Speed of sound in outer planet atmospheres

\ Planetary and Space Science 36 "0888# 56Ð66

PERGAMON Speed of sound in outer planet atmospheres

Ralph D[ Lorenz

Lunar and Planetary Laboratory\ University of Arizona\ Tucson AZ 74610Ð9981\ U[S[A[
Received 2 March 0887^ received in revised form 3 August 0887^ accepted 5 September 0887

Abstract

I compute speed of sound pro_les for the four giant planets using simple atmosphere models\ and explore the e}ect on the pro_les
of ortho ] para hydrogen conversion\ and the drop in mixing ratio of condensible species at the tropopause[ The speed of sound is in
general somewhat lower "principally due to lower temperature and higher relative molecular mass# in Uranus and Neptune than in
Saturn and Jupiter[ Furthermore\ the two outer planets show dramatic "½09)# changes in sound speed due to the condensation of
methane\ suggesting that sound speed measurement on a probe is a useful diagnostic of vertical structure[ Sound Speed measurements
for Jupiter and Saturn need to be made with much higher accuracy "½9[91) for Jupiter and 9[0) for Saturn# to usefully constrain
structure and transport[ Some instrumental considerations are discussed[ Þ 0888 Elsevier Science Ltd[ All rights reserved[

0[ Introduction "{acoustic pyrometry|# is given by Kleppe "0885#[ Third\
the transit time of an acoustic wave across wide spans of
The speed of sound is a common diagnostic for tem! ocean provides information on the ocean temperature
perature in terrestrial science\ and has been long proposed over vast "×0999 km wide# regions that would otherwise
for measurement in planetary atmospheres\ as a diag! be di.cult to reach\ "e[g[\ Spiesberger and Tappert\ 0885#[
nostic for composition\ temperature and hydrogen trans! Fourth\ the speed of sound is an easy laboratory par!
port[ In this paper I review the concepts and instruments ameter to measure\ and can be used to determine ther!
to date\ and investigate by means of model atmospheres modynamic properties and equations of state "e[g[\
what speed of sound measurements might tell us about Estrada!Alexanders et al[\ 0883#[ Finally\ SODAR
the atmospheres of the outer planets\ and how accurately "Sound Detection And Ranging# methods are used in
the speed of sound and supporting measurements have boundary layer research] sound pulses are transmitted
to be made in order to usefully constrain models[ upwards from the ground and echoes from clouds and:or
temperature discontinuities sensed by their echo[ The
1[ Review re~ection of sound from clear!air inhomogeneities was
noted by Tyndall over the English channel "his 0785 book
Terrestrial measurements of the speed of sound are is still a very readable and worthwhile reference#*useful
employed in _ve notable areas[ First is to measure air modern reviews are given by Ne} and Coulter "0875# and
temperature in micrometeorological applications*a sig! Weill and Lehmann "0889#[
ni_cant advantage is that the temperature of the air is
sensed directly enabling measurements over very short In these applications\ the composition of the medium
temporal and spatial scales\ not limited by the thermal "and hence its relative molecular mass and speci_c heat#
time constant of a sensor[ Second\ acoustic thermometry is either known or assumed\ so that the sound speed
is widely employed in industrial applications\ such as to relates directly to temperature[ For planetary appli!
measure the temperature of ~ue gasses from burners^ the cations\ although temperature can be constrained by the
high temperature and particulate loading of these gas measurement of sound speed\ it is generally more useful
streams poses a signi_cant reliability and lifetime penalty to determine temperature separately and thence constrain
on sensors placed in them[ A review of the technique the medium properties[

Tel[] ¦0 419 510 4474^ fax] ¦0 419 510 3822^ e!mail] rlorenzÝlpl[ Acoustic measurements for spacecraft were proposed
arizona[edu as early as 0855 "Hanel and Strange\ 0855#\ before in!situ
planetary measurements of any kind had been made[
Their concept was to measure the sound speed in a tem!
perature!controlled spiral duct\ thus constraining the
relative molecular mass and speci_c heat[ The application

