10. Observational Constraints on Planetary Interiors 107 10 Observational Constraints on Planetary Interiors 10.1 How Can External Measurements tell us about what’s Inside? This is the central issue of inversion theory. Typically, we are looking at something that emanates from inside (e.g. gravity field of some anomalous structure, magnetic field from a core) or at the response of the structure to some perturbation (e.g. propagation of seismic waves, changes in length of day due to tides). In all cases, the information obtained is not point by point, but some kind of average or some “moment” of the body. For example, the moment of inertia of a body is not a point by point description of the density structure but a particular kind of average. In a few cases, most notably in seismology, a well posed inversion may exist (though even then there are caveats). In most cases, the “inversion” is highly non-unique, even when the quantity being inverted is precisely related to what is being measured (e.g., the size of a density anomaly responsible for a gravity anomaly). The non-uniqueness is even greater if one goes the next step to temperature or composition or whatever. Actual set of measurements Properties of planet directly related to what’s measured Properties inferred (e.g. gravity) ⇒ (e.g. density anomalies) ⇒ (e.g. temperature anomalies) [Highly accurate, though subject to truncation problems, e.g. finite set ofspherical harmonics] [Non-unique] [Very non-unique] The best inversion work makes use of physical constraints and multiple (unrelated) data sets rather than treating the problem as merely a mathematical challenge. (Here, I’m expressing a philosophical bias!) 10.2 The Kinds of Data We Can Use 10.2.1 Gravity Planetary gravity fields can be measured to exquisite accuracy by spacecraft. This is done by detecting the Doppler shift on the communication (tracking) signals sent by the spacecraft to Earth. Here’s an example from the Galileo mission:10. Observational Constraints on Planetary Interiors 108 Figure 10.1 In this example, there is a velocity change of order (3 x 105 km/sec).(3 x103Hz)/(1010Hz) ~ 100 m/sec, about what you’d expect for a fast flyby of a body that has an escape velocity of ~2km/sec. But the very precise details of the curve contain more information than merely the mass of Europa. There are three rather distinct pieces that make up the observed gravity field: (i) The dominant term is indistinguishable from that due to a point mass. This tells us the planetary mass, from which we can get mean density, an essential parameter constraining composition. (ii) In most cases (excluding only very slowly rotating bodies), the next largest effect is the response of the planet to it’s own rotation. Subject to some caveats about the validity of hydrostatic equilibrium, this tells us moment of inertia of the planet, and sometimes (with giant planets) even higher moments of the mass distribution.10. Observational Constraints on Planetary Interiors 109 In the case of synchronously rotating satellites (e.g., the Galilean satellites, and Titan), the permanent tidal bulge and its associated gravity is of the same order of magnitude as the rotational response. (The tidal response is actually three times larger than the rotational response but in the form of a prolate deformation along the line to the planet.) (iii) Smaller terms, including non-axisymmetric terms, tell us about the dynamic structure of the planet... convection or zonal flows. Lithospheric structure (the ability of the planet to support loads) or crustal structure (thickness from place to place) are also constrained (using topography as well); in a sense these are also part of the dynamics of a planet. 10.2.2 Topography This can be measured by altimetry(solid planets) or occultation (gaseous planets). Altimetry is often done with a laser (e.g. the MOLA experiment on MGS, the spacecraft orbiting Mars). It can also be done with radar. Occultation can be done with a spacecraft or with natural sources (i.e. stars being occulted by a planet). Here is a schematic of how MOLA works. The pulse length is ~8 nanoseconds. Figure 10.2 Topography can be measured by altimetry (solid planets) or occultation (gaseous planets). Altimetry is often done with a laser (e.g. the MOLA experiment on MGS, the spacecraft orbiting Mars). It can also be done with radar. Cassini is providing some altimetry data for Titan (mostly not published yet). Occultation can be done with a10. Observational Constraints on Planetary Interiors 110 spacecraft or with natural sources (i.e. stars being occulted by a planet). Above is a schematic of how MOLA works. The pulse length is ~8 nanoseconds. Shown below is a typical result from MOLA. Figure 10.3 Topography is a natural complement to gravity studies. In a purely hydrostatic system, it is overdetermined because then the physical surface will be exactly coincident with a surface of constant gravitational potential (i.e. topography is determined by gravity and vice-versa). In that case (really only relevant to gaseous planets) no new information emerges but you can test whether hydrostaticity was a correct assumption. In the non-hydrostatic case, topography can tell you about the mantle and lithosphere. Of course, topography (in the sense of an image, radar or visual, or in the sense of a hypsometric map) can also tell you about tectonic and volcanic processes.10. Observational Constraints on Planetary Interiors 111 10.2.3 Rotational State and Tidal Response The response of a planet to external forces or torques or to angular momentum redistribution among internal reservoirs (core and mantle, mantle and atmosphere/ocean) can tell you about the moment of inertia, the fluidity or otherwise of a core, etc. Examples include: Forced precession of a planet (which is part of the method used to get the moment of inertia of Earth, Moon and Mars), and amplitude of the daily solid body tide (essential for deciding whether Europa has an ocean). Tidal response may also tell you the anelasticity (the Q) of the body, which is related to the viscosity, etc. This can come from observing the out of phase component of the response or from observing the consequences of net torque (as in the movement of Moon away from Earth). The obliquity of a planet is affected by external torques whose strength depends on the planet moment of inertia. As a consequence, it may be possible to