury here. Mercury is the innermost planet of the Solar System, with a semimajor axis which is about one third of the one of the Earth, i.e. some 58 million km, and a surprisingly large orbital eccentricity, which is 0.206. These two elements favor a spin-orbit resonance, i.e. the rotation rate of Mercury is commensurate with its orbital rate. Their ratio is 3/2, Mercury performing a revolution about the Sun in 88 days, while a rotation period is 58 days. You can notice a 3/2 ratio between these two numbers.

The 3:2 spin-orbit resonance of Mercury
The 3:2 spin-orbit resonance of Mercury

Why is this configuration possible as an equilibrium state? If you neglect the dissipation (the authors do not) and the obliquity (the authors do, and they are probably right to do it), you can write down a second-degree ODE (ordinary differential equation), which rules the spin. In this equation, the triaxiality of Mercury plays a major role, i.e. Mercury spins the way it spins because it is triaxial. Another reason is its orbital eccentricity. This ODE has equilibriums, i.e. stable spin rates, among them is the 3:2 spin-orbit resonance.

And what about the obliquity? It is actually an equilibrium as well, known as Cassini State 1, in which the angular momentum of Mercury is tilted from the normal to its orbit by 2 arcminutes. This tilt is a response to the slow precessing motion (period: 300,000 years) of the orbit of Mercury around the Sun.

Let us forget the obliquity. There are several possible spin-orbit ratios for Mercury.

Possible rotation states

If you went back to the ODE which rules the spin-rate of Mercury, you would see that there are actually several equilibrium spin rates, which correspond to p/2 spin-orbit resonances, p being an integer. Among them are the famous synchronous resonance 1:1 (p=2), the present resonance of Mercury (p=3), and other ones, which have never been observed yet.

If we imagine that Mercury initially rotated pretty fast, then it slowed down, and crossed several resonances, e.g. the 4:1, the 7:2, 3:1, 5:2, 2:1… and was trapped in none of them, before eventually being trapped in the present 3:2 one. Or we can imagine that Mercury has been trapped for instance in the 2:1 resonance, and that something (an impact?) destabilized the resonance…
And what if Mercury had been initially retrograde? Why not? Venus is retrograde… In that case, the tides would have accelerated Mercury, which would have been trapped in the synchronous resonance, which is the strongest one. This would mean that this synchronous resonance would have been destabilized, to allow trapping into the 3:2 resonance. Any worthwhile scenario of the spin evolution of Mercury must end up in the 3:2 resonance, since it is the current state. The scenario of an initially retrograde Mercury has been proposed to explain the hemispheric repartition of the observed impacts, which could be a signature of a past synchronous rotation. Could be, but is not necessarily. Another explanation is that the geophysical activity of Mercury would have renewed the surface of only one hemisphere, making the craters visible only on the other part.

Anyway, whatever the past of Mercury, it needed a dissipative process to end up in an equilibrium state. This dissipative process is the tides, assisted or not by core-mantle friction.

The tides

Because of the differential attraction of the Sun on Mercury, you have internal friction, i.e. stress and strains, which dissipate energy, and slow down the rotation. This dissipation is enforced by the orbital eccentricity (0.206), which induces periodic variations of the Sun-Mercury distance.
An interesting question is: how does the material constituting Mercury react to the tides? A critical parameter is the tidal frequency, i.e. the way you dissipates depends on the frequency you shake. A derivation of the tidal torque raised by the Sun proves to be a sum of periodic excitations, one of them being dominant in the vicinity of a resonance. This results in an enforcement of all the spin-orbit resonances, which means that a proper tidal model is critical for accurate simulations of the spin evolution.
A pretty common way to model the tides is the Maxwell model: you define a Maxwell time, which is to be compared with the period of the tidal excitation (the shaking). If your excitation is slow enough, then you will have an elastic deformation, i.e. Mercury will have the ability to recover its shape without loss of energy. However, a more rapid excitation will be dissipative. Then this model can be improved, or refined, in considering more dissipation at high frequencies (Andrade model), or grain-boundary slip (Burgers model)… There are several models in the literature, which are supported by theoretical considerations and lab experiments. Choosing the appropriate one depends on the material you consider, under which conditions, i.e. pressure and temperature, and the excitation frequencies. But in any case, these physically realistic tidal models will enforce the spin-orbit resonances.

Considering only the tides assumes that your body is (almost) homogeneous. Mercury has actually an at least partially molten outer core, i.e. a global fluid layer somewhere in its interior. This induces fluid-solid boundaries, the outer one being called CMB, for core-mantle boundary, and you can have friction there. The authors assumed that the CMB was formed after the trapping of Mercury into its present 3:2 spin-orbit resonance, which is supported by some studies. This is why they neglected the core-mantle friction.

