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Physical parameters for the Saturn atmosphere computed by using voyager data
Adv. Space Res. Vol. 7, No. 12, pp. (12)33—(12)37, 1987 Printed in Great Britain. All rights reserved.
0273—1177/87 $0.00 + .50 Copyright © 1987 COSPAR
PHYSICAL PARAMETERS FOR THE SATURN ATMOSPHERE COMPUTED BY USING VOYAGER DATA B. Petropoulos and A. Georgakilas Research Centerfor Astronomy and Applied Mathematics, Academy of Athens, 14, Anagnostopoulou St., Athens 106 73, Greece
ABSTRACT We have computed the following physical parameters for the atmosphere of Saturn: 1) Temperature, 2) Pressure, 3) Density, 4) Density Scale, 5) Number Density, 6) Viscosity, 7) Mean Pressure Scale, 8) Mean Particle Velocity, 9) Mean Collisional Frequency, 10) Columnar Mass, and ii)Mean Free Path. Voyager 2 measurements have been used in order to compute the above parameters from 0 to 300 km above the top of the clouds. From 0 to 300 km below the top of the clouds, ground based measurements have been used. INTRODUCTION Ground based telescopic and spacecraft observations show that the atmosphere of Saturn is covered by clouds /1/. The top of the clouds is taken as zero altitude. Between 1973 and 1981 the atmosphere of Saturn over the clouds has been explored by the following probes: 1) Pioneer-il (5 April 1973-1 September 1979, 2) Voyager-i (5 September 1977-end 1980), and 3) Voyager-2 (20 August 1977—August 1981). In order to construct a model and to compute the pressure as a function of altitude above the clouds of the atmosphere of Saturn, Caldwell /2/ and Cess et al. /3/ have used ground based IR spectroscopy data. This model was extended by Canaan et al. /4/ to alternative latitudes and by Bezard et al. /5/ to Saturn’s upper troposphere employing Voyager data. Below the top of the clouds Gulkis and Poynter /6/ have computed the distribution of the temperature versus the altitude. In the present work we have used Voyager’s measurements in order to compute the physical parameters of the atmosphere of Saturn from 0 to 300 km altitude and to correct the temperature distribution given by Gulkis and Poynter /6/ from 0 to-300 km. These results as well as other Voyager measurements have been used as input data in order to compute the physical parameters of Saturn atmosphere from -300 to 0 km. INPUT DATA AND COMPUTED PHYSICAL PARAMETERS We have assumed that the pressure can be computed by integrating the hydrostatic equation: dp
-gp dz
(1)
where p is the pressure, g is the local acceleration of gravity, andp is the density. the following assumptions were contained in the integration. 1) The gas mixture follows the perfect gas equation state:
p
p L’R T
(2)
where ~ is the molecular weight, T is the temperature, and R is the universal gas constant. 2) The temperature varies with the altitude by a series of constant lapse rates. We have integrated relations (1) and (2) in order to compute pressures and densities from —300 to 300 km. Relations (4), (5), (6), (7), (8), (9) from (12)33
(12)34
B. Petropoulos and A. Georgakilas
the work of Petropoulos et al. /7/ have been used to compute the following physical parameters: 1) Pressure, 2) Density, 3) Density Scale, 4) Number Density, 5) Viscosity, 6) Mean Pressure Scale, 7) Mean Particle Velosity, 8) Mean Collisional Frequency, 9) Columnar Mass, and 10) Mean Free Path. The following input data have been used for these computations: 1) The radiu5 of the planet measured by Voyager R 60,000 km/l/, 2) The chemical composition 0.93 ~2 and 0.07 He /8/, 3) The mean molecular weight, computed by taking into account the above chemical composition, m 2.15, 4) The pressure and temperature measured by Voyager at zero altitude, Pa 1000 mb and To 131 ±5K (IRIS-experiment) /8/, 5) The mean distribution of the temperature from 0 to 300 km measured by Voyager and infrared spectrometry (IRIS-experiment) /8/, /9/ which are very~close to the temperature profiles measured by radio occultation data of Voyager /8/, and 6) The distribution of the temeprature from 0 to -300 km computed by the following relation: /6/ dT/dz
-g/Cp,
where g is the gravitational acceleration /1/ and Cp is the specific heat at constant pressure. The calculated profile of the temperature as a function of pressure is given in figure 1. The other physical parameters from 0 to 300 km altitude computed in this work are given in figures 3, 4, 6, and 7. In figures 2, and 5 we give the pressures and densities computed from -300 km to 300 km, respectively. CONCLUSIONS As we show in figure 1, our proposed model gives temperatures as a function of the pressure which are very close to the measurements of the IRISexperiment and radio occultation. Consequently, the temperatures and pressures computed in this work seem to be correct. The computed profiles (figures 1, 2, 3) cam be used to determine the altitudes where the minor chemical components of the Saturn atmosphere (given by Encrenaz work /10/) solidify and form the cloud hazes observed by Voyager. We find that CH 4 clouds at 4]. km and 92 km are possible. This is consistent with Bezard et al. /5/ observations. possible at negative altitudes.
