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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.
Properties of planet
directly related to
what’s measured
Actual set of measurements
(e.g. gravity)
[Highly accurate, though subject
to truncation problems, e.g. finite
set ofspherical harmonics]
⇒
(e.g. density
anomalies)
[Non-unique]
Properties inferred
⇒
(e.g. temperature
anomalies)
[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:
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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.
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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 a
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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 nonhydrostatic 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.
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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 deduce the moments of
inertia of Mercury or Jupiter. These are much less direct than measurement of precession,
and the inferences depend on theoretical assumptions about the history of the body. We
will talk about these when we come to discussions of specific planets. Libration (meaning
a small oscillation back and forth away from a uniform rotation state, as measured now
for Mercury and expected for Europa) can also give important information, especially for
the fluidity of the interior.
10.2.4 Seismicity and Seismology (broadly defined)
The sources of wave generation tell you about the dynamics of the planet (e.g. plate
tectonics, volcanic events, turbulent excitation in giant planets, etc.) The propagation
characteristics of these waves can be inverted to infer planetary structure (e.g. sound
speed as a function of depth or even as a function of latitude and longitude on a constant
pressure surface, as in seismic tomography). In practice this has not yet had a major payoff except for Earth (and to a very limited extent for the Moon).
Here is the web address (still functional) for the French seismic experiment on Netlander
that was scheduled to go to Mars in about 2006 but is now cancelled. JPL also had
involvement in this.
http://ganymede.ipgp.jussieu.fr/GB/projets/netlander/sismo/
Seismic network experiments for Mars and the Moon might take place in a decade or so.
There are no current pans for Venus.
10.2.5 Heat Flow
This is essential for characterizing the internal state (thermal structure) of a planet. Most
bodies have their outgoing radiation dominated by absorbed sunlight, making the
determination of heat flow difficult by remote means. The exceptions are the giant
planets, which are distant enough and energetic enough to have a measurable excess
luminosity, and Io or Enceladus, which are so energetic that you can see the IR excess
directly as hot spots on the surface. Otherwise, you need in situ measurements of surface
conductive heat flow, which have only been done for Earth and (rather poorly) for the
10. Observational Constraints on Planetary Interiors
Moon. Passive microwave
observations might detect a
subsurface that has a different
temperature from the surface
(but this has never been
successfully demonstrated
except for atmospheres).
Microwave observations can
also be used to constrain
composition.
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Figure 10.4
10.2.6 Surface Thermodynamic and Chemical State
This is very important for giant planets, where we believe the atmosphere also tells us
something about the interior. The atmosphere is actually used as a boundary condition on
interior models. On solid planets, the inferences are much less direct, but still useful (see
next item too).
10.2.7 Petrology (broadly defined)
By petrology, I mean anything at the surface or in the atmosphere that comes from inside
and can be recognized as such ... xenoliths, noble gases, etc. Yes, giant planets have
petrology! On Earth, Moon and plausibly Mars and Venus, basaltic composition is used
to constrain mantle composition, melting depth, etc.
10.2.8 Intrinsic Magnetic Field and Paleomagnetism
The magnetic field, like gravity, can be mapped externally, sometimes even at least partly
by flyby. When it is large enough and dominated by long wavelength structure (low order
harmonics), it is attributable to core dynamics and thus tells us about the deep interior of
the planet (composition, fluidity and dynamic state). The field may have time variability,
which tells us about the fluid velocities (but this has only paid off for Earth thus far).
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Figure 10.5
Above is an illustration of the kind of data obtained during the MGS mission (see
Connerney JEP, Acuna MH, Wasilewski PJ, et al.
Magnetic lineations in the ancient crust of Mars
SCIENCE 284: (5415) 794-798 APR 30 1999)
When (as in this case) the field is attributable to crustal fields, usually smaller spatial
scale than a global dipole, it may tell us about past dynamo action and can be used to
constrain geologic history. On Earth, it was essential for telling us about plate tectonics.
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On Mars it has told us about early crustal history and perhaps (according to some people)
about a plate tectonic episode. We will talk about this in more detail much later in the
course.
10.2.9 Electromagnetic Response
Electromagnetic induction is the generation of eddy currents within a planet arising from
a time-variable external field. It has told us about high temperatures (and possibly the
presence of a core) inside the Moon and about the likely presence of a salty water ocean
inside Europa and Callisto.
Figure 10.6
Here (above) is an illustration for Europa flyby 14: The data are the wiggly lines and the
various curves are models. Field amplitudes are in nanoTesla. The best fit line
corresponds to the induction response of a salty ocean. Taken from: Kivelson MG,
Khurana KK, Russell CT, et al.
