Equilibrium rotational stability and figure of Mars

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90° from the location of the massive Tharsis volcanic province. We demonstrate, using general physical arguments supported by a fluid Love number analysis, that the so-called non-hydrostatic theory is an inaccurate framework for analyzing the rotational stability of planets, such as Mars, that are characterized by long-term elastic strength within the lithosphere. In this case, the appropriate correction to the gravitational figure is the equilibrium rotating form achieved when the elastic lithospheric shell (of some thickness LT) is accounted for. Moreover, the current rotation vector of Mars is shown to be stable when the correct non-equilibrium theory is adopted using values consistent with recent, independent estimates of LT. Finally, we compare observational constraints on the figure of Mars with non-equilibrium predictions based on a large suite of possible Tharsis-driven true polar wander (TPW) scenarios. We conclude, in contrast to recent comparisons of this type based on a non-hydrostatic theory, that the reorientation of the pole associated with the development of Tharsis was likely less than 15° and that the thickness of the elastic lithosphere at the time of Tharsis formation was at least ∼50 km. Larger Tharsis-driven TPW is possible if the present-day gravitational form of the planet at degree 2 has significant contributions from non-Tharsis loads; in this case, the most plausible source would be internal heterogeneities linked to convection.     

Polar wander on Mars: Evidence in the geoid

The geoid of Mars is dominated by its equilibrium figure and by the effect of the Tharsis rise. To investigate the rotational stability of Mars prior to the rise of Tharsis, we produced a residual non-hydrostatic geoid without Tharsis. First the hydrostatic component of the present-day flattening was removed. This procedure was performed using a 6% non-hydrostatic component of flattening, a value set by the spin axis precession rate of Mars. Then zonal spherical harmonics up to degree 6 centered on Tharsis were removed. Finally, the resultant residual geoid was evaluated for rotational stability by comparing polar and equatorial moments at 4050 trial pole positions. If the spin axis of ancient Mars was secularly stable, our analysis indicates that substantial polar wander has occurred with the rise of Tharsis. Stable spin axis positions on the non-hydrostatic residual figure of Mars are 15° to 90° from the present-day poles. This result is consistent with previously proposed paleopoles based on magnetic anomalies, geomorphology, and grazing impacts.     

Reorientation of planets with elastic lithospheres

The orientation of a planet is controlled by the positions of the principal axes of the inertia tensor relative to the planetary surface. Using the theory for the deflection of thin elastic shells the principal axes are computed after emplacement of an arbitrary axisymmetrical load. The partial compensation of the load and the partial relaxation of rotational flattening are included in the computation. It is found that the amount of reorientation is independent of lithosphere thickness. The parameters controlling the amount of reorientation are the location of the load and the size of the load compared to the rotational flattening. The results indicate that the Tharsis rise has probably reoriented Mars by only 3 to 9° and certainly less that 18°. The position of the Caloris Basin on Mercury indicates that if the surrounding lava sheet controls the planetary orientation then the lava sheet is probably less than 2000 m thick.     

Tectonic tests of proposed polar wander paths for Mars and the Moon

We have tested the polar wander paths recently proposed for Mars by Schultz and Lutz-Garihan and for the Moon by Runcorn through a comparison of the lithospheric stress field predicted for rapid global reorientations against observed tectonic features. We have employed the theory of Vening Meinesz and of Melosh to calculate the reorientation stresses, and we argue that the formation of normal faults or graben in broad regions surrounding the former rotation poles should be the minimum tectonic signature of a reorientation that generates lithospheric stresses in excess of the extensional strength of near-surface material. Such regions of normal faults are not present in the vicinity of the most recent proposed paleopoles for Mars, despite the large magnitude of the predicted shear stress (1–2 kbar). The minimum tectonic criterion would not be relaxed by invoking gradual polar wander or by considering the superposition of stresses associated with the global lithospheric response to the Tharsis rise. We conclude that polar wander of the magnitude and timing proposed by Schultz and Kutz-Garihan did not occur. It follows either that Tharsis has always been located near the Martian equator or that Tharsis began to dominate the nonhydrostatic figure prior to the end of heavy bombardment so that any tectonic signature of reorientation has since been obliterated by cratering. The predicted directions of stresses that would result from the most recent episode of proposed polar wander on the Moon, including stresses produced by reorientation of both the rotational and tidal figures, show little or no correspondence to observed tectonic features in the vicinity of the postulated nearside paleopole. The magnitude of the predicted reorientation stress is at most a few tens of bars, however, so that the tectonic test of polar wander on the Moon is inconclusive.     

