Polar wander of an ice shell on Europa

Ojakangas, G. W.; Stevenson, D. J.

doi:10.1016/0019-1035(89)90053-5

Cited by 75 publications

(42 citation statements)

References 23 publications

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“…If we use equation 2.7 from ref. 38 to estimate the value of C w , and reasonable geophysical values for a floating early lunar crust in the magma ocean epoch (Poisson's ratio = 0.25, thickness of the lithosphere = 2 km, degree-2 rigidity = 10 GPa) we obtain C w = 0.97, which implies that the crust will be largely compensated during this time. In reality, the case of a growing crust in the magma ocean epoch calls for a bottom-loading approach, but the implied nearly complete state of compensation justifies using the top-loading approach, which equals the bottom-loading value in the limit of complete isostasy.…”

Section: S4 Equations For Compensated and Uncompensated Topographymentioning

confidence: 53%

“…38. The probability of finding the characteristic compensated and uncompensated topography C 2,0 /C 2,2 ratios by chance is based on the statistics of the ratios of the The blue dots show the power using data outside of large basins ( 1σ).…”

Section: Methods Summarymentioning

confidence: 99%

“…The C 2,m gravity spherical harmonic coefficient resulting from completely compensated or completely uncompensated topography can be obtained from the relationships for top-loaded crust developed by Ojakangas and Stevenson (1989) 38 ,…”

Section: S4 Equations For Compensated and Uncompensated Topographymentioning

confidence: 99%

“…This is because some initial C 2,0 and C 2,2 values will result in the largest moment of inertia being in a non-polar axis, which would result in polar wander, and thereafter a different C 2,0 /C 2,2 value. The criteria for this reorientation are, in normalized harmonics (Ojakangas and Stevenson (1989) 38 eq. 3.2-3.4),…”

Section: S91 -Topography Statisticsmentioning

confidence: 99%

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The tidal–rotational shape of the Moon and evidence for polar wander

Garrick‐Bethell

Perera

Nimmo

et al. 2014

Nature

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Summary paragraph: The origin of the Moon's large-scale topography is important for understanding lunar geology 1 , lunar orbital evolution 2 , and the Moon's orientation in the sky 3 .Previous hypotheses for its origin have included late accretion events 4 , large impacts 5 , tidal effects 6 , and convection processes 7 . However, testing these hypotheses and quantifying the Moon's topography is complicated by the large basins that have formed since the crust crystallized. Here we estimate the low-order lunar topography and gravity spherical harmonics outside these basins and show that the bulk of the degree-2 topography is consistent with a crustbuilding process controlled by early tidal heating throughout the Moon. The remainder of the degree-2 topography is consistent with a frozen tidal-rotational bulge that formed later, at a semimajor axis of 32 Earth radii. The probability of the degree-2 shape having these two separate tidal characteristics by chance is less than 1%. We also infer that internal density contrasts eventually reoriented the Moon's polar axis 36  4°, to the present configuration we observe today. Together, these results link the geology of the near and far sides, and resolve longstanding questions about the Moon's low-order shape, gravity, and history of polar wander. 2 Main TextThe theory of equilibrium figures of rotating fluid bodies is a classic problem in geophysics, and it has been helpful in understanding the shapes of the Sun and planets. However, the origin for the Moon's shape has remained an open problem in the last century 2,6,[8][9][10] , and the body's deviations from any simple tidal-rotational (spherical harmonic degree-2) figure are large 11 . This difficulty is surprising given the Moon's presumably simple early thermal history: born hot and quickly cooled, one might expect the Moon to be described by a simple figure of equilibrium.Researchers have traditionally suggested that the Moon's degree-2 spherical harmonic gravity coefficients, which have been used as proxies for the degree-2 shape, are especially large when compared to higher degree coefficients 9,12 . Figure 1 shows a power law or "Kaula's rule" fit to degrees n = 3 to 50 for the Moon's gravity 13 and topography data 14 . The power at degree 2 is 4.5 times and 2.6 times the power expected from extrapolating the best-fit power law, for gravity and topography, respectively, supporting the idea that the degree-2 coefficients are unique. Indeed, the fraction of excess power for topography is greater than the excesses for Venus, Earth, and Mars (SI). Authors have tried to interpret the Moon's strong degree-2 power as a frozen tidalrotational state inherited from when the Moon was closer to the Earth, known as the fossil bulge hypothesis 6 . An open problem, however, has been that the ratio of the C 2,0 and C 2,2 spherical harmonic coefficients is different from the expected value by a factor of 2. 6 (refs. 2,10).Adding to the fossil bulge idea and motivated by tidal processes in Europa's ice shell 15 , GarrickBet...