Clouds of NH3 and NH2SH are
Physical parameters computed in this work can be used in order to study the meteorology of Saturn and can be taken into account f or the construction of new spaceprobes which will explore the Saturn atmosphere. REFERENCES 1.
A. Ingersoll, The New Solar System, Cambridge University Press, 1981.
2.
J. Caldwell, The atmosphere of Saturn, An infrared perspective, ~arus
3.
30,493 (1977). R.D. Cess, J. Caldwell, A Saturnian stratospheric seasonal climatic model, Icarus 38, 349 (1979).
4.
B.E. Calson, J. Caidwell, R.D. Cess, A model of Saturn’s seasonal stratosphere of the time of Voyager encounters, .3. Atmos. Sci. 37, 1883 (1980).
5.
B. Bezard, D. Gautier, A seasonal model of the Saturnian upper troposphere comparison with Voyager infrared measurements, Icarus 60, 274 (1984).
6.
S. Gulkis, R. Poynter, Thermal radio emission from Jupiter and Saturn, _E~~jq~ ~, 36 (1972).
7.
B. Petropoulos, C. Banos, A reference model for the upper atmosphere of Jupiter, Astron. Astrop)~s. Su Se~ 5~, 145 (1984).
The Saturn Atmosphere
(12)35
8.
G.S. Orton, Thermal infrared constraints on ammonia ice particles as candidates for clouds in the atmosphere of Saturn, Icarus 53, 293 (1983).
9.
G.L. Tyler, V.R. Eshleman, ID. Anderson, G.S. Levy, G.F. Lindal, G.E. Wood T.A. Croft, Radio science with Voyager 2 of Saturn: Atmosphere & ionosphere and the masses of Saturn and lapetus, Science 215, 553, 1982.
10.
Th. Encrenaz, Primodial matter in the outer solar system: A study of its chemical composition from remote spectroscopic analysis, S2aceSci. Rev. 3~, 35 (1984).
.001
1
-
,1/,,’ 2~~~l//
J______
‘7/,
~‘1/~’ 010
—
7
P(b)
/ .100
1.000 80
100
120
140
T(K)
Fig.1 Temperature versus pressure for the atniosphere of Sattirn:(1) IRIS experUnent of Voyager at 36:5 N /8/ (2) Computed values of the present work. (3) IRIS experiment of Voyager at 31°S /8/ (4) Radio occultation measurements of Voyager /8/, /9/.
4
(12)36
B. Petropoulos and A. Georgakilas
iog P (mb) FiLt.2. Computed pressure versus altitude front -300 to 300 km for the atmosphere of Saturn, Ps (km) 6,0
0.4
0.45
0.5
0.55
0.6
Vs x Fig.3 (1) Computed viscosity versus altitude for the atmosphere of Saturn(2)Computed pressure scale versus altitude for the atmosphere of Saturn.
3)
~og N D (cm
!
~
log F~(m) Fig. 4 (1) Computed mean free path versus altitude for the atmosphere of Saturn (2) Computed number density versus altitude for the atmosphere of Saturn.
The Saturn Atmosphere
(12)37
!? T5~0i03.0 3) log D (gr/cm Fig.5 Computed density versus altitude from -300 to 300 1m for the atmosphere of Saturn.
900
50
Ds (kin) 100 150
950
1000
1050
200
250
1100
1150
~ (m/sec) Pig.6(1) Computed density scale versus altitude for the atmosphere of Saturn(2) Computed mean particle velocity versus altitude for the atmosphere of Saturn. log CF (sec1)
log C Fig.7 (1) Computed collisional frequency versus alt itude for the atmosphere of Sattirn(2) Computed columnar mass versus alt]tude for the atmosphere of Saturn.