Tectonic patterns on a reoriented planet: Mars

Both geologic and free-air-gravity data suggest that the positive mass anomaly associated with the Tharsis volcanoes may have reoriented Mars' lithosphere by as much as 25°. Since Mars is oblate (with flattening $\text{? ?0.005}$), rotation of the lithosphere over the equatorial bulge by 25° produces membrane stresses of several kilobars, large enough to initiate faulting. These stresses were first evaluated by F.A. Vening-Meinesz (1947, Trans. Amer. Geophys. Union28, 1–61) who treated the lithosphere as a thin elastic shell. The fracture patterns which result from these stresses are determined by the relation between stress and faulting proposed by E.M. Anderson (1951, The Dynamics of Faulting, Oliver & Boyd, Edinburgh). Plots of the magnitude and direction of stresses in a reoriented planet show that near Tharsis the dominant fault type should be north-south- trending normal faults. This normal fault province is centered about 30°N latitude and extends about 45° east and west in longitude. Similar faults should occur at the antipodes, north of Hellas Planitia. The polar regions should be occupied by roughly north-south-trending thrust faults which extend close to the equator south of Tharsis and north of Hellas. The regions between Tharsis and Hellas are subject to compression on a NE-trending axis and extension along a NW axis east of Tharsis (west of Tharsis the directions are NW compression and NE extension), thus predicting a zone of NNW and ENE strike slip faults east of Tharsis (NNE and WNW west of Tharsis). Although these patterns, except for the north-south normal faults north of Tharsis, have not yet been recognized, the discovery of such a tectonic system of the same age as Tharsis would provide strong support for the reorientation idea. Stresses due to reorientation appear to have little to do with Valles Marineris, since the stress normal to the axis of the Valles is predicted to be compressive, whereas geologic evidence suggests extension.     

Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2003

Every three years the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the north poles of rotation and the prime meridians of the planets, satellites, and asteroids. This report introduces a system of cartographic coordinates for asteroids and comets. A topographic reference surface for Mars is recommended. Tables for the rotational elements of the planets and satellites and size and shape of the planets and satellites are not included, since there were no changes to the values. They are available in the previous report (Celest. Mech. Dyn. Astron., 82, 83–110, 2002), a version of which is also available on a web site.     

The Martian Nonhydrostatic Components of Moment-of-Inertia

The author puts forward the proposal in this paper that all the terrestrial planets (Venus, the Earth, and Mars) as well as the Moon deviate from hydrostatic equilibrium to some degree. The Earth's level of deviation of these four celestial bodies is minimum, and that of Mars is maximum. Moreover, the author estimates Martian nonhydrostatic components of the principal moments-of-inertia using five models for the interior of Mars. Comparison with other terrestrial planets shows that setting the range of mean moment-of-inertia ratio, I/MR², in 0.345 ~ 0.355for Mars is reasonable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ancient dorsa-related stresses of the tharsis region on Mars

Topographic information, surface structures and construction of the Martian Tharsis bulge are used to estimate the previous stresses across the low-lying peripheral margins of the crustal blocks in terms of simple compensation models. Hot mantle activity, crustal roots, isostasy, and late-stage extensive lithosphere thickening together with volcanic building have been in combined response to the high-elevated Tharsis bulge. The initial phases of the Tharsis building have been dominated by the mantle plume doming, followed by extrusional dome raising. The volcanism has been most important bulge building factor only after thickening of the crust. During the initial mantle-generated doming and igneous activity the thin-lithosphere block tectonics has been very important. There has been a compressional peripheral zone around the bulge giving rise to dorsa formation while the high bulge crests have been in tensional state. The situation may be favorable for comparative studies with other planets. We may have something to learn from this block tectonics on the one-plate planet Mars even in respect to the Earth's plate tectonic paradigm.On leave from Dept. of Astronomy, University of Oulu, Finland.     