9921Ð9522:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved[
PII] S 9 9 2 1 Ð 9 5 2 2 " 8 7 # 9 9 9 8 8 Ð 2

57 R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66

in mind was to resolve the relative abundances of CO1\ where g is the ratio of speci_c heats\ T is the temperature
N1 and Ar in the then!unknown Martian atmosphere[ in Kelvin\ R9 is the universal gas constant "7203 J K−0
mol−0#[ M is the mean relative molecular mass "RMM# of
Acoustic sensors have been ~own on Soviet Venus the gas mixture\ the sum of the RMMs of the component
landers\ although with the intent of detecting acoustic gasses Mi\ weighted by their mole fraction Xi[
emission due to thunder[ Although events were detected
"Ksanfomality et al[\ 0872a# it is unclear whether these Note that the ratio of speci_c heats is weighted by
were indeed due to thunder\ or merely aeroacoustic noise the mass fractions of the components\ rather than their
caused by the turbulent air~ow over the probe "both mixing ratio[ As discussed in Hanel and Strange "0855#\
sources peak at frequencies of a few Hertz#[ Data from this makes the lines of varying composition on a plot of
these sensors was used\ on the surface\ to constrain the g vs M curved\ rather than straight[
surface windspeeds "Ksanfomality et al[\ 0872b#[
On Titan\ where the nitrogen!dominated atmosphere
More recently\ the _rst outer planet acoustic measure! approaches its condensation temperature and com!
ment has been sent on its way[ The Surface Science Pack! pressibility e}ects become signi_cant "e[g[\ Lindal et al[\
age "SSP# on the ESA Huygens probe to Titan includes 0872#\ the ideal gas formula may not be strictly appli!
"Zarnecki et al[\ 0886# an acoustic sounder[ This device\ cable[ However\ in the atmosphere of the outer planets\
acting as a SODAR "Sonic Detection and Ranging# will dominated by hydrogen and helium\ the ideal gas law is
measure topographic roughness at the landing site prior su.ciently accurate for the regions of interest\ despite the
to impact\ in the same way as a radar altimeter[ Addition! cold temperatures[ Chapter 4 of Lewis "0884# discusses
ally\ it will also constrain the depth of any liquid hydro! nonidealities at great depths in the Jovian planets\ but
carbon deposit the probe might land in by sensing an echo these are at too high pressure and temperatures to be
from the bottom\ and possibly detect acoustic backscatter relevant for measurement by spacecraft\ the subject of
from raindrops during the descent[ The package also the present paper[
includes a speed of sound instrument\ to constrain the
composition of surface liquid and facilitate the measure! An additional factor\ beyond the molecular compo!
ment of lake depth[ This sensor will also operate in the sition\ is the spin state of hydrogen molecules "See\ e[g[\
atmosphere\ sampling every 09 m altitude or so*a better Massie and Hunten\ 0871\ and Appendix VIII of
altitude resolution than the temperature sensors of the Chamberlain and Hunten\ 0876#[ The two spin states\
Huygens Atmospheric Structure Instrument "{HASI|\ ortho and para\ have signi_cantly di}erent speci_c heats
Fulchignoni et al[\ 0886#[ The combination of the HASI at constant pressure and hence ratios of speci_c heats]
temperature measurement and the SSP speed of sound see Fig[ 0[ The two states have an equilibrium ratio that
may provide useful information on the altitude variation depends on temperature\ see Fig[ 1[ In the high tem!
of the methane mixing ratio "via its e}ect on the relative perature limit\ the fraction of hydrogen fp in the para
molecular mass#\ which varies from around 7) near the form is 14)^ at temperatures below 099 K "and thus
surface to about 1) at the tropopause\ e[g[\ Yelle et al[ relevant to the tropopause regions in the outer planet
"0886#[ atmospheres#\ the para fraction rises above 49)[ Because
hydrogen is the dominant constituent\ this otherwise
In this paper\ I consider what might be learned from a obscure physical e}ect assumes considerable importance\
speed of sound measurement in the outer planets[ The and can modify the lapse rate measurably "Massie and
present NASA Planetary Exploration Roadmap includes Hunten\ 0871#\ and substantially in~uence convective
plans for a Jupiter multiprobe mission and a Neptune processes "Conrath and Gierasch\ 0873^ Smith and Gier!
orbiter "which might include an atmosphere probe#[ asch\ 0884#[
Additionally\ now that Cassini is safely on its way and
could conceivably provide a relay capability for a fast! 3[ Model atmospheres and speeds of sound
track Discovery!class Saturn probe mission in the latter
half of the next decade\ it is appropriate to consider that Model atmospheres for the four outer planets have
body too[ Uranus is considered also\ for completeness[ I been constructed to determine speed of sound pro_les[
defer discussion of Titan\ from which sound speed These models are not especially rigorous\ and include
measurements may be expected in 1993\ to a future paper[ only one condensible constituent for simplicity\ but do
serve to show the di}erent regimes in the four planets\
2[ Speed of sound*a diagnostic of composition and and how the sound speed is related to the ortho ] para
transport hydrogen and the mixing ratio pro_le of the condensible
species[
The sound speed in an ideal gas may be given by "e[g[\
Rogers and Mayhew 0856^ Hanel and Strange\ 0855# Data for the pressure ] temperature pro_les was
obtained from Sei} et al[ "0886#\ Ingersoll et al[ "0873#\
c zgTR9:M Conrath et al[ "0880# and Gautier et al[ "0884#\ for Jupiter\
Saturn\ Uranus and Neptune\ respectively[ A point in the

