Apollo 8 tracking data analyzed for evidence of lunar mass concentration

Murphy, J. P.

Siry, J. W.

English

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LUNAR MASCON EVIDENCE
FROM APOLLO ORBITS
JAMES P. MURPHY
JOSEPH W. IIRY
JULY 1969
® GODDARD SPACE FLIGHT CENTER
GREENBELT, MARYLAND
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X-550-69-312
LUNAR MASCON EVIDENCE FROM APOLLO ORBITS
James P. Murphy
Joseph W. Siry
Mission & Trajectory Analysis Division
July 1969
GODDARD SPACE FLIGHT CENTER
Greenbelt, Maryland
PRECEDING PAGE BUNK NOT FILMED.
LUNAR MASCON EVIDENCE FROM APOLLO ORBITS
James P. Murphy
Joseph W. Siry
Mission & Trajectory Analysis Division
Goddard Space Flight Center
Greenbelt, Maryland
ABSTRACT
Apollo VIII tracking data have been analyzed to obtain new evidence for a
mascon in the neighborhood of Sinus Aestuum. Data from elliptical and nearly
circular lunar orbits of Apollo VIII can be interpreted in terms of a mascon in
this region at a depth of approximately 100 kilometers which has a mass on the
order of 5 x 10 6 lunar masses and gives rise to a gravitational anomaly at the
lunar surface of roughly 250 milligals.
iii
LUNAR MASCON EVIDENCE FROM APOLLO ORBITS
Analyses of the gravitational field of the moon in terms of spherical harmonic
expansions of its potential have been presented by several investigators. 1-4
Certain features of the effect of the moon's gravitational field upon the motions
of spacecraft in the Lunar Orbiter series have been interpreted by Muller and
Sjog.en in terms of lunar mass concentrations, or mascons. `' They identified
six mascons associated with major ringed maria and also found evidence for at
least one and possibly two additional mascons in the region between Sinus Aestuum
and Sinus Medii. They assumed that this represented a feature which was once
similar to a ringed sea and has since been obscured by impact debris. They
noted that data from a key orbit which might have shod further light on this in-
teresting region were, unfortunately, missing.
Apollo VIII completed ten orbital revolutions of the moon at Christmastime
in 1968. During the first two lunar revolutions the perilune height was 110 kil-
ometers, the apolune height was 310 kilometers, and the period was 129 minutes.
A coplanar circularizing maneuver carried out between the second and third lunar
revolutions put Apollo VIII into a nearly circular orbit having a perilune height
of 110 kilometers, an apolune height of 113 kilometers and a period of 119 min-
utes. 6 In the case of both the elliptical and the nearly circular orbits, the in-
clination was 12 0 retrograde and the orientation of the orbit was such that the
spacecraft passed over the region between Sinus Aestuum and Sinus Medii which
is located at the center of the lunar disc. During the first two lunar revolutions
1
the spacecraft travelled over this area at altitudes of approximately 310 kilome-
ters, while during the last eight lunar revolutions it passed over nearly the same
area at altitudes close to 112 kilometers. (Cf. Fig. 1. )
The Apollo spacecraft are tracked by means of the Unified S-band Tracking
System which was developed by the Goddard Space Flight Center especially for
use in the Apollo program. This system reflects experience gained through the
use of earlier Doppler and ranging systems for tracking which were develops a
and operated by the Jet Propulsion Laboratory and the Goddard Space Flight C(
ter. The Unified S-band Tracking System operates at a frequency of about 2 ;11V
Mllz. It is deployed in the NASA Manned Space Flight Network which is olw rrr
by Goddard. Typical tracking data sampling intervals are one minute, and s-,.
seconds.