Polar wander of Mars: Evidence from giant impact basins

We investigate the polar wander of Mars in the last ∼4.2 Ga. We identify two sets of basins from the 20 giant impact basins reported by Frey [Frey, H., 2008. Geophys. Res. Lett. 35, L13203] which trace great circles on Mars, and propose that the great circles were the prevailing equators of Mars at the impact times. Monte Carlo tests are conducted to demonstrate that the two sets of basins are most likely not created by random impacts. Also, fitting 63,771 planes to randomly selected sets of 5, 6, or 7 basins indicated that the identified two sets are unique. We propose three different positions for the rotation pole of Mars, besides the present one. Accordingly, Tharsis bulge was initially formed at ∼50 N and moved toward the equator while rotating counterclockwise due to the influence of the two newly forming volcanic constructs, Alba Patera and Elysium Rise. The formation of the giant impact basins, subsequent mass concentrations (mascons) in Argyre, Isidis, and Utopia basins, and surface masses of volcanic mountains such as Ascraeus, Pavonis, Arsia and Olympus, caused further polar wander which rotated Tharsis bulge clockwise to arrive at its present location. The extensive polar motion of Mars during 4.2-3.9 Ga implies a weak lithosphere on a global scale, deduced from a total of 72,000 polar wander models driven by Tharsis bulge, Alba Patera and Elysium Rise as the major mass perturbations. Different compensation states, 0-100%, are examined for each of the surface loads, and nine different thicknesses are considered for an elastic lithosphere. The lithosphere must have been very weak, with an elastic thickness of less than 5 km, if the polar wander was driven by these mass perturbations.     

The kinematical mechanism for the perturbation of the rotational axis in the rotation of the elastic Earth

Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation. First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation, A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation of the figure axis.     

The global martian volcanic evolutionary history

Viking mission image data revealed the total spatial extent of preserved volcanic surface on Mars. One of the dominating surface expressions is Olympus Mons and the surrounding volcanic province Tharsis. Earlier studies of the global volcanic sequence of events based on stratigraphic relationships and crater count statistics were limited to the image resolution of the Viking orbiter camera. Here, a global investigation based on high-resolution image data gathered by the High-Resolution Stereo Camera (HRSC) during the first years of Mars Express orbiting around Mars is presented. Additionally, Mars Orbiter Camera (MOC) and Thermal Emission Imaging System (THEMIS) images were used for more detailed and complementary information. The results reveal global volcanism during the Noachian period (>3.7 Ga) followed by more focused vent volcanism in three (Tharsis, Elysium, and Circum-Hellas) and later two (Tharsis and Elysium) volcanic provinces. Finally, the volcanic activity became localized to the Tharsis region (about 1.6 Ga ago), where volcanism was active until very recently (200-100 Ma). These age results were expected from radiometric dating of martian meteorites but now verified for extended geological units, mainly found in the Tharsis Montes surroundings, showing prolonged volcanism for more than 3.5 billions years. The volcanic activity on Mars appears episodic, but decaying in intensity and localizing in space. The spatial and temporal extent of martian volcanism based on crater count statistics now provides a much better database for modelling the thermodynamic evolution of Mars.     

