Nonhydrostatic effects and the determination of icy satellites' moment of inertia

被引:37
作者
Gao, Peter [1 ]
Stevenson, David J. [1 ]
机构
[1] CALTECH, Div Geol & Planetary Sci, Pasadena, CA 91125 USA
关键词
Callisto; Enceladus; Ganymede; Interiors; GRAVITY-FIELD; GALILEAN SATELLITES; INTERNAL STRUCTURE; MASS ANOMALIES; CALLISTO; GANYMEDE; INTERIOR; PLANETS; MODELS; TITAN;
D O I
10.1016/j.icarus.2013.07.034
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We compare the moment of inertia (MOI) of a simple hydrostatic, two layer body as determined by the Radau-Darwin Approximation (RDA) to its exact hydrostatic MOI calculated to first order in the parameter q = Omega R-2(3)/GM, where Omega, R, and M are the spin angular velocity, radius, and mass of the body, and G is the gravitational constant. We show that the RDA is in error by less than 1% for many configurations of core sizes and layer densities congruent with those of solid bodies in the Solar System. We then determine the error in the MOI of icy satellites calculated with the RDA due to nonhydrostatic effects by using a simple model in which the core and outer shell have slight degree 2 distortions away from their expected hydrostatic shapes. Since the hydrostatic shape has an associated stress of order rho Omega R-2(2) (where rho is density) it follows that the importance of nonhydrostatic effects scales with the dimensionless number sigma/rho Omega R-2(2) , where sigma is the nonhydrostatic stress. This highlights the likely importance of this error for slowly rotating bodies (e.g., Titan and Callisto) and small bodies (e.g., Saturn moons other than Titan). We apply this model to Titan, Callisto, and Enceladus and find that the RDA-derived MOI can be 10% greater than the actual MOI for nonhydrostatic stresses as small as similar to 0.1 bars at the surface or similar to 1 bar at the coremantle boundary, but the actual nonhydrostatic stresses for a given shape change depends on the specifics of the interior model. When we apply this model to Ganymede we find that the stresses necessary to produce the same MOI errors as on Titan, Callisto, and Enceladus are an order of magnitude greater due to its faster rotation, so Ganymede may be the only instance where RDA is reliable. We argue that if satellites can reorient to the lowest energy state then RDA will always give an overestimate of the true MOI. Observations have Shown that small nonhydrostatic gravity anomalies exist on Ganymede and Titan, at least at degree 3 and presumably higher. If these anomalies are indicative of the nonhydrostatic anomalies at degree 2 then these imply only a small correction to the MOI, even for Titan, but it is possible that the physical origin of nonhydrostatic degree 2 effects is different from the higher order terms. We conclude that nonhydrostatic effects could be present to an extent that allows Callisto and Titan to be fully differentiated. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:1185 / 1191
页数:7
相关论文
共 29 条
  • [11] Gravity field and interior of Rhea from Cassini data analysis
    Iess, Luciano
    Rappaport, Nicole J.
    Tortora, Paolo
    Lunine, Jonathan
    Armstrong, John W.
    Asmar, Sami W.
    SomenZi, Lucia
    Zingoni, Francesco
    [J]. ICARUS, 2007, 190 (02) : 585 - 593
  • [12] Gravity Field, Shape, and Moment of Inertia of Titan
    Iess, Luciano
    Rappaport, Nicole J.
    Jacobson, Robert A.
    Racioppa, Paolo
    Stevenson, David J.
    Tortora, Paolo
    Armstrong, John W.
    Asmar, Sami W.
    [J]. SCIENCE, 2010, 327 (5971) : 1367 - 1369
  • [13] The gravity field of the Saturnian system from satellite observations and spacecraft tracking data
    Jacobson, R. A.
    Antreasian, P. G.
    Bordi, J. J.
    Criddle, K. E.
    Ionasescu, R.
    Jones, J. B.
    Mackenzie, R. A.
    Meek, M. C.
    Parcher, D.
    Pelletier, F. J.
    Owen, W. M., Jr.
    Roth, D. C.
    Roundhill, I. M.
    Stauch, J. R.
    [J]. ASTRONOMICAL JOURNAL, 2006, 132 (06) : 2520 - 2526
  • [14] Shapes of two-layer models of rotating planets
    Kong, D.
    Zhang, K.
    Schubert, G.
    [J]. JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS, 2010, 115
  • [15] THE LUNAR FOSSIL BULGE HYPOTHESIS REVISITED
    LAMBECK, K
    PULLAN, S
    [J]. PHYSICS OF THE EARTH AND PLANETARY INTERIORS, 1980, 22 (01) : 29 - 35
  • [16] Mystery of Callisto: Is it undifferentiated?
    McKinnon, WB
    [J]. ICARUS, 1997, 130 (02) : 540 - 543
  • [17] On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto
    McKinnon, William B.
    [J]. ICARUS, 2006, 183 (02) : 435 - 450
  • [18] Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites
    Mosqueira, I
    Estrada, PR
    [J]. ICARUS, 2003, 163 (01) : 198 - 231
  • [19] 3-LAYERED MODELS OF GANYMEDE AND CALLISTO - COMPOSITIONS, STRUCTURES, AND ASPECTS OF EVOLUTION
    MUELLER, S
    MCKINNON, WB
    [J]. ICARUS, 1988, 76 (03) : 437 - 464
  • [20] Murray C.D. Dermott., 2000, Solar System Dynamics