This paper

This paper is part of a long-term study on the process of spin-orbit resonance. The authors studied the probabilities of capture (when you slow down until reaching a spin-orbit resonance, will you stay inside or leave it, still slowing down?), proposed numerical integrators adapted to this problem…
In this specific paper, they write down the ODE ruling the dynamics in considering the frequency-dependent tides (which they call realistic), and solve it analytically with a perturbation method, i.e. first in neglecting a perturbation, that they add incrementally, to eventually converge to the real solution. They checked their results with numerical integrations, and they also studied the stability of the solutions (the stable solutions being attractors), and the probabilities of capture.

In my opinion, the main result is: the stable attractor is not periodic but quasi-periodic. Fine, but what does that mean?

If we neglect the influence of the other planets, then the variations of the spin rate of Mercury is expected to be a periodic signal, with a period of 88 days. This is due to the periodic variations of the Sun-Mercury distance, because of the eccentricity. This results in longitudinal librations, which are analogous to the librations of the Moon (we do not see 50% of the surface of the Moon, but 59%, thanks to these librations). The authors say that this solution is not stable. However, a stable solution is the superimposition of these librations with a sinusoid, which period is close to 15 years, and an amplitude of a few arcminutes (to be compared to 15 arcminutes, which is the expected amplitude of the 88-d signal). So, it is not negligible, and this 15-y period is the one of the free (or proper) oscillations of Mercury. A pendulum has a natural frequency of oscillations, here this is exactly the same. But contrarily to a pendulum, the amplitude of these oscillations does not tend to 0. So, we could hope to detect it, which would be a direct observation of the tidal dissipation.

Measuring the rotation

What can we observe? We should first keep in mind that the authors addressed the early Mercury, when being trapped into the 3:2 spin-orbit resonance, which was pretty homogeneous. The current Mercury has a global fluid layer, which means a larger (about twice) amplitude of the 88-d signal, and a different dissipative process, the tides being assisted by core-mantle friction. As a consequence, there is no guarantee that the 15-y oscillation (actually a little shorter, some 12 years, because of the fluid core) would still exist, and that would require a dedicated study. But measuring it would be an information anyway.

How to measure it? The first observations of the rotation of Mercury in 1965 and of the librations in 2007 were Earth-based, radar observations, which are sensitive to the velocity. This means that they are more likely to detect a rapid oscillation (88 d, e.g.) than a slow one (12 years…). Observations of the surface of Mercury by the spacecraft MESSENGER confirmed those measurements. In 2018 the ESA/JAXA (Europe / Japan) joint mission Bepi-Colombo will be sent to Mercury, for orbital insertion in 2025 and hopefully a 2-y mission, with a better accuracy than MESSENGER. So, we could hope a refinement of the measurements of the longitudinal motion.

Purple: The 88-d oscillation. Green: Superimposed with the 15-y one. Keep in mind that Bepi-Colombo will orbit Mercury during some 2 years.
Purple: The 88-d oscillation. Green: Superimposed with the 15-y one. Keep in mind that Bepi-Colombo will orbit Mercury during some 2 years.

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.

Inferring the interior of Venus from the tides

Hi there! Today’s post presents you the study Tidal constraints on the interior of Venus, by Caroline Dumoulin, Gabriel Tobie, Olivier Verhoeven, Pascal Rosenblatt, and Nicolas Rambaux. This study has recently been accepted for publication in Journal of Geophysical Research: Planets. The idea is: because of its varying distance to the Sun, Venus experiences periodic variations. What could their measurements tell us on the interior?

Venus vs. the Earth

Venus is sometimes called the twin sister of the Earth, because of its proximity and its size. However, their physical properties show crucial differences, the most crucial one being the atmosphere.

Inclination3.86°7.155°Obliquity177.36°23.439°Orbital period224.701 d365.256 dSpin period243.025 d0.997 dSurface pressure92 bar1.01 barMagnetic field(none)25-65 μTMean density5,243 kg/m35,514 kg/m3

Venus Earth
Semimajor axis (AU) 0.723332 1.000001
Eccentricity 0.0068 0.0167

As you can see:

  • Venus has a retrograde and very slow rotation,
  • it has a very thick and dense atmosphere,
  • it has no magnetic field.

For a magnetic field to exist, you need a rotating solid core, a global conductive fluid layer, and convection, which is triggered by heat transfers from the core to the mantle. The absence of magnetic field means that at least one of these conditions is not fulfilled. Given the size of Venus and its measured k2 by the spacecraft Magellan (explanations in the next section), it has probably a fluid global layer. However, it seems plausible that the heat transfer is missing. Has the core cooled enough? Is the surface hot enough so that the temperature has reached an equilibrium? Possible.

Probing the interior of Venus is not an easy task; an idea is to measure the time variations of its gravity field.

Tidal deformations

The orbital eccentricity of Venus induces variations of its distance to the Sun, and variations of the gravitational torque exerted by it. Since Venus is not strictly rigid, it experiences periodic deformations, which frequencies are known as tidal frequencies. These deformations can be expressed with the potential Love number k2, which gives you the amplitude of the variations of the gravity field. Since the gravity field can be measured from deviations of the spacecraft orbiting the planet, we dispose of a measurement, i.e. k2 = 0.295 ± 0.066. It has been published in 1996 from Magellan data (see here a review on the past exploration of Venus). You can note the significant uncertainty on this number. Actually k2 should be decorrelated from the other parameters affecting the trajectory of the spacecraft, e.g. the flattening of the planet, the atmosphere, which is very dense, motor impulses of the spacecraft… This is why it was impossible to be more accurate.

