Tag Archives: Mercury

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?).

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New clues on the interior of Mercury

Hi there! Thanks for coming on the Planetary Mechanics Blog.

Today I will tell you about new results on the interior of the planet Mercury, by Ashok Kumar Verma and Jean-Luc Margot.
Mercury has been orbited during 4 years by the spacecraft MESSENGER, and gravity data have been derived from the deviations of the spacecraft. These data tell us how the mass is distributed in the planet.

 

Planet Mercury facts

Mercury is the innermost planet of the Solar System. Its radius is about one third of the one of the Earth, and its closeness to the Sun associated with the absence of an atmosphere induces large temperature variations between the day and the night. Another consequence is its very slow rotation, i.e. a Hermean (Mercurian) day lasts 58 terrestrial days, while its revolution around the Sun lasts 88 days, which is exactly 50% longer! This phenomenon is called a 3:2 spin-orbit resonance state, it is a unique case in the Solar System but is somehow analogous to the spin-orbit synchronization of our Moon. It is a consequence of the Solar tides, which despin the planet.

A last interesting fact I would like to mention is that Mercury is too dense for a such a small planet. This suggests that in the early ages of the Solar System, the proto-Mercury was much bigger, and differentiated between a core of pretty heavy elements and a less dense mantle. And then, Mercury has been stripped from this mantle, either slowly, or because of a catastrophic event, i.e. an impact.

 

The missions to Mercury

Sending a spacecraft to Mercury is a challenge, once more because of the proximity of the Sun. Not only the spacecraft should be protected from the Solar radiations, heat,… but it also tends to fall on the Sun instead of visiting the planet. For these reasons, only two spacecrafts have visited the Mercury up to now:

  • the US spacecraft Mariner 10 made 3 flybys of Mercury in 1974-1975. It mapped 45% of the surface and measured a magnetic field,
  • the US spacecraft MESSENGER orbited Mercury during 4 years between March 2011 and April 2015. It gave us invaluable information on the planet, including the ones presented here,
  • and let me mention the European-Japanese mission Bepi-Colombo, which should be launched to Mercury in April 2018.

 

The rotation of Mercury

The rotation of Mercury is in a resonant state, known as 3:2 spin-orbit resonance. This is a dynamical equilibrium reached after dissipation of its rotational energy, in which

  • Mercury rotates about one axis,
  • this axis is nearly perpendicular to its orbit, the deviation, named obliquity, being a signature of the interior,
  • the rotation and orbital periods are commensurate, here with a ratio 3/2. Around this exact commensurability are small librations, due to the periodic variations of the Solar gravitational torque acting on Mercury. The main period of these librations is the orbital one, i.e. 88 days, which is a direct consequence of Mercury’s eccentric orbit. They are supplemented by smaller oscillations, at harmonics of the orbital period (44 d, 29 d, 22 d, etc…), and at the periods of the other planets, meaning that they result from the planetary perturbations on the orbit of Mercury. The largest of these perturbations is expected to be due to Jupiter, but it has not been measured yet.

 

What the rotation can tell us

An issue in the pre-MESSENGER era was: does Mercury have an at least partially molten (outer) core? We now know that it has, thanks to Peale’s experiment, due to the late Stan Peale. The idea was this: the viscous core responds like a fluid to short-period excitations, and like a rigid body for long-period (secular) excitations. And the good thing is that the librations (called longitudinal physical librations) are due to a 88 d-oscillations, while the obliquity is due to a secular one (actually an oscillation which is some 200 kyr periodic, i.e. the rotation of the orbital plane of Mercury). So, in measuring these 2 quantities, one should be able to invert for the size of the core. This was achieved in 2007 thanks to radar measurements of the rotation of Mercury, and confirmed from additional Earth-based measurements, and MESSENGER data, since.

We now know that Mercury has a large molten core, which does not rule out the presence of a solid inner core. For that, additional investigations should be conducted.

