The coefficient variances at degree I, for the Konopliv et al. [1993] and GLGM-2 are
depicted in Figure 1. The sigma variances, for GLGM-2, where the sigmas from the
GLGM-2 gravity field solution for each coefficient, Clm and Slm, have been substituted
into the above equation are also shown. The Konopliv et al., [1993] have a power greater
than that indicated by Kaula's rule, whereas the power in the coefficients of GLGM-2 are
strongly attenuated at the higher degrees. We experimented with the application of a
weaker constraint: 30 x lOe-5/1 2 and derived a solution identical in data content and
weighting to GLGM-2, but where the weaker constraint was applied (LGM-309b). As
illustrated in Figure 1, the power of the coefficients is still below the power law of 15 x 105/1 2 . However, close examination of the anomaly map for the LGM-309b solution shows
that the presence of substantially greater striping and other artifacts on the lunar far side.
Gravity anomalies
When evaluated on the surface, with a reference radius of 1738 lan, and after removal of
the appropriate hydrostatic terms, the gravity anomalies have a dynamic range of -294 to
+358 mGals.
In contrast the gravity anomalies of the Konopliv et al. [1993] solution
have a larger dynamic range of -454 to 529 mGals, because of the power contained in the
high degree terms.
The field resolves the major near side mass concentrations (or "mascons") first deduced
from Lunar Orbiter tracking [Muller and Sjogren, 1968], including Imbrium, Serenitatis,
Crisium, Smythii, and Humorum. Mare Orientale, the youngest ringed impact basin on
the Moon, is resolved as an axisymmetric low centered between the inner and outer rook
rings, wit a positive anomaly at its center of + 125 mGals. South-Pole Aitken, the largest
known impact basin in the Solar System, with a diameter of 2500 lan, and a rim to floor
depth determined from Clementine laser altimetry of 12 lan [Zuber et al., 1994], has
overall a modest gravity anomaly of only -100 mGals to -125 mGals. Considering the size
and depth of this basin, and the shallow magnitude of the gravity anomaly, this feature
must be approximately 90 percent compensated [Zuber et al., 1994].
Although no direct tracking is available for large sections of the lunar far side, the field still
resolves far side basins such as Hertzsprung, Meendeleev, Tsiolkovsky, Mare
Moscoviense, Korolev, and Freundlich-Sharonov. Consistent with the work of previous
investigators, we find that most basins on the lunar far side appear as gravity lows, in
contrast to the lunar near side.
GLGM-2 exhibits greater detail in the equatorial regions, than at high latitudes. This
characteristic is a result of the data sampling and the orbit geometry of the contributing
satellites, and is not a genuine feature of the lunar gravity field
Tests with the RMS of fit
We performed extensive tests with the RMS of fit to the satellite tracking data. Since we
had no withheld data, we selected a series of arcs that were representative of each set of
data. These results are summarized in Table 3. We fit all the satellites, with the exception
of Lunar Orbiter 3, the Apollo-16 sub satellite, to comparable or improved levels over
Lun6Od. The increase associated with Lunar Orbiter 3 is puzzling, and perhaps indicates
some mismodeling associated with that satellite. The fit to the ApoUo-16 subsatellite data
indicates that our a priori weights for that satellite (3 cm/s) were probably too low. We
182
depicted in Figure 1. The sigma variances, for GLGM-2, where the sigmas from the
GLGM-2 gravity field solution for each coefficient, Clm and Slm, have been substituted
into the above equation are also shown. The Konopliv et al., [1993] have a power greater
than that indicated by Kaula's rule, whereas the power in the coefficients of GLGM-2 are
strongly attenuated at the higher degrees. We experimented with the application of a
weaker constraint: 30 x lOe-5/1 2 and derived a solution identical in data content and
weighting to GLGM-2, but where the weaker constraint was applied (LGM-309b). As
illustrated in Figure 1, the power of the coefficients is still below the power law of 15 x 105/1 2 . However, close examination of the anomaly map for the LGM-309b solution shows
that the presence of substantially greater striping and other artifacts on the lunar far side.
Gravity anomalies
When evaluated on the surface, with a reference radius of 1738 lan, and after removal of
the appropriate hydrostatic terms, the gravity anomalies have a dynamic range of -294 to
+358 mGals.
In contrast the gravity anomalies of the Konopliv et al. [1993] solution
have a larger dynamic range of -454 to 529 mGals, because of the power contained in the
high degree terms.
The field resolves the major near side mass concentrations (or "mascons") first deduced
from Lunar Orbiter tracking [Muller and Sjogren, 1968], including Imbrium, Serenitatis,
Crisium, Smythii, and Humorum. Mare Orientale, the youngest ringed impact basin on
the Moon, is resolved as an axisymmetric low centered between the inner and outer rook
rings, wit a positive anomaly at its center of + 125 mGals. South-Pole Aitken, the largest
known impact basin in the Solar System, with a diameter of 2500 lan, and a rim to floor
depth determined from Clementine laser altimetry of 12 lan [Zuber et al., 1994], has
overall a modest gravity anomaly of only -100 mGals to -125 mGals. Considering the size
and depth of this basin, and the shallow magnitude of the gravity anomaly, this feature
must be approximately 90 percent compensated [Zuber et al., 1994].
Although no direct tracking is available for large sections of the lunar far side, the field still
resolves far side basins such as Hertzsprung, Meendeleev, Tsiolkovsky, Mare
Moscoviense, Korolev, and Freundlich-Sharonov. Consistent with the work of previous
investigators, we find that most basins on the lunar far side appear as gravity lows, in
contrast to the lunar near side.
GLGM-2 exhibits greater detail in the equatorial regions, than at high latitudes. This
characteristic is a result of the data sampling and the orbit geometry of the contributing
satellites, and is not a genuine feature of the lunar gravity field
Tests with the RMS of fit
We performed extensive tests with the RMS of fit to the satellite tracking data. Since we
had no withheld data, we selected a series of arcs that were representative of each set of
data. These results are summarized in Table 3. We fit all the satellites, with the exception
of Lunar Orbiter 3, the Apollo-16 sub satellite, to comparable or improved levels over
Lun6Od. The increase associated with Lunar Orbiter 3 is puzzling, and perhaps indicates
some mismodeling associated with that satellite. The fit to the ApoUo-16 subsatellite data
indicates that our a priori weights for that satellite (3 cm/s) were probably too low. We
182