Relative crater production rates on planets

Dynamical histories of planetesimals in specified orbits, calculated by Wetherill (1975) and others, have estimates of relative numbers of impacts on different planets. These impact rates, $\text{F}$, are converted to crater production rates, F, by means of tables developed in this paper. Conversions are dependent on impact velocity and surface gravity. Crater retention ages can then be derived from (crater density)/(crater production rate). Such calculations of impact rates and their histories give the only basis, independent of sample dating, for establishing absolute geologic histories of the planets, contrary to published implications that this can be done by comparison of photos alone. A survey of the results, from orbits of interplanetary objects studied to date, indicates that the terrestial planets have crater production rates within a factor ten of each other, and that planet's crater retention ages can probably be determined with a factor of ±3. Further calculations of orbital histories of additional interplanetary bodies are suggested to put photogeologic analyses from spacecraft imagery on a firmer basis.Applications to Mars, as an example, using least-squares fits to crater-count data, suggest an average age of 0.3 to 3 b.y. for two types of channels. The Tharsis volcanics are found to be slightly younger than the channels (strongly confirmed by photomorphology since they are not cut by channels) and Olympus Mons is about 0.06 to 0.6 b.y. old, contrary to recent assertions that Olympus Mons is 2.5 b.y. old and most Martian volcanic provinces older than 3 b.y. Data strongly support the hypothesis that Martian channels formed in a fluvial climate that persisted on Mars until the Tharsis volcanism caused a change in the Martian obliquity state, as outlined by Toon, Ward, and Burns (1977).     

Mars

Mars is the fourth planet out from the sun. It is a terrestrial planet with a density suggesting a composition roughly similar to that of the Earth. Its orbital period is 687 days, its orbital eccentricity is 0.093 and its rotational period is about 24 hours. Mars has two small moons of asteroidal shapes and sizes (about 11 and 6 km mean radius), the bigger of which, Phobos, orbits with decreasing semimajor orbit axis. The decrease of the orbit is caused by the dissipation of tidal energy in the Martian mantle. The other satellite, Deimos, orbits close to the synchronous position where the rotation period of a planet equals the orbital period of its satellite and has hardly evolved with time. Mars has a tenous atmosphere composed mostly of CO with strong winds and with large scale aeolian transport of surface material during dust storms and in sublimation-condensation cycles between the polar caps. The planet has a small magnetic field, probably not generated by dynamo action in the core but possibly due to remnant magnetization of crustal rock acquired earlier from a stronger magnetic field generated by a now dead core dynamo. A dynamo powered by thermal power alone would have ceased a few billions of years ago as the core cooled to an extent that it became stably stratified. Mars' topography and its gravity field are dominated by the Tharsis bulge, a huge dome of volcanic origin. Tharsis was the major center of volcanic activity, a second center is Elysium about 100° in longitude away. The Tharsis bulge is a major contributor to the non-hydrostaticity of the planet's figure. The moment of inertia factor together with the mass and the radius presently is the most useful constraint for geophysical models of the Martian interior. It has recently been determined by Doppler range measurements to the Mars Pathfinder Lander to be (Folkner et al. 1997). In addition, models of the interior structure use the chemistry of the SNC meteorites which are widely believed to have originated on Mars. According to the models, Mars is a differentiated planet with a 100 to 200 km thick basaltic crust, a metallic core with a radius of approximately half the planetary radius, and a silicate mantle. Mantle dynamics is essential in forming the elements of the surface tectonics. Models of mantle convection find that the pressure-induced phase transformations of -olivine to -spinel, -spinel to -spinel, and -spinel to perovskite play major roles in the evolution of mantle flow fields and mantle temperature. It is not very likely that the -spinel to perovskite transition is present in Mars today, but a few 100 km thick layer of perovskite may have been present in the lower mantle immediately above the core-mantle boundary early in the Martian history when mantle temperatures were hotter than today. The phase transitions act to reduce the number of upwellings to a few major plumes which is consistent with the bipolar distribution of volcanic centers of Mars. The phase transitions also cause a partial layering of the lower mantle which keeps the lower mantle and the core from extensive cooling over the past aeons. A relatively hot, fluid core is the most widely accepted explanation for the present lack of a self-generated magnetic field. Growth of an inner core which requires sub-liquidus temperatures in the core would have provided an efficient mechanism to power a dynamo up to the present day. Received 10 May 1997     