R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66 58

Fig[ 0[ The speci_c heats at constant pressure "cp# of para and ortho hydrogen\ also as a function of temperature[

Fig[ 1[ The equilibrium para hydrogen fraction as a function of temperature "e[g[\ Massie and Hunten\ 0871#[

69 R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66

Fig[ 2[ Model Pressure!Temperature pro_les for the four outer planets\ generated as described in the text[

pressure ] temperature pro_le is selected "Pad\ Tad# below saturation curve until the minimum temperature "cold
which a simple lapse rate L describes the pro_le[ trap# is reached\ and then held constant at that value[
While the pro_les thus generated "Fig[ 3# do not take into
Above "Pad\ Tad# the temperature versus altitude is account e[g[ meteoric delivery or photochemical destruc!
describe by a polynomial in altitude "z\ km#\ T"z# Ta! tion at high altitude\ they are adequate for the present
d−Lz¦k0z0[4¦k1z1\ with k0 and k1 tuned so that the purpose[
resultant P:T pro_le agrees with those in the references
above[ The pro_les are indicated in Fig[ 2\ and the par! If there were no vertical transport in the atmosphere\
ameters used are listed in Table 0[ the ortho ] para hydrogen ratio would be expected to
follow the temperature dependence in Fig[ 1 "from Massie
The condensible species is assumed to have some _xed and Hunten\ 0871#[ This yields the equilibrium pro_les
abundance at depth^ this mixing ratio is held constant in Fig[ 4[ On the other hand\ if gas has recently upwelled
up through lower and lower pressures until the species from the warm interior "where the equilibrium para frac!
becomes saturated "I use the saturation vapor pressure tion is 9[14# the {Normal| pro_le "the thick line in Fig[ 4#
relations from Reynolds "0868## and is then held to the would result[ In reality\ the pro_les will lie between these
curves\ depending how vigorous the vertical motions are\
Table 0 and how e.cient aerosols are at catalysing rapid re!
Parameters used to generate model atmospheres equilibration[ Chamberlain and Hunten "0876# suggest
typical timescales of weeks to years for equilibration to
Parameter Jupiter Saturn Uranus Neptune occur\ with the timescale determined mainly by the pres!
ence of paramagnetic catalysts[ In a laboratory or indus!
Gravity "ms−1# 13[8 09[3 09[3 02[7 trial setting\ the walls of the reaction vessel are the
1[2 1[02 1[2 1[7 catalyst] in a planetary atmosphere\ aerosols are the most
M 0[7 9[63 9[76 0[1 likely candidate "molecular oxygen\ being paramagnetic\
Lapse "Kkm−0# 1[9 0[9 0[9 0[9 can also accelerate equilibration\ but is not abundant
019 64 in the highly reducing outer planet atmospheres#[ These
Pad "bar# 079 9[91 9[902 69 aspects are explored in some detail in Massie and Hunten
Tad "K# 9[95 1E!2 7E!2 9[07 "0871#[
k0 "Kkm−0[4# 9[95 9[04 8E!3
k1 "Kkm−1# 4E!2 NH2 CH3 9[08 Using these model atmospheres\ I compute the speed
XHe 9[025 1E!3 9[91 CH3 of sound for two pro_les of the ortho ] para ratio] one
9[914
Condensible H1O
3E!3
Deep abundance