 

The gravity field

The most basic model of gravity is the point-mass, which just gives us a mean density of the planet. This can be obtained from planetary ephemerides, i.e. in studying how Mercury affects the motion of the other planets, and with more accuracy from the deviations of the spacecraft. We know since Mariner 10 that Mercury has a density of 5.43 g/cm3, while 1g/cm3 is expected for ice, 3.3 g/cm3 for silicates, and 8 g/cm3 for iron.

A more accurate model is to see Mercury has a triaxial ellipsoid. This requires to add two parameters in the gravity field: J2 and C22, also know as Stokes coefficients. A positive J2 means that the body is flattened at its poles, while C22 represents the equatorial ellipticity of the planet. A positive polar flattening is expected as a consequence of the rotation of the planet, while the equatorial ellipticity can result from differential gravitational action of the Sun, i.e. the tides.

Knowing these two Stokes coefficients is possible from gravity data, and this would give us the triaxility of the mass distribution in Mercury. But something is missing: we do not know its radial distribution, i.e. heavier elements are expected to be in the core. For that, we need the polar momentum C, which could be derived from the obliquity, knowing the Stokes coefficient.

For a spherical homogeneous body, C=2/5 MR2, M being the mass and R the radius, and is smaller when heavier elements are concentrated in the core.

 

The tidal Love coefficient k2

The tides tend to alter the shape of the planet. In addition to a mean shape, there are periodic variations, which are due to the variations of the distance between Mercury and the Sun.

The amplitude of these variations depend on the Love parameter k2, which characterizes the response of the material to the periodic excitations. Actually, k2 depends on the frequency of excitation, in the specific case of Mercury k2@88d and k2@44d affect the gravity field. But distinguishing these two quantities requires a too high accuracy in the data, this is why k2 is often mentioned without precising the frequency involved.

If Mercury were spherical and fluid, k2 would be 1.5, while it would be null if Mercury were fully rigid. Actually, all the natural bodies are somewhere between these two end-members.

The frequency-dependence of the tides is based on the assumption that if you impose a slow deformation of a viscous body, it will not loose any internal energy and slowly recover its shape after (elastic deformation). However, rapid solicitations induce permanent deformations. The numbers associated with these two different regimes depend on the interior of the planet.

 

In this paper

This study, Mercury’s gravity tides, and spin from MESSENGER radio data, by A.K. Verma and J.-L. Margot, has been accepted for publication in Journal of Geophysical Research – Planets. It presents

  • an updated gravity field for Mercury,
  • an updated Love number,
  • an updated spin orientation.

These results are based on measurements of the instantaneous gravity field of Mercury. This is particularly interesting for the determination of the spin, since classical methods are based on the observation of the surface, while the gravity field is ruled by the whole planet. This means that here, the rotation of the whole planet is observed, not just its surface. This allows to constrain the possible differential rotation between the surface and the core.

For the gravity field of Mercury, a 40th order solution is considered, because Mercury is something more complicated than a triaxial ellipsoid. The second order Stokes coefficients are consistent with previous studies, which were also based on MESSENGER data. Some higher-order coefficients are identified as well.

This is the second determination of the Love number k2 = 0.464, which implies than the mantle of Mercury is pretty hot.

 

Some perspectives

We are some years away from the orbital insertion of the European / Japanese mission Bepi-Colombo, which is expected to be ten times more accurate than MESSENGER. So, results like the ones presented here are in some sense preparing the Bepi-Colombo’s measurements. This mission will also secure the results, and providing independent determinations.

Knowing Mercury is also a way to understand planetary formation. There are many discoveries of exoplanets, which orbit close to their parent star, but are so far from us that we cannot hope to send spacecrafts orbiting them. So, understand the way Mercury has been formed helps understanding the other planetary systems.

I hope that one day we will be able to measure the frequency-dependence of the Love numbers, this would be very helpful to constrain the tidal models.

 

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