The tracking data obtained during the lunar orbit phase of the Apollo -\ lli
mission occurred in ten sets separated by the periods when the spacecraft passed
behind the moon during each revolution. Studies of the lunar gravitational field
are being conducted on the basis of these data with the aim of improving the capa-
bility for determining and predicting Apollo orbits in later missions. These
efforts are being reported upon elsewhere. 7
The present analysis is based upon a set of orbits each of which was deter-
mined using tracking data for a single revolution and a gravitational model which
included a triaxial lunar field and effects due to the earth and the sun. The values
used for the unnormalized lunar harmonic coefficients were J2 = 2.072 x 10 4
and C22 = 0.202 x 10 4 .	
x
2
F__
The residuals of the range rate tracking data with respect to the lunar or-
bits clearly revealed marked positive derivatives in the neighborhood of the
meridian at longitude -8° which passes through the Sinus Aestuum region. This
can be seen from Figs. 1 through 3. Typical residuals of Doppler data obtained
from orbits determined for the first and seventh lunar orbit revolutions of Apollo
VIII are plotted vs time in Figs. 2 and 3, respectively. Subsets of these two
sets of residuals obtained in the neighborhood of Sinus Aestuum which were taken
from the same differential corrections are plotted vs position along the retro-
grade orbit in the upper and lower portions of Fig. 1. Spacecraft positions in
the two revolutions are indicated by surface tracks which are correspondingly
marked in the central portion of Fig. 1. The Apollo lunar landing sites are also
shown there. Apollo VIII crossed the meridian at longitude -8 0 in the first and
seventh revolutions at 11 hours, 11 minutes, U. T. , and 23 hours, 16 minutes,
U. T. , respectively, on December ?^:, 1968. The altitudes of the spacecraft
above the lunar surface at these times were approximately 310 kilometers and
112 kilometers, respectively.
Preliminary estimates indicate that the range rate residual derivatives ob-
served near Sinus Aestuum during the first two lunar revolutions of Apollo VIII
had maxima whose average value was about 0. 15 mm/sec t . Similarly, an esti-
mate of about 0. 56 mm/sec t , or 56 milligals, was obtained for the mean of the
maximum values of range rate residual derivatives obtained near this region
during the last four lunar revolutions of Apollo VIII. These two mean values were
3
r
based upon two-way Doppler data. The probable error of the arithmetic mean
in the former case was about one milligal and in the latter case about three-
quarters of a milligal. Here the probable error of the arithmetic mean was taken
to be the ratio Q /^Vn in which the quantity, Q, given by the expression
n	 1 1/2
2 ]k	 E rni	/ (n - 1)	 (1)
m=1
denotes the probable error of a single measure when k has the familiar value
0. 67449, n denotes the number of measures in the set under consideration which,
here, is the set of maximum values of the range rate residual derivatives, and
the rm denc to the residuals of these measures relative to the mean of this set.
These forraulas, due toBessel, apply to Gaussian distributions.
They may not reflect the true state of affairs, however, if the force model
or the tracking system description is inappropriate. In the presence of bias-
like effects, for example, the error associated with the mean may not tend toward
zerc, as t;he number of measures increases indefinitely. It is possible, theo-
retically, to calculate probable errors in these cases, too, although, in practice,
it is not always a simple matter actually to carry through the process. In a
number of instances of this type, however, a useful characterization or estimate
of the uncertainty of the mean is provided by the quantity obtained through the
evaluation of the expression (1) for the case in which k = 0.67449 or, alterna-
tively, for the case in which k has another value such as unity. Evaluation of the
expression (1) for the former case yields uncertainty estimates of about one and
a half milligals for each of the two mean values given above.
4
The locations as.^ooiated with these mean values were within a couple of
degrees or so of the meridian at longitude -8 0 . The spacecraft orbits traversed
this meridian within about a degree of latitude 10'. In this portion of the orbit
the direction from the tracking station toward the spacecraft was close to the
nadir direction from the spacecraft toward the lunar center, hence positive de-
rivatives of the range rate residuals can be ident i fied with acceleration incre-
ments in directions toward the moon's center or its surface, and maximum val-
ues of range rate residual derivatives and means of these maxima can be viewed
as estimates of acceleration increment maxima.