R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66 60

Fig[ 3[ Mixing ratio pro_les of the condensible species[ In the Jovian atmosphere the condensible "water# is too scarce here to have an appreciable
e}ect[ In Saturn|s case the e}ect is marginal\ while for both Uranus and Neptune the condensible is present at a few percent[ The mixing ratios fall
o} at the coldtrap of each planet[

according to the equilibrium pro_les in Fig[ 4\ and the follow the temperature pro_les fairly closely[ Figures 6Ð
other with a _xed normal value of 2 "para 09 zoom in on areas of particular interest\ where the
fraction 9[14#^ for each of these cases the condensible e}ects of condensation and ortho ] para conversion are
species is held to the pro_les in Fig[ 3\ or at a constant manifest in the sound pro_les] each case is discussed
deep abundance[ separately below[

For convenience\ P"z# is computed assuming hydro! A straightforward error analysis indicates that uncer!
static equilibrium using the {deep| composition through! tainties on the speed of sound propagate quadratically
out^ the role of the condensible in a}ecting the P:T pro_le into uncertainty in M and g[ Thus to detect the few )
through altitude!dependent relative molecular mass is change in speci_c heat due to ortho!para conversion in
neglected in this study[ Furthermore\ the e}ects of noble the Jovian atmosphere requires that the sound speed to
gasses and non!condensing constituents "e[g[\ the ½1) be measured to a fraction of a percent[
of methane in the Saturnian atmosphere# is ignored*in
principle therefore the absolute values of sound speed Also\ in this same example\ uncertainty in composition
shown in Figs 5Ð09 could be o}set by several percent "and hence assumed M# is commensurate with the result!
from their true values\ but the shapes are the subject of ant uncertainty in g[ For Jupiter\ this is less of a concern\
interest here[ Similarly\ although such e}ects may be in that the hydrogen ] helium ratio is well!determined
signi_cant\ the in~uence of ortho ] para hydrogen con! "Von Zahn and Hunten\ 0885# and all other constituents
version on the lapse rate is ignored[ For simplicity\ the are present at levels below 9[4) "Niemann et al[\ 0885#[
ratio of speci_c heats for the condensible constituent is In the other planets\ however\ tropospheric mixing ratios
assumed to be constant with temperature\ and a value of of methane and ammonia are rather higher\ yet fall across
0[2 was assumed for all condensible species[ cold!traps where clouds form[ In these cases\ the speed
of sound curves show a sharp change in slope[
4[ Results and required accuracies
The speed of sound measurement for Jupiter would
The sound speeds for the four atmospheres are shown have to be better than 9[1) accurate to detect either the
in Fig[ 5^ as might be expected the shape of the curves onset below some altitude of a water abundance equal to
that measured by Galileo "although wetter regions on
Jupiter may be rather easier to detect#\ or the e}ect of

