Various investigations concerning Jupiter, Uranus and Saturn are discussed. Revisions in the Galilean satellite ephemerides led to a new interpretation of earth-based measurements of Jovian oblateness which agrees with Pioneer measurements. In the area of scintillation theory, a semi-qualitative result was obtained for spike profiles produced by finite stellar disks viewed through Kolmogorov turbulence. It was also possible to set limits on the systematic distortion of stellar occulation profiles by turbulence which minimize the systematic distortion problem. The position of Miranda was studied for the purpose of obtaining an accurate prediction of a possible stellar occultation by Miranda in 1977, following an occultation of the same star by Uranus. In addition, using thermodynamic calculations, a model was developed for the adiabiatic cooling of Jovian-type planets and an observational test of the model was proposed. The dynamic structure of Saturn's rings was also studied

Hubbard, W. B.

English

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Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19760016040 2020-03-22T16:03:51+00:00Z
University of Arizona
Department of Planetary Sciences
Lunar and Planetary laboratory
NASA Grant NSG 7045
"Interiors of the Giant Planets"
Semiannual Report 14
Period October 1, 1975 - April 1, 1976
(NASA-CR-146984) INTERIOFS OF THE GIANT	 N76-23128
PLANET S Semiannual Report, 1 Cct. 1975 - 1
Apr. 1976 (Arizona Univ., Tucson.) 12 p HC
$3.50	 CSCL 03E	 UnclasG3/91 26842
MAY 197t.-1
RECEIVED
NASA STI FACRRY,
la INFUi BRANCH,
Submitted: 12 May 1976
W. B. Hubbard
Principal Investigator
-I-
1. Personnel working on this grant, during this reporting period:
Dr. W. B. Hubbard (Principal Investigator, k time)
Dr. R. J. Greenberg (Co-Investigator, 	 time)
Mr. W. L. Slattery (Graduate student, } time)
Ms. Nancy Moore (Secretary, k time)
II. Overview and Summary
Occultations and Geodesy: Reinterpretation of the 1973 mutual
Galilean satellite phenomena by another NASA-supported group has led
to important revisions to the satellite ephemerides. In the case of
lo, we have shown these revisions to be consistent with a new inter-
pretation of the 0 Sco-measured Jovian oblateness, which now agrees
with the Pioneer 10/11 value. There are now no significant discre-
pancies between earth-based and spacecraft measurements of this
important parameter.
In the area of scintillation theory, a semiquantitative result
was developed for spike profiles produced by finite stellar disks
viewed through Kolmogorov turbulence. We a'e also able to set
limits for the first time on the systematic distortion of stellar
occultation intensity profiles by turbulence. The limits are such
that the systematic distortion is not a serious problem.
Greenberg and Hubbard carried out a study of the position of
Miranda for the purpose of obtaining an accurate prediction of a
possible stellar occultation by Miranda in 1977, following an
9-2-
occultation of the same star by Uranus. Such a measurement would
be of great importance for understadding the dynamics of the Uranian
system and hence the gravity field of Uranus. Present calculations
Indicate that the Miranda shadow will miss the earth by 5000 km,
but the study is still in progress.
High Pressure Physics and Planetary Interiors: Using thermo-
dynamic calculations reported previously, Hubbard developed a
semianalytic theory for the cooling of a Jovian-type planet. The
theory is both simpler and more accurate than earlier calculations.
We find that the simple cooling model fits available Jovian para-
meters and the age of the solar system quite well. On the basis of
cooling theory, there is no strong reason for preferring the space-
craft measurement of the Jovian effective temperature over the .
ground-based one. The spacecraft value of T  2 127°K gives a cooling
age-of about 5x 109 years, while the earth-based value of T  - 134°K-
gives an age of about 4x109 years.
We have proposed an observational test of the adiabatic cooling
model for Jovian-type planets. An average pole-equator effective
temperature difference of +2°K is predicted for Jupiter, and.some-
what more for Saturn.
Satellite Dynamics: Greenberg's theory of the long-period
variations of Miranda's longitude has been compared with Naval
Observatory astrometry. Encouraging results have been obtained and
incorporated into consideration of the possibility of a stellar
V
-3-
occultation by Miranda. Work on the dynamical structure of Saturn's
Rings has continued. A fundamental problem with the Franklin and
Colombo model has been discovered which has important implications
for the evolution of the rings and of the asteroid belt.
III. Occultation
During this period, Aksnes and Franklin published a paper in^
which they reinterpreted some of the 1973 observations of Galilean
satellite mutual occultation and eclipse phenomena. They found that
the best way to interpret these data was to introduce large correc-
tions to the standard ephemerides of the Galilean satellites. This
result was of great interest because it offered a possibility to
reconcile earth-based and spacecraft-based measurements of Jupiter's
oblateness. The 1971 occultation of B Sco by Jupiter was followed
by an occultation by lo. Thus the position of to with respect to
Jupiter's rotation axis was precisely known. Aksnes and Franklin's
new to ephemeris permitted us to relocate lo's position with respect
to the center of mass as well, which caused the occultation-derived
Jovian oblateness to increase substantially from 0.060 to 0.063.