Other parameters can be used to quantify the tides. Among them are

  • the topographic Love number h2, which quantified the deformations of the surface. Observing the surface of Venus is a task strongly complicated by the atmosphere. Magellan provided a detailed map thanks to a laser altimeter. Mountains have been detected. But these data do not permit to measure h2.
  • The dissipation function Q. If I consider that the deformations of the gravity field are periodic and represented by k2 only, I mean that Venus is elastic. That mean that it does not dissipate any energy, it has an instantaneous response to the tidal solicitations, and the resulting tidal bulge always points exactly to the Sun. Actually there is some dissipation, which results as a phase lag between the tidal bulge and the Venus – Sun direction. Measuring this phase lag would give k2/Q, and that information would help to constrain the interior.

A 3-layer-Venus

Such a large body is expected to be denser in the core than at the surface, and is usually modeled with 3 layers: a core, a mantle, and a crust. Venus also have an atmosphere, but this is not a very big deal in this specific case. These are not necessarily homogeneous layers, the mantle and the core are sometimes assumed to have a global outer fluid layer. If this would happen for the core, then we would have a solid (rigid) inner core, and a fluid (molten) outer core. This interior must be modeled to estimate the tidal quantities. More precisely, you need to know the radial evolution of the density, and of the velocities of the longitudinal (P) and transverse (S) seismic waves. These two velocities tell us about the viscosity of the material.

Possible interior of Venus (not to scale). Copyright: The Planetary Mechanics Blog

Modeling the core from PREM

PREM is the Preliminary Reference Earth Model. It was published in 1981, and elaborated from thousands of seismic observations. Their inversions gave the radial distribution of the density, dissipation function, and elastic properties for the Earth. It is now used as a standard Earth model.

The lack of data regarding the core of Venus prompted the authors, and many of their predecessors, to rescale PREM from the Earth to Venus.

Modeling the mantle from Perple_X

The properties of the mantle of Venus depend on its composition and the radial distribution of its temperature, its composition itself depending on the formation of the planet. The authors identified 5 different models of formation of Venus in the literature, which affect 5 variables: mass of the core, abundance of uranium (U), K/U ratio (K: potassium), Tl/U ratio (Tl: thallium), and FeO/(FeO+MgO) ratio (FeO: iron oxide, MgO: magnesium oxide). Only 3 of these 5 models were kept, two being end-members, and the third one being pretty close to the Earth. These 3 models were associated with two end-members for temperature profiles, which can be found in the scientific literature. This then resulted in 6 models, and their properties, i.e. density and velocities of the P- and S-waves, were obtained thanks to the Perple_X code. This code gives phase diagrams in a geodynamic context, i.e. under which conditions (pressure and temperature) you can have a solid, liquid, and / or gaseous phase(s) (they sometimes coexist) in a planetary body.

Numerical modeling of the tidal parameters

Once the core and the mantle have been modeled, a 60-km-thick crust have been added on the top, and then the tidal quantities have been calculated. For that, the authors used a numerical algorithm elaborated in Japan in 1974, using 6 radial functions y. y1 and y3 are associated with the radial and tangential displacements, y2 and y4 are related to the radial and tangential stresses, y5 is associated with the gravitational potential, while y6 guarantees a property of the continuity of the gravitational force in the structure. These functions will then give the tidal quantities.

Results

The results essentially consist of a description of the possible interiors and elastic properties of Venus for different values of k2, which are consistent with the Magellan measurements. But the main information is this: Venus may have a solid inner core. Previous studied had discarded this possibility, arguing that k2 should have been 0.17 at the most. However, the authors show that considering viscoelastic properties of the mantle, i.e. dissipation, would result in a smaller pressure in the core, i.e. <300 GPa, for a k2 consistent with Magellan. This does not mean that Venus has a solid inner core, this just means that it is possible. Actually, the authors also get interior models with a fully fluid core.
The atmosphere would alter k2 by only 3 to 4%.

The authors claim that the uncertainty on k2 is too large to have an accurate knowledge on the interior, and they hope that future measurements of k2 and of k2/Q, which has never been measured yet, would give better constraints.

The forthcoming and proposed missions to Venus

For this hope to be fulfilled, we should send spacecrafts to Venus in the future. The authors mention EnVision, which applies to the ESA M5 call (M for middle-class). This is a very competitive call, and we should know the finalists very soon. If selected, EnVision would consist of an orbiter on a low and circular orbit, which would focus on geology and geochimical cycles. It should also measure k2 with an accuracy of 3%, and give us a first measurement of k2/Q.

In America, two missions to Venus have been proposed for the Discovery program of NASA: VERITAS (Venus Emissivity, Radio Science, InSAR, Topography, and Spectroscopy) and DAVINCI (Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging). They have both been rejected.

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.

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.