61 R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66

Fig[ 4[ Para hydrogen fraction pro_les[ The thin lines correspond to local equilibrium "the temperature pro_le is operated on by the function in
Fig[ 0#[ The thick line indicates the {Normal| "high temperature equilibrium# value\ that might be expected if upwelling from the interior were
rapid[

para hydrogen "Fig[ 6#[ For a useful measurement "rather 5[ Instrumental considerations
than a mere detection#\ an accuracy of perhaps 09 times
better is needed\ so Jupiter seems per se a marginal pros! The speed of sound measurement advocated by Hanel
pect for this technique[ and Strange "0855# used the phase di}erence between a
number of transducers in a temperature!controlled spiral
For Saturn\ again the condensible detection is some! duct[ While suitable for a _xed in!situ measurement with
what marginal owing to the relatively low abundance[ plenty of time to equilibrate\ such a technique may be
The e}ect of ortho ] para conversion is about 9[4)\ so a di.cult for a probe plummeting through an atmosphere
sensor with a resolution of 9[4Ð0 ms−0\ or 0 part in 0999\ with strong vertical variation in temperature] the heaters
could make a useful contribution "Fig[ 7#[ in the duct would have to compensate for a rapidly!
changing gas temperature] naturally\ most information
The technique really comes into its own for the two on the external gas temperature is lost[ However\ if the
outermost giant planets\ which have both higher con! temperature!regulation challenges could be overcome\
densible abundance\ and lower temperatures "hence phase di}erence measurements o}er intrinsically high
higher equilibrium para hydrogen fractions#[ Detection accuracy[
of layers where the equilibrium para hydrogen fraction
is attained above layers where it is closer to the high! The time!of!~ight measurement may be a viable alter!
temperature value might indicate aerosol or cloud layers[ native\ and is the technique implemented on the Huygens
Models might be able to reconstruct the vertical mixing SSP instrument "Zarnecki et al[\ 0886#[ Time is one of the
rate from the observed para hydrogen ratio\ if the recom! simplest things to measure in an instrument^ the measure!
bination rate can be adequately constrained[ ment uncertainty is therefore dominated by the uncer!
tainty in the pathlength[ This might be ameliorated either
The musically!inclined reader might note that the by sti} construction and:or measuring in real time "per!
change in sound speed due to the change in methane haps by optical means# the pathlength[ As on SSP\ the
abundance across the Neptune cold trap would change propagation time in both directions should be measured
the note of a whistle "say\ an F at 249 Hz# to an F!sharp
"Fè\ at 269 Hz#[

R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66 62

Fig[ 5[ Speed of sound pro_le for the four planets\ assuming equilibrium para hydrogen fraction\ and variable condensible abundance[ The kinks in
the curves are due to the sharp change in mixing ratio of condensible species[

to eliminate the e}ects of air~ow "indeed\ the di}erence poorer[ The frequency of operation might be chosen to
in sound speeds along and against the vehicle|s direction maximize the signal to noise "higher frequencies are atten!
of descent might place a useful independent constraint uated more strongly*probably not an important issue
on the probe descent velocity#[ for such short pathlengths*while lower frequencies
su}er more aeroacoustic noise#[
Resonant!cavity methods "i[e[\ whistles#\ alluded to
frivolously in the previous section\ might in fact make a The speed of sound measurement in itself can provide
viable sound speed sensor[ Measuring the frequency of a useful constraints on transport and condensation[ It is
whistle excited by the draught of the probe|s descent likely to be more valuable yet combined with other
would again be straightforward[ Turbulence may be an measurements] condensation might be indicated via the
accuracy!limiting factor for all techniques\ and adequate lapse rate\ and optical extinction measured by a radi!
gas ~ow needs to be ensured so that the instrument tracks ometer\ or by SODAR\ detecting backscatter from rain!
external composition variations adequately[ drops[ Frequency!dependent backscatter would allow the
dropsize distribution to be constrained[
An experimental programme would probably be
required to determine the most accurate sensors\ and All the interpretations of sound speed described in
their range of operation[ The high pressure limit is prob! this paper require that the gas temperature be known
ably driven by the probe itself^ the temperatures beyond accurately[
which transducers cannot operate are very high "cf their
use in exhaust gas measurement#[ Piezoelectric trans! 6[ Conclusions
ducers would be ultimately limited by their Curie tem!
perature "where they become depolarized\ typically a few The models outlined in this paper\ while neither rig!
hundred degrees Centigrade#\ although this is not likely orous nor complete\ describe the vertical variation of
to be a signi_cant limitation except for very deep "099 sound speed within each atmosphere[ It is found that
bar¦# probes[ variations in sound speed are a very accessible diagnostic
of the relative molecular mass and ortho ] para hydrogen
The low pressure limit will be determined by sig! ratio in the atmospheres of Uranus and Neptune\ but
nal ] noise considerations] at lower pressure the coupling
of the atmosphere to the transducer becomes poorer and