Galileo magnetometer measurements: A stronger case for a subsurface ocean at Europa
SCIENCE 289: (5483) 1340-1343 AUG 25 2000
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Above, the jagged line is the data and the thick solid line is a model based on a
conducting subsurface layer (interpreted to be a salty ocean.)
Radio emission (including but not exclusively microwave) can tell us about subsurface
temperature structure. Before Galileo probe, we already knew that Jupiter’s atmosphere
was very hot deep down because of thermal radio emissions from 400K to even 700K
temperature levels.
10.2.10
Exotica (things that have not yet succeeded)
Neutrino absorption could tell us an independent average of composition (to test seismic
models).
(Anti)neutrino emission could tell us about the radioactivity content of a planet.
DC electrical fields could tell us about the toroidal magnetic field in the core. (This has
been attempted without success).
Ch. 10 Problems
10.1) (a) A spacecraft in low altitude orbit (closest approach 5000km above the cloud
tops) around Jupiter should be able to detect gravity anomalies that cause a
deviation in the spacecraft trajectory that is of the same order of magnitude as
one wavelength of the microwave link between spacecraft and Earth, during the
time that it takes to cover a significant fraction of an orbit. About what accuracy
does this imply for determination of the gravity field of Jupiter (expressed in the
form “one part in 10n” where it is your job to find n)? This should only take you
a line or two and the answer you obtain (if you do it right) is indeed the claimed
accuracy of the Juno mission currently under consideration by NASA.
(b) What might you obtain if you used a laser link instead of microwaves? (In
practice, this would be very difficult to do but theoretically possible and under
consideration).
(c) In each case, how much plasma would be needed to potentially mess up the
measurement? (Assume the plasma exerts a pressure of ρv2 on the spacecraft
where ρ is the density and v is relative velocity. Assume the spacecraft is about
the size of large SUV and but only a third of the mass.) Express your answer as
a number density assuming the plasma is mostly protons (and electrons, but they
don’t count for much mass.) Of course, a uniform plasma would provide an
effect that could be modeled and removed so it is really fluctuations that cause a
problem.
(d) In each case, what is your possible sensitivity to temperature anomalies (and
therefore density anomalies) deep inside Jupiter, assuming they have a
characteristic dimension of ~1000km? (Could you see temperature anomalies of
1K or 10K or what?) You don’t need to know the actual temperature inside
Jupiter in order to do this.
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(e) Alternatively, you could look for anomalies in the zonal flow. Jupiter’s
rotation causes a change in the gravity field at the surface of ~2% (relative to the
gravity for a spherical body) and this is assumed to arise from a uniform “rigid
body” rotation. (It’s not a rigid body, of course.) What change in gravity might
you expect if, say, 10% of the planet were rotating at a velocity that differed
from this by a mere 1 meter/sec? (This is a differential rotation, but it would be
around the same axis of rotation). This is a proposed part of the Juno mission.
10.2
(a) The Cassini spacecraft has collected data for the gravity field of Enceladus.
(Published in Science April 4, 2014). By tracking the spacecraft using Doppler,
we can detect changes in spacecraft velocity as small as 0.1mm/s. If there is a
flyby at 50km altitude with relative velocity vs ~10km/s then what is the smallest
mass anomaly on the surface that the spacecraft can detect? (Approximate as a
point mass at closest approach). If this mass anomaly were an ocean the areal
extent of Lake Superior, what depth (i.e., thickness) ocean could be detected?
(Don’t forget to take the ice-water density difference into account. The ocean is
assumed to be in place of ice).
(b) The spacecraft flew through a plume of material erupting from Enceladus. The
plume mass loss rate is (dM/dt)p ~ 1 kg/s (for one line of vents) and can be
thought of as a thin sheet of horizontal length L~100km. The plume material is
flowing at vp ~200m/s relative to Enceladus. The drag force exerted on the
spacecraft as it crosses the plume is ~ ρvs2A, for spacecraft cross sectional area A
and plume density ρ. Show that the change in velocity of the spacecraft due to the
material it encounters is of order (vs /vp ). (A/M).(dM/dt)p /L where (A/M) is the
effective cross-sectional area to mass ratio of the Cassini spacecraft (~0.3
m2 /kg). Hence demonstrate that this is sufficient to be detectable. (Note:
The result does not depend on the thickness of the plume in the direction the
spacecraft is moving, unless of course the spacecraft happened to be moving
along the 100km sheet rather than across it. ) This effect was in fact detected.