The estimates of the acceleration increment maxima obtained from the ellip-
tical and nearly circular lunar orbits of Apollo VIII can be interpreted in terms
of a mascon located beneath the lunar surface within a couple of degrees or so
of the meridian at longitude -8 0 . If the mascon is assumed to be equally close
to latitude 10° , its depth, d, can be found by means of the relation:
a l	(d + h2 ) 2
a2	(d + h1)2
	 (2)
on the basis of the acceleration increment :xima a l , and a2, associated with
the heights h l , and h2 , respectively, which were cited above. The depth esti-
mated on this basis turns out to be about a hundred kilometers. The uncertainties
estimated earlier for the acceleration increment maxima throtgh the evaluation
of expression (1) are reflected in a corresponding uncertainty of the order of
twenty-five kilometers in the depth. The mascon mass, estimated on the basis
5
of Newton's laws, is about 3. 8 x 10 20 grams, or five millionths of the lunar mass.
Such a mass concentration of five "micromoons" gives rise to a gravitational
anomaly at the nominal lunar surface of about a quarter of a gal. The uncer-
tainties just indicated imply uncertainties on the order of twenty-five percent
in the mascon mass and the associated gravitational anomaly.
Sets of residuals of three-way Doppler data also were obtained from Apollo
VIII using additional tracking sites. These data were more numerous than the
two-way Doppler data, however, they exhibited greater scatter. They were
generally consistent with the results derived from the two-way Doppler data.
There are other factors, as was indicated previously, which could also af-
feet the values of parameters characterizing a mascon. These include possilde
perturbing effects of spacecraft control jets and venting systems, the choice of
the reference model of the lunar gravitational field used in the primary orbit
determinations, and the selection of the data spans employed in these orbital
differentiEd corrections. Information available concerning the operation of the
spacecraft reaction control system, the water boiler venting, and the waste water
dumps ir&,mtes that perturbations of the orbit associated with these activities
did not affect the present results in a significant way. A limited amount of
checking has been done using a spherically symmetric model of t'he lunar gravi-
tational field. The indications obtained are, in general, qualitatively consistent
with the results described above which were based upon a tri.axial model for the
lunar field. It is recognized, though, that this type of comparative analysis could
6
yield larger variations than those which were found to occur. This was seen to
be the case, for example, in recent work of Muller and Sjogren. 8
The acceleration increment maxima observed during the flight of Apollo VIII
occur witlun a couple of degrees or so of the acceleration peak of the Sinus
Aestuum mascon feature which they found earlier. 5 This provides the basis for
the above assumption concerning its latitude, and an indication of the consistency
of the two estimates of this feature's meridian.
The present results include estimates of the depth and the mass of the Sinus
Aestuum mascon feature as well as the magnitude of the surface gravity anomaly
which is associated with it.
It is of interest to note that the estimate of the acceleration increment maxi-
mum given above for Apollo VIII in its nearly circular lunar orbit at 112 kilome-
ters altitude is consistent with the acceleration value normalized to 100 kilome-
ters altitude which they reported for this region, and that the value for the depth
of the Sinus Aestuum mascon feature based upon the two types of Apollo VIII
lunar orbits is consistent with the general range of depths which they and their
colleagues reported on the basis of the analysis of distinct spacecraft. 9
Their findings were based upon the tracking of Lunar Orbiter spacecraft by
means of the NASA Deep Space Network operated by the Jet Propulsion Labora-
tory. As was noted above, the results reported here are eased upon Apollo VIII
tracking data obtained by means of the NASA Manned Space Flight Network's
Unified S-band Tracking System. The results reported here thus include a
7
direct confirmation of a mascon feature for which they found evidence. This
confirmation is independent in the sense that it is based upon data obtained from
a different tracking system operating in a different n,twork. The present re-
sults were derived using computer programs and types of computers which are
different from the ones employed in their analysis of the Lunar Orbiter data.
The confirmation is thus independent ir. this sense also.
It is planned to refine these results and to continue the analysis in terms of
representations involving spherical harmonics, mass points and mass concen-
trations of various shapes using tracking data obtained from Apollo, Lunar Or-
biter and Anchored IMP spacecraft. Later Apollo flights involve not only ttio
orbits of the command module of the type flown in the Apollo VIII mission but,
in addition, a lunar module in an orbit which approaches to within about fifteen
kilometers of the lunar surface before its rocket engine is fired. It is antici-
pated that Apollo missions of this type may afford opportunities to obtain im-
proved resolution in the estimation of mascon depths and masses.