The Pioneer-derived oblateness is 0.0647, so it is clear that the
corrections to . lo's ephemeris are in the right ball park. The
discrepancy in the position of the Jovian center of mass is now down
to less than 200 km. We believe that this result is an important
-4-
REPRODUCIBILITY orTTTr,
ONGINAL PAGE, IS Pit h r I ,
reconciliation of a number of different earth-based and spacecraft-
based observations. The paper has been submitted to Icarus.
Hubbard continued work in collaboration with Jokipii on scin-
tillation theory applied to stellar occultations by planetary
atmospheres, with the objective of unde#atanding more clearly what
the possible systematic effects of turbulence on,such data might be.
The 1971 B Sco data were reexamined in detail by applying a semi-
quantitative theory of scintillation to high time resolution data
from the Cornell group as well as the lower time resolution data
from Texas. We were able to confirm most of the preliminary results
of Young, although our more quantitative calculations show that
there is no substantial evidence for anisotropic turbulence in thei{
Jovian atmosphere. Our theory agrees well with observed spike
properties. However, we anticipate a continuing lively debate in
i
this somewhat contentious field.
Hubbard and Jokipii also looked into the systematic effects of
scintillation on intensity profiles. Young suggested that the
scattering could distort the profiles, which would gravely reduce
the utility of stellar occultation as a tool for studying planetary
dimensions and planetary atmospheres. Although the systematic
effects are indeed present, one requires implausible levels of turbu-
lence to produce an important distortion.
Both of the scintillation papers have been submitted to Icarus,
and were presented in brief form at the Austin UPS ineeting.
-5-
Greenberg and Hubbard started a new analysis of the position.
of Miranda, for the purpose of predicting a possible stellar occul-
tation by Miranda In 1977, following an occultation by Uranus two
hours previously. We used Greenberg's theory of perturbations on
Miranda's orbit by other satellites to evaluate the magnitude of
possible uncertainties in the longitude of Miranda. New observa-
tions supplied by the Naval Observatory seem to confirm the
correctness of Greenberg^s theory, and we presently calculate that
the shadow of Miranda will pass to the north of the earth by several
thousand km. After we have analyzed data from the 1976 apparition,
we plan to issue a prediction. Unfortunately, an occultation by
Miranda appears unlikely.
IV. Interior Structure and Equations of State
Hubbard carried out an independent study of cooling rates-for
Jovian-type pianets. This work was motivated by reports from other
groups that the present effective temperature of Jupiter as measured
by the Pioneer spacecraft was consistent with a primordial cooling
model, while an earlier earth-based determination was not. Specifi-
cally, Low and his collaborators obtained a Jovian T  = 134 0 , while
Orton and colleagues recently reported T  s 127°K. Pollack and his
coworkers found that Jupiter would cool to T . = 134°K within about
2.6X109
 years, thus seemingly eliminating this model from consideration.
REPRODUCI13ILiTY OF ' 11
-6-
	 ORIGINAL PAGE IS POOR
In view of our recent work on obtaining Jovian interior thermo-
dynamics to improved accuracy, these results were incorporated in a
semianalytic cooling model for the purpose of providing an indepen-
dent check on the other calculations. We find that the age of
Jupiter varies approximately as Te-1114,and that the age difference
between 134°K and 127°K is a little more than 10 9 years. Furthermore,
we get a total cooling age to 134°K of approximately 4.0x10 9 years,
significantly longer than the earlier study. It turns out that the
cooling time is most sensitive to Te , and only weakly sensitive to
the ratio of solar influx to interior heat flux. Uncertainties in
the cooling time due to unknown Rarameters pertaining to the interior
structure are probably less than 20t. Thus we conclude that the
adiabatic cooling mo.del works well for Jupiter, and at'present the
earth-based value and the spacecraft value for T  lie on either side
of 'the "correct" value, with neither to be preferred for theoretical
reasons at the moment.
As a byproduct of the study of Jovian adiabatic cooling models,
an interesting prediction resulted. in order to match interior con-
vection to the surface boundary condition provided by the atmosphere's
heat radiation, the variation of gravity over the surface of Jupiter
tends to produce a "polar brightening". It turns out that the solar
Input flux is distributed uniformly by convection, but the variation
of g causes an asymmetry. In the case of Jupiter, the average polar
effective temperature should exceed the equatorial value by about 2°K.
f	 L
For Saturn, the variation should be somewhat larger because of the
greater g-variation.	 No observational data as yet confirm or
refute this prediction.
The above results have been submitted to Icarus.
Slattery is nearing completion of a thorough study of Jovisn
and Saturnian interior models fitted to presently available con-
straints.	 These results will be reported in detail in the next
{{,
semiannual re port.
1
=	 s
V.	 Satellite Dynamics
Greenberg's theory of the effect of Ariel and Umbriel on
Miranda's motion predicted that in the mid to late 1970's Miranda
3
would be -10° in orbital longitude ahead of the position obtained
from extrapolation of the elements published by previous authors.
(A paper describing this theory Is in press
	