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Section: S4 Equations For Compensated and Uncompensated Topographymentioning

confidence: 53%

Section: Methods Summarymentioning

confidence: 99%

Section: S4 Equations For Compensated and Uncompensated Topographymentioning

confidence: 99%

Section: S91 -Topography Statisticsmentioning

confidence: 99%

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The tidal–rotational shape of the Moon and evidence for polar wander

Garrick‐Bethell

Perera

Nimmo

et al. 2014

Nature

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“…In the meanwhile, stress directions inferred for many bands, are consistent with stresses resulting from sliding of the crust of Europa as a single unit (Schenk and McKinnon 1989). Such a reorientation, denominated as polar wander, may result from spatial variations in the thickness of the shell (Ojakangas and Stevenson 1989). Such polar wander probably also explains symmetry patterns in the distribution of chaotic terrain, pits, and uplift features (Greenberg et al, 2003;Schenck et al, 2008].…”

Section: Europan Oceanmentioning

confidence: 56%

Europa Lander Mission: A Challenge to Find Traces of Alien Life

Zelenyǐ¹,

Korablev

Vorobyova³

et al. 2010

Proc. IAU

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Abstract. An international effort dedicated to science exploration of Jupiter system planned by ESA and NASA in the beginning of next decade includes in-depth science investigation of Europa. In parallel to EJSM (Europa-Jupiter System Mission) Russian Space Agency and the academy of Science plan Laplace-Europa Lander mission, which will include the small telecommunication and science orbiter and the surface element: Europa Lander. In-situ methods on the lander provide the only direct possibility to assess environmental conditions, and to perform the search for signatures of life. A critical advantage of such in situ analysis is the possibility to enhance concentration and detection limits and to provide ground truth for orbital measurements. The science mission of the lander is biological, geophysical, chemical, and environmental characterizations of the Europa surface. Remote investigations from the orbit around Europa would not be sufficient to address fully the astrobiology, geodesy, and geology goals. The science objectives of the planned mission, the synergy between the Europa Lander and EJSM mission elements, and a brief description of the Laplace-Europa Lander mission are presented.

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A numerical method for reorientation of rotating tidally deformed viscoelastic bodies

Wal

Vermeersen

2017

JGR Planets

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Existing approaches for simulating the true polar wander (TPW) of a viscoelastic body can be divided into three categories: (i) a linear dynamic approach which uses the linearized Liouville equation (e.g., Wu and Peltier (1984) and Mitrovica et al. (2005)); (ii) a nonlinear dynamic approach which is based on the quasi‐fluid approximation (e.g., Sabadini and Peltier (1981), Ricard et al. (1993), and Cambiotti et al. (2011)); and (iii) a long‐term limit approach which only considers the fluid limit of a reorientation (e.g., Matsuyama and Nimmo (2007)). Several limitations of these approaches have not been studied: the range for which the linear approach is accurate, the validity of the quasi‐fluid approximation, and the dynamic solution for TPW of a tidally deformed rotating body. We establish a numerical procedure which is able to determine the large‐angle reorientation of a viscoelastic celestial body that can be both centrifugally and tidally deformed. We show that the linear approach leads to significant errors for loadings near the poles or the equator. Second, we show that slow relaxation modes can have a significant effect on large‐angle TPW of Earth or other planets. Finally, we show that reorientation of a tidally deformed body driven by a positive mass anomaly near the poles has a preference for rotating around the tidal axis instead of toward it. At a tidally deformed body which does not have a remnant bulge, positive mass anomalies are more likely to be found near the equator and the plane perpendicular to the tidal axis, while negative mass anomalies tend to be near the great circle that contains the tidal and rotational axes.

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Polar wander of an ice shell on Europa

Cited by 75 publications

References 23 publications

The tidal–rotational shape of the Moon and evidence for polar wander

The tidal–rotational shape of the Moon and evidence for polar wander

Europa Lander Mission: A Challenge to Find Traces of Alien Life

A numerical method for reorientation of rotating tidally deformed viscoelastic bodies

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