Generalized YORP evolution: Onset of tumbling and new asymptotic states

Asteroids have a wide range of rotation states. While the majority spin a few times to several times each day in principal axis rotation, a small number spin so slowly that they have somehow managed to enter into a tumbling rotation state. Here we investigate whether the Yarkovsky-Radzievskii-O'Keefe-Paddack (YORP) thermal radiation effect could have produced these unusual spin states. To do this, we developed a Lie-Poisson integrator of the orbital and rotational motion of a model asteroid. Solar torques, YORP, and internal energy dissipation were included in our model. Using this code, we found that YORP can no longer drive the spin rates of bodies toward values infinitely close to zero. Instead, bodies losing too much rotation angular momentum fall into chaotic tumbling rotation states where the spin axis wanders randomly for some interval of time. Eventually, our model asteroids reach rotation states that approach regular motion of the spin axis in the body frame. An analytical model designed to describe this behavior does a good job of predicting how and when the onset of tumbling motion should take place. The question of whether a given asteroid will fall into a tumbling rotation state depends on the efficiency of its internal energy dissipation and on the precise way YORP modifies the spin rates of small bodies.     

Tharsis block tectonics on Mars

The concept of block tectonics provides a framework for understanding many aspects of Tharsis and adjoining structures. This Tharsis block tectonics on Mars is manifested partly by mantle-related doming and partly by response to loading by subsequent volcanic construction. Although the origin of the volcanism from beneath Tharsis is a subject of controversy explanations have to include inhomogenities in Martian internal structure, energy distribution, magma accumulation and motion below the lithosphere. Thermal convection can be seen as a necessary consequence for transient initial phase of Martian cooling. This produced part of the elevated topography with tensional stresses and graben systems radial to the main bulge. The linear grabens, radial to the Tharsis center, can be interpreted to indicate rift zones that define the crustal block boundaries. The load-induced stresses may then have contributed on further graben and ridge formation over an extended period of time.On leave from Dept. of Astronomy University of Oulu, Oulu, Finland.     

A plume tectonics model for the Tharsis province, Mars

Morphological and structural data from the whole Tharsis province suggest that a number of shallow grabens radially oriented about the Tharsis bulge on Mars are underlain by dykes, which define giant radiating swarms similar to, e.g. the Mackenzie dyke swarm of the Canadian shield. Mechanisms for graben formation are proposed, and the depth, width, and height of the associated dykes are estimated. Structural mapping leads to define successive stages of dyke emplacement, and provide stress-trajectory maps that indicate a steady source of the regional stress during the whole history of the Tharsis province. A new tectonic model of Tharsis is presented, based on an analogy with dyke swarms on the Earth that form inside hot spots. This model successfully matches the following features: (1) the geometry of the South Tharsis Ridge Belt, which may have been a consequence of the compressional stress field at the boundary between the uplifted and non-uplifted areas in the upper part of the lithosphere at the onset of hot spot activity; (2) extensive lava flooding, interpreted as a consequence of the high thermal anomaly at the onset of plume (hot spot) activity; (3) wrinkle ridge geometry in the Tharsis hemisphere, the formation of which is interpreted as a consequence of buoyant subsidence of the brittle crust in response to the lava load; (4) Valles Marineris limited stretching by preliminary passive rifting, and uplift, viewed as a necessary consequence of adiabatic mantle decompression induced by stretching. The geometrical analysis of dyke swarms suggests the existence of a large, Tharsis-independent extensional state of stress during all the period of tectonic activity, in which the minimum compressive stress is roughly N---S oriented. Although magmatism must have loaded the lithosphere significantly after the plume activity ceased and be responsible for additional surface deformations, there is no requirement for further loading stress to explain surficial features. Comparison with succession of magmatic and tectonic events related to hot spots on the Earth suggests that the total time required to produce all the surface deformation observed in the Tharsis province over the last 3.8 Ga does probably not exceed 10 or 15 Ma.     