in Icarus.)
	
We have
compared recent Naval Observatory astrometry with the theory and
findood agreement.
	
10°	 orrec	 n wcrucial fac	 rg. 	 The	 c tio 	 as a	 to	 in our
_ computation regarding the possibility of a stellar occultation by
i
Miranda next year (See section III).	 Only a few more degrees would
have made are occultation observable from earth.
_ Greenberg visited the Center for Astrophysics in Cambridge,
Mass, in January for consultation on the problem of the dynamics of
Saturn's rings.	 Our correction to the dynamically determined density
of ring B was confirmed. 	 It now agrees closely with optically
E
s
-8-
determined values as Greenberg reported at the December meeting of
the AAS Division on Dynamical Astronomy. On the other hand, we have
discovered a new problem with Franklin and Colombo's theory. it is
still not understood how a resonance with Mimes could clear a region
as wide as Cassini's Division. Ring particles' eccentricities are
enhanced over the entire region, but these disturbances are coherent
so particles can still remain densely packed without collisions.
Only particles in a very narrow band of semi-major axes near the
resonance receive forced eccentricities great enough to require
collisions. if the resonance hypothesis is accepted, it would
appear that these relatively few` particles have swept clear the
entire Division. This result lends support to suggestions that an
analogous mechanism created the Kirkwood Gaps or even prevented the
growth of a full-sized planet at the asteroid belt.
VI. Publications and Presentations during this reporting period
(a) Published Papers:
1. "Comparison of Geometrical Effects in Radio and Stellar
Occultations". by W. B. Hubbard, Icarus, 26, 175 (1975).
2. "Ray Propagation in Oblate Atmospheres", by W. S. Hubbard,
Icarus, 27, 387 (1976).
3. "Temperature of the Atmosphere of Jupiter from
Pioneer 10111 Radio Occultations", by A. Wore,
P. Woiceshyn, and W. B. Hubbard, Geophys. Kes. Letter_,
3, 113 (1976).
R(b) Papers submitted for publication:
1. "Orbit-orbit Resonances in the Solar System", by
R. Greenberg, Vistas in Astronomy, in press.
2. "Stellar Occultations by Turbulent Planetary Atmos-
_	 pheres: A Heuristic Scattering Model", by
W. B. Hubbard and J. R. Jokipil, submitted to Icarus.
3. "Stellar Occultations by a Turbulent Planetary Atmos-
phere: The B Sco Events", by J. R. Jokipii and
W. B. Hubbard, submitted to Icarus.
4. "DeSitter's Theory Flattens Jupiter", by W. B. Hubbard,
submitted to Icarus.
5. "The Jovian Surface Condition and Cooling Rate", by
W. B. Hubbard, submitted •to Icarus,
(c} Presentations:
1. "The Location of Cassini's Division in Saturn's Rings".
by R. Greenberg, AAS Div. on Dynamical Astronomy,
Pasadena, December. Abstract to appear in B.A.A.S.
2. "Dynamics of Cassini's Division in Saturn's Rings",
by R. Greenberg, AAS/DPS, Austin, March. Abstract to
appear in B.A.A.S.
3. "Effects of Turbulence on Atmospheric Profiles from
Radio and Stellar Occultations", by W. B. Hubbard and
J. R. Jokipii, AAS/DPS, Austin, March. Abstract to
appear in B.A.A.S.
a-10-
4. invited review paper by W. B. Hubbard on Giant Planet
Interiors, AGU, San Francisco, December.
VII. Financial Status
	 +
Expenditures are on schedule (see attached graph).
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Interiors of the giant planets

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