0273—1177/87 $0.00 + .50 Copyright © 1987 COSPAR
PHYSICAL PARAMETERS FOR THE SATURN ATMOSPHERE COMPUTED BY USING VOYAGER DATA B. Petropoulos and A. Georgakilas Research Centerfor Astronomy and Applied Mathematics, Academy of Athens, 14, Anagnostopoulou St., Athens 106 73, Greece
ABSTRACT We have computed the following physical parameters for the atmosphere of Saturn: 1) Temperature, 2) Pressure, 3) Density, 4) Density Scale, 5) Number Density, 6) Viscosity, 7) Mean Pressure Scale, 8) Mean Particle Velocity, 9) Mean Collisional Frequency, 10) Columnar Mass, and ii)Mean Free Path. Voyager 2 measurements have been used in order to compute the above parameters from 0 to 300 km above the top of the clouds. From 0 to 300 km below the top of the clouds, ground based measurements have been used. INTRODUCTION Ground based telescopic and spacecraft observations show that the atmosphere of Saturn is covered by clouds /1/. The top of the clouds is taken as zero altitude. Between 1973 and 1981 the atmosphere of Saturn over the clouds has been explored by the following probes: 1) Pioneer-il (5 April 1973-1 September 1979, 2) Voyager-i (5 September 1977-end 1980), and 3) Voyager-2 (20 August 1977—August 1981). In order to construct a model and to compute the pressure as a function of altitude above the clouds of the atmosphere of Saturn, Caldwell /2/ and Cess et al. /3/ have used ground based IR spectroscopy data. This model was extended by Canaan et al. /4/ to alternative latitudes and by Bezard et al. /5/ to Saturn’s upper troposphere employing Voyager data. Below the top of the clouds Gulkis and Poynter /6/ have computed the distribution of the temperature versus the altitude. In the present work we have used Voyager’s measurements in order to compute the physical parameters of the atmosphere of Saturn from 0 to 300 km altitude and to correct the temperature distribution given by Gulkis and Poynter /6/ from 0 to-300 km. These results as well as other Voyager measurements have been used as input data in order to compute the physical parameters of Saturn atmosphere from -300 to 0 km. INPUT DATA AND COMPUTED PHYSICAL PARAMETERS We have assumed that the pressure can be computed by integrating the hydrostatic equation: dp
-gp dz
(1)
where p is the pressure, g is the local acceleration of gravity, andp is the density. the following assumptions were contained in the integration. 1) The gas mixture follows the perfect gas equation state:
p
p L’R T
(2)
where ~ is the molecular weight, T is the temperature, and R is the universal gas constant. 2) The temperature varies with the altitude by a series of constant lapse rates. We have integrated relations (1) and (2) in order to compute pressures and densities from —300 to 300 km. Relations (4), (5), (6), (7), (8), (9) from (12)33
(12)34
B. Petropoulos and A. Georgakilas
the work of Petropoulos et al. /7/ have been used to compute the following physical parameters: 1) Pressure, 2) Density, 3) Density Scale, 4) Number Density, 5) Viscosity, 6) Mean Pressure Scale, 7) Mean Particle Velosity, 8) Mean Collisional Frequency, 9) Columnar Mass, and 10) Mean Free Path. The following input data have been used for these computations: 1) The radiu5 of the planet measured by Voyager R 60,000 km/l/, 2) The chemical composition 0.93 ~2 and 0.07 He /8/, 3) The mean molecular weight, computed by taking into account the above chemical composition, m 2.15, 4) The pressure and temperature measured by Voyager at zero altitude, Pa 1000 mb and To 131 ±5K (IRIS-experiment) /8/, 5) The mean distribution of the temperature from 0 to 300 km measured by Voyager and infrared spectrometry (IRIS-experiment) /8/, /9/ which are very~close to the temperature profiles measured by radio occultation data of Voyager /8/, and 6) The distribution of the temeprature from 0 to -300 km computed by the following relation: /6/ dT/dz
-g/Cp,
where g is the gravitational acceleration /1/ and Cp is the specific heat at constant pressure. The calculated profile of the temperature as a function of pressure is given in figure 1. The other physical parameters from 0 to 300 km altitude computed in this work are given in figures 3, 4, 6, and 7. In figures 2, and 5 we give the pressures and densities computed from -300 km to 300 km, respectively. CONCLUSIONS As we show in figure 1, our proposed model gives temperatures as a function of the pressure which are very close to the measurements of the IRISexperiment and radio occultation. Consequently, the temperatures and pressures computed in this work seem to be correct. The computed profiles (figures 1, 2, 3) cam be used to determine the altitudes where the minor chemical components of the Saturn atmosphere (given by Encrenaz work /10/) solidify and form the cloud hazes observed by Voyager. We find that CH 4 clouds at 4]. km and 92 km are possible. This is consistent with Bezard et al. /5/ observations. possible at negative altitudes.