Mars geodesy,rotation and gravity

This review provides explanations of how geodesy, rotation and gravity can be addressed using radioscience data of an orbiter around a planet or of the lander on its surface.The planet Mars is the center of the discussion.The information one can get from orbitography and radioscience in general concerns the global static gravitational field, the time variation of the gravitational field induced by mass exchange between the atmosphere and the ice caps, the time variation of the gravitational field induced by the tides, the secular changes in the spacecraft's orbit induced by the little moons of Mars named Phobos and Deimos, the gravity induced by particular targets, the Martian ephemerides, and Mars' rotation and orientation.The paper addresses as well the determination of the geophysical parameters of Mars and, in particular, the state of Mars' core and its size, which is important for understanding the planet's evolution.Indeed, the state and dimension of the core determined from the moment of inertia and nutation depend in turn on the percentage of light elements in the core as well as on the core temperature, which is related to heat transport in the mantle.For example, the radius of the core has implications for possible mantle convection scenarios and, in particular, for the presence of a perovskite phase transition at the bottom of the mantle.This is also important for our understanding of the large volcanic province Tharsis on the surface of Mars.     

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites

This paper is the entire report of the IAU Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites, including three annexes. Tables give the recemmended values for the directions of the north poles of rotation and the prime meridians of the planets and satellites. Reference surfaces for mapping these bodies are described. The annexes discuss the guiding principles, given in the body of the report, present explanatory notes, and provide a bibliography of the rotational elements and reference surfaces of the planets and satellites, definitions, and algebraic expressions of relevant parameters.     

On Stable Chaos in the Asteroid Belt

The twenty most chaotic objects found among first hundred of numbered asteroids are studied. Lyapunov time calculated with and without inner planets indicates that for eleven of those asteroids the strongest chaotic effect results from the resonances with Mars. The filtered semimajor axis displays an abrupt variation only when a close approach to Mars takes place. The study of the behaviour of the critical argument for candidate resonances can reveal which is responsible for the semimajor axis variation. We have determined these resonances for the asteroids in question. For the asteroids chaotic even without the inner planets we have determined the most important resonances with Jupiter, or three-body resonances. This revised version was published online in July 2006 with corrections to the Cover Date.     

Lineament Analysis and Geophysical Modelling of the Alba Patera Region on Mars

Global data sets of images, topography and gravity are available for Mars from several orbiter missions. At the eve of new global data from Mars Global Surveyor (MGS), the capabilities of 3D geophysical modelling based on areal topography and gravity data combined with geologic-tectonic image interpretation is demonstrated here. A unique structure is chosen for the model calculations: the Alba Patera volcanic complex at the northern border of the Tharsis rise. Five groups of graben are discriminated: Ceraunius Fossae, Catenae, Tantalus Fossae (radial group) radial to the Tharsis rise, mainly associated to the formation of Tharsis, and Alba and Tantalus Fossae (circular group), younger than the other graben and circular around Alba Patera. Combining 3D elastic flexure of the lithosphere due to a 3D topographic surface load with 3D gravity models results in a rather thick lithosphere (150–200 km) and thick crust (60–100 km). In another model estimate it has been assumed that the circular grabens are induced by the stresses from the surface load of Alba Patera. In a first order calculation the surface stresses under a point load have been determined resulting in a good correlation of the stress maximum with the location of the circular grabens for a 50-km thick lithosphere. This is in accordance with earlier results from this method, but in contradiction with the thick lithosphere derived from flexure-gravity models. One possibility for this contradiction may be that the different models represent two evolutionary points of Alba Patera. (1) The correlation of stresses with the circular grabens may represent an older stage of evolution with a thinner lithosphere. (2) The flexure-gravity models represent a younger to present stage with a thick lithosphere. The results of the lithosphere thicknesses are compared with an admittance calculation and different thermal evolution models which determine comparable thicknesses (150 km). More detailed models including 3D stress models should wait for new data sets from MGS. The results from the lineament analysis and geophysical modelling are summarized in an evolution model for Alba Patera.