63 R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66

Fig[ 6"a#[ Detail of the speed of sound pro_le for Jupiter\ over the 9[1Ð1 bar range[ The curves for di}erent cases of condensible mixing ratio cannot
be discriminated "above the cold trap the water abundance is too small#\ but the non!equilibrium ortho ] para ratio causes a di}erence of ½1 ms−0
from the equilibrated cases^ "b# detail of the speed of sound pro_le in the 4Ð09 bar range[ The deep abundance of water makes a ½1 ms−0 di}erence
in sound speed[

R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66 64

Fig[ 7"a#[ Detail of the speed of sound pro_le for Saturn\ over the 9[1Ð0 bar range[ The curves for di}erent cases of condensible mixing ratio cannot
be discriminated "above the cold trap the ammonia abundance is too small#\ but the non!equilibrium ortho ] para ratio causes a di}erence of ½4
ms−0 from the equilibrated cases^ "b# detail of the speed of sound pro_le in the 4Ð09 bar range[ The deep abundance of ammonia makes a ½1 ms−0
di}erence in sound speed[

65 R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66

Fig[ 8[ Detail of the speed of sound pro_le for Uranus\ over the 9[1Ð1 bar range[ The very low temperatures allow a large para hydrogen fraction\
and even at the cold trap the methane abundance is signi_cant\ so all the curves are separate[ The in~uence of condensation on the sound speed "via
RMM# is striking[

Fig[ 09[ Detail of the speed of sound pro_le for Neptune\ over the 9[0Ð1 bar range[ The methane mixing ratio pro_le again makes a di}erence of
some 39 ms−0 below 1 bar[ Above about 9[7 bar\ the e}ects of the methane mixing ratio and the ortho ] para ratio are approximately equal\ so the
dashed and dotted curves merge[