ACXNOWLEDGEMENTS
Wn thank James W. Ryan and his colleagues of Goddard's Manned Flight
Support Directorate for their help relating to tracking data processing; J. P.
Mayer, W. R. Lacy, A. J. Loyd, R. K. Osburn, R. M. Swalin and their as-
sociates at the NASA Mantled Spacecraft Center for information concerning per-
turbing forces associated with the spacecraft; F. O. Vonbun for lielpful
discussions.
8
REFERENCES
1. to 4. J. Lorell, in Measure of the Moon, Z. Kopal, Ed. (Gordon and Breach;
New 'York, 1967); Robert H. Tolson; and John P. Gapcynski, "An An-
alysis of the Lunar Gravitational Field as Obtained from Lunar Orbiter
Tracking Data" presented at IQSY/COSPAR Assemblies (London, Eng-
land), July 17-18, 1967; William H. Michael, Jr. , "Physical Properties
of the Moon as Obtained from Lunar Orbiter Data," presented at the
Fourteenth General Assembly of the International Union of Geodesy and
Geophysics Meeting, Lucerne, Switzerland, September 1967; W. Thomas
Blackshear, ''Progress on Lunar Gravitational Potential Determination
by Analysis of Lunar Orbiter Tracking Data," Transactions of the Amer-
ican Geophysical Union, 50, 124 (1969).
5. P. M. Muller and W. L. Sjogren, "Mascons: Lunar Mass Concentra-
tions," Science, 161, 680-684 (1968).
6. Data Evaluation Branch, Manned Flight Plans and Analysis Division,
''MSFN Metric Tracking Performance Report AS-503, Report No.
X-832-69-69" (Goddard Space Flight Center, Greenbelt, Maryland).
7. T. L. Felsentreger, J. P. Murphy, J. W. Ryan and L. M. Salter,
"Lunar Gravity Field Determined from Apollo 8 Tracking Data" (in press).
8. P. M. Muller and W. L. Sjogren, "A New Reduction of Lunar Orbiter
Radio Tracking Data in Describing the Lunar Near-Side Gravity Field,"
Transactions of the American Geophysical Union, 50, 124 (1969).
9
REFERENCES (Continued)
9. P. Gottlieb and P. Laing in "Mass Distributions Inferred from Lunar
Orbiter Tracking Data," Transactions of the American Geophysical
Union, 50, 124 (1969).
10
FIGURE CAPTIONS
Figure 1. Doppler residuals from Lunar Orbits of Apollo VIII on December 24,
1568. The upper and lower portions of the Fig. depict residuals ob-
tained in the neighborhood of Sinus Aestuum during the first and seventh
revolutions, respectively. The residuals are plotted vs. position
along the retrograde orbit. The positions in the two revolutions are
indicated by surface tracks which are correspondingly marked in the
central portion of the Fig. The Apollo Lunar landing sites are also
shown.
Figure 2. Apollo VIII First Lunar Orbit Dopper Residuals
Figure 3. Apollo VIII Seventh Lunar Orbit Doppler Residuals
Cz
41
-40	 -30	 -20	 -10	 0	 10	 20	 30	 40
LONGITUDE
•
•
•
FIRST LUNAR ORBIT	 • •	 • •!
310 Km ABOVE	 • • • • • • • !•
SINUS AESTUUM
Hz 0
SINUS	
:'-AESTUUM
5 	
- `^d'dd' 
^10
'	 Al7
0 00 0	 +1
0	
O
00
O	 O	 O
O	 0
O	 Hz 0
O
O	 0
SEVENTH LUNAR ORBIT	 0
112 Km ABOVE	 0SINUS AESTUUM
	
0
00
O
0 0 0010 	
-1
Figure 1 . Doppler residuals from Lunar Orbits of Apol to VI I I on December 24, 1968.
The upper and lower portions of the Fig. depict residuals obtained in the neighbor-
hood of Sinus Aestuum during the first and seventh revolutions, respectively. The
residuals are plotted vs. position along the retrograde orbit. The positions in the
two revolutions are indicated by surface tracks which are correspondingly marked in
the central portion of the Fig. The Apollo Lunar landing sites are also shown.
11
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Lunar mascon evidence from apollo orbits

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