Clouds of NH3 and NH2SH are
Physical parameters computed in this work can be used in order to study the meteorology of Saturn and can be taken into account f or the construction of new spaceprobes which will explore the Saturn atmosphere. REFERENCES 1.
A. Ingersoll, The New Solar System, Cambridge University Press, 1981.
2.
J. Caldwell, The atmosphere of Saturn, An infrared perspective, ~arus
3.
30,493 (1977). R.D. Cess, J. Caldwell, A Saturnian stratospheric seasonal climatic model, Icarus 38, 349 (1979).
4.
B.E. Calson, J. Caidwell, R.D. Cess, A model of Saturn’s seasonal stratosphere of the time of Voyager encounters, .3. Atmos. Sci. 37, 1883 (1980).
5.
B. Bezard, D. Gautier, A seasonal model of the Saturnian upper troposphere comparison with Voyager infrared measurements, Icarus 60, 274 (1984).
6.
S. Gulkis, R. Poynter, Thermal radio emission from Jupiter and Saturn, _E~~jq~ ~, 36 (1972).
7.
B. Petropoulos, C. Banos, A reference model for the upper atmosphere of Jupiter, Astron. Astrop)~s. Su Se~ 5~, 145 (1984).
The Saturn Atmosphere
(12)35
8.
G.S. Orton, Thermal infrared constraints on ammonia ice particles as candidates for clouds in the atmosphere of Saturn, Icarus 53, 293 (1983).
9.
G.L. Tyler, V.R. Eshleman, ID. Anderson, G.S. Levy, G.F. Lindal, G.E. Wood T.A. Croft, Radio science with Voyager 2 of Saturn: Atmosphere & ionosphere and the masses of Saturn and lapetus, Science 215, 553, 1982.
10.
Th. Encrenaz, Primodial matter in the outer solar system: A study of its chemical composition from remote spectroscopic analysis, S2aceSci. Rev. 3~, 35 (1984).
.001
1
-
,1/,,’ 2~~~l//
J______
‘7/,
~‘1/~’ 010
—
7
P(b)
/ .100
1.000 80
100
120
140
T(K)
Fig.1 Temperature versus pressure for the atniosphere of Sattirn:(1) IRIS experUnent of Voyager at 36:5 N /8/ (2) Computed values of the present work. (3) IRIS experiment of Voyager at 31°S /8/ (4) Radio occultation measurements of Voyager /8/, /9/.
4
(12)36
B. Petropoulos and A. Georgakilas
iog P (mb) FiLt.2. Computed pressure versus altitude front -300 to 300 km for the atmosphere of Saturn, Ps (km) 6,0
0.4
0.45
0.5
0.55
0.6
Vs x Fig.3 (1) Computed viscosity versus altitude for the atmosphere of Saturn(2)Computed pressure scale versus altitude for the atmosphere of Saturn.
3)
~og N D (cm
!
~
log F~(m) Fig. 4 (1) Computed mean free path versus altitude for the atmosphere of Saturn (2) Computed number density versus altitude for the atmosphere of Saturn.
The Saturn Atmosphere
(12)37
!? T5~0i03.0 3) log D (gr/cm Fig.5 Computed density versus altitude from -300 to 300 1m for the atmosphere of Saturn.
900
50
Ds (kin) 100 150
950
1000
1050
200
250
1100
1150
~ (m/sec) Pig.6(1) Computed density scale versus altitude for the atmosphere of Saturn(2) Computed mean particle velocity versus altitude for the atmosphere of Saturn. log CF (sec1)
log C Fig.7 (1) Computed collisional frequency versus alt itude for the atmosphere of Sattirn(2) Computed columnar mass versus alt]tude for the atmosphere of Saturn.