R[D[ Lorenz : Planetary and Space Science 36 "0888# 56Ð66 66

challenge available instrumental accuracies for Jupiter[ Cosmic Research 10\ 050Ð056 "translated from Kosmicheskii Issle!
Saturn is a marginal prospect*with modest technical dovania 10\ 107Ð113[
e}ort a suitable instrument could be constructed[ Lewis\ J[S[\ 0884[ Physics and Chemistry of the Solar System[ Academic
Press\ San Diego[
Given the modest mass\ power and data requirements Lindal\ G[ F[\ Wood\ G[ E[\ Hotz\ H[ B[\ Sweetnam\ D[ N[\ Eshleman\
of a speed of sound sensor\ it may be a valuable and cost! V[ R[ and Tyler\ G[ L[\ 0872[ The atmosphere of Titan*an analysis
e}ective complement to other instrumentation on future of the Voyager 0 radio occulation measurements[ Icarus 42\ 237Ð
outer planet probes[ 252[
Massie\ S[T[\ Hunten\ D[M[\ 0871[ Conversion of para and ortho hydro!
References gen in the Jovian planets[ Icarus 38\ 102Ð115[
Ne}\ W[D[\ Coulter\ R[L[\ 0875[ Acoustic remote sensing[ In]
Chamberlain\ J[W[\ Hunten\ D[M[\ 0876[ Theory of Planetary Atmo! Lenschow\ D[H[\ "Ed[#\ Probing the Atmospheric Boundary Layer[
spheres\ 1nd ed[ Academic Press\ San Diego[ American Meteorological Society\ Boston\ pp[ 190Ð127[
Niemann\ H[B[\ Atreya\ S[K[\ Carignan\ G[R[\ Donahue\ T[M[\ Hab!
Conrath\ B[J[\ Gierasch\ P[J[\ 0873[ Global variation of the para hydro! erman\ J[A[\ Harpold\ D[N[\ Hartle\ R[E[\ Hunten\ D[M[\ Kasprzak\
gen fraction in Jupiter|s atmosphere and implications for dynamics W[T[\ Maha}y\ P[R[\ Owen\ T[C[\ Spenser\ N[W[\ Way\ S[H[\ 0885[
on the outer planets[ Icarus 46\ 073Ð193[ The Galileo probe mass spectrometer] Composition of Jupiter|s
atmosphere\ Science 161\ 735Ð738[
Conrath\ B[J[\ Pearl\ J[C[\ Appleby\ J[F[\ Lindal\ G[F[\ Orton\ G[S[\ Prinn\ R[G[\ Larson\ H[P[\ Caldwell\ J[J[\ Gautier\ D[ 0873[ Com!
Bezard\ B[\ 0880[ Thermal structure and energy balance of Uranus[ position and chemistry of Saturn|s atmosphere[ In] Gehrels\ T[\ Mat!
In] Bergstrahl\ J[T[\ Miner\ E[D[\ Matthews\ M[S[ "Eds#\ Uranus[ thews\ M[S[\ "Eds#\ Saturn[ University of Arizona Press\ Tucson[ pp[
University of Arizona Press\ Tucson[ pp[ 193Ð141[ 77Ð038[
Reynolds\ W[C[\ Thermodynamic Properties in SI[ Stanford University\
Estrada!Alexanders\ A[F[\ Trusler\ J[P[M[\ Zarari\ M[P[\ 0884[ Deter! 0868[
mination of thermodynamic properties from the speed of sound[ Rogers\ G[F[C[\ Mayhew\ Y[C[ Engineering Thermodynamics] Work
International Journal of Thermophysics 05\ 552Ð562[ and Heat Transfer\ Longman\ London\ 0856[
Sei}\ A[\ Kirk\ D[B[\ Knight\ T[C[D[\ Mihalov\ J[D[\ Blanchard\ R[C[\
Fegley\ B[ Jr[\ Gautier\ D[\ Owen\ T[\ Prinn\ R[G[\ Spectroscopy and Young\ R[E[\ Schubert\ G[\ von Zahn\ U[\ Lehmacher\ G[\ Milos\
chemistry of the atmosphere of Uranus[ In] Bergstrahl\ J[T[\ Miner\ F[S[\ Wang\ J[\ 0885[ Structure of the atmosphere of Jupiter] Galileo
E[D[\ Matthews\ M[S[\ "Eds#\ Uranus[ University of Arizona Press\ Probe measurements[ Science 161\ 738Ð740[
Tucson[ pp[ 036Ð192[ Smith\ M[D[\ Gierasch\ P[J[\ 0884[ Convection in the outer planet
atmospheres including orth!para hydrogen conversion[ Icarus 005\
Fulchignoni\ M[\ Angrilli\ F[ Bianchini\ G[\ Bar!Nun\ A[\ Barucci\ M[\ 048Ð068[
Borucki\ W[\ Coradini\ M[\ Coustenis\ A[\ Ferri\ F[\ Grard\ R[ J[\ Spiesberger\ J[L[\ Tappert\ F[D[\ 0885[ Kaneohe acoustic thermometer
Hamelin\ M[\ Harri\ A[M[\ Leppelmeier\ G[W[\ JLopez!Moreno J[\ further validated with rays over 2699 km and the demise of the
McDonnell\ J[A[M[\ McKay\ C[\ Neubauer\ F[M[\ Pedersen\ A[\ idea of axially trapped energy[ Journal of the Acoustical Society of
Picardi\ G[\ Pirronello\ V[\ Pirjola\ R[\ Rodrigo\ R[\ Schwingenschuh\ America 88\ 062Ð073[
C[\ Sei}\ A[\ Svedhem\ H[\ Thrane\ E[\ Vanzani\ V[\ Visconti\ G[\ Tyndall\ J[ Sound[ Appleton\ New York\ 0785[
Zarnecki\ J[\ 0886[ The Huygens atmospheric structure instrument Von Zahn\ U[\ Hunten\ D[M[\ 0885[ The helium mass fraction in Jup!
"HASI#[ In] Wilson\ A[\ "Ed[#\ Huygens] Science\ Payload and iter|s atmosphere[ Science 161\ 738Ð740[
Mission[ ESA SP!0066\ European Space Agency\ Noordwijk\ The Weill\ A[\ Lehmann\ H[!R[\ 0889[ Twenty years of acoustic sounding*
Netherlands[ pp[ 052Ð065[ a review and some applications[ Zeitschrift fur Meteorologie 39\ 130Ð
149[
Gautier\ D[\ Conrath\ B[J[\ Owen\ T[\ De Pater\ I[\ Atreya\ S[K\ 0884[ Yelle\ R[V[\ Strobell\ D[F[\ Lellouch\ E[\ Gautier\ D[\ 0886[ Engineering
The troposphere of Neptune[ In] Cruikshank\ D[P[ "Ed[#[ Neptune models for Titan|s Atmosphere[ In] Wilson\ A[\ "Ed[#\ Huygens]
and Triton[ University of Arizona Press\ Tucson[ pp[ 436Ð501[ Science\ Payload and Mission\ ESA SP!0066\ European Space
Agency\ Noordwijk\ The Netherlands[ pp[ 142Ð145[
Hanel\ R[A[\ Strange\ M[G[\ 0855[ Acoustic experiment to determine Zarnecki\ J[C[\ Banaszkiewicz\ M[\ Bannister\ M[\ Boynton\ W[V[\
the composition of an unknown planetary atmosphere[ Journal of Challenor\ P[\ Clark\ B[\ Daniell\ P[M[\ Delder_eld\ J[\ English\
the Acoustical Society of America 39\ 785Ð894[ M[A[\ Fulchignoni\ M[\ Garry\ J[R[C[\ Geake\ J[E[\ Green\ S[F[\
Hathi\ B[\ Jaroslawski\ S[\ Leese\ M[R[\ Lorenz\ R[D[\ McDonnell\
Ingersoll\ A[P[\ Beebe\ R[F[\ Conrath\ B[J[\ Hunt\ G[E[\ 0873[ Structure J[A[M[\ Merryweather!Clarke\ N[\ Mill\ C[S[\ Miller\ R[J[\ Newton\
and dynamics of Saturn|s atmosphere[ In] Gehrels\ T[\ Matthews\ G[\ Parker\ D[J[\ Svedhem\ L[H[\ Turner\ R[F[\ Wright\ M[J[\ The
M[S[\ "Eds#\ Saturn[ University of Arizona Press\ Tucson[ pp[ 084Ð surface science package\ In] Wilson\ A[ "Ed[#\ Huygens] Science\
127[ Payload and Mission[ ESA Special Publication SP!0066\ pp[ 066Ð
084[
Kleppe\ J[A[\ 0885[ High temperature acoustic pyrometry[ Sensors 02\
06Ð11[

Ksanfomality\ L[V[\ Scarf\ F[L[\ Taylor\ W[L[\ 0872a[ The electrical
activity of the atmosphere of Venus[ In] Hunten\ D[M[\ et al[\ "Eds#\
Venus[ University of Arizona[

Ksanfomality\ L[V[\ Goroshkova\ N[V[\ Khondryev\ V[K[\ 0872b[
Wind velocity near the surface of Venus form acoustic measurements[