incorporated satellite-to-satellite tracking, no direct infonnation is available for portions of
the lunar far side that cannot be seen from Earth. In addition, the Lunar Orbiters and
Apollo spacecraft were placed in orbits whose periapses were close to the lunar equator - so
that even knowledge of the higher latitude regions of the lunar near side is less detailed.
Clementine, in contrast was inserted into an elliptical lunar orbit, with a mean periapse
altitude of 415 km. Clementine now provides a powerful constraint on the low degree and
order field, through degree and order twenty, whereas the historical data provide
distributed regions of high resolution coverage ± 30° of the lunar equator.
The earliest models of the lunar potential were derived from radiometric tracking of the
Lunar Orbiters. Because of the primitive nature of the computers available at the time,
investigators were limited in the size of the models that they could develop. So, alternate
methods, other than decomposition of the gravity field into spherical harmonics, were
employed. Muller and Sjogren [1968], Wong et al. [1971], Sjogren et al. [1972, 1974a,
1974b, 1974c], for instance, mapped the line of sight accelerations or estimated discrete
masses over the lunar surface. Liu and Laing [1971] developed an eighth degree and order
model, with zonals complete through degree fifteen, and Michael and Blackshear [1972]
developed a 13th degree and order model. However these models have a maximum
resolution of 26 degrees (780 km) on the lunar surface - woefully inadequate given the
altitudes from which much of the satellite tracking data have been acquired. Ferrari [1977]
and Ananda [1977] developed gravity solutions using the long periodic variations in the
orbital elements of the Apollo 15 and 16 subsatellites and the Lunar Orbiter 5 spacecraft
This method has the merit of implicitly accounting for the effects of the gravity field on the
lunar far side. Bills and Ferrari [1980] combined the data of Wong et al. [1971], the data
of Ananda [1977], and incorporated lunar laser ranging. Lunar laser ranging is sensitive
to the low degree and order harmonics through their influence on the lunar librations
[Dickey et al., 1994], and provides a complimentary and independent means to determine
the low degree and order field.
Konoplivet al. [1993] reanalyzed the available Lunar Orbiter and Apollo data, and derived
a 60th degree and order model. Taking advantage of the high speed and memory capacity
of modem computers, the field of Konopliv et al. [1993], known as Lun6Od, was the first
serious attempt to exhaust the available signal in the tracking data in a spherical harmonic
model. Their work was also of great value for the scientific community, since they
undoubtedly rescued the historic tracking data from almost certain oblivion. Although the
model fits the satellite data admirably, the coefficients have excessive power. When the
anomalies are evaluated on the lunar surface, striping is apparent over the entire planet -
which vanishes when the anomalies are evaluated at an altitude of 100 kIn.
Therefore in our analysis, our objective was to derive a high degree and order spherical
harmonic model useful for geophysical analyses. This field should have the following
characteristics: (1) it should attenuate the power of the high degree tenns compared to
Lun6Od, to avoid the excessive striping apparent in that model; (2) it must fit the data at
least as well as Lun6Od; (3) the model should incorporate Clementine tracking data.
DATA
The data used in GLGM-2 consist of Doppler tracking of the U. S. Lunar Orbiters 1 to 5,
the Apollo 15 and 16 subsatellites, and the Clementine spacecraft. The orbits of these
spacecraft are reviewed in Konopliv et al. [1993] and Lemoine et al. [1995]. Lunar
Orbiters 1 to 3 had low inclinations (11 ° to 21°). Lunar Orbiters 4 and 5 had near polar
inclinations of 85°. The Apollo subsatellites were deployed in retrograde, near-circular
177
the lunar far side that cannot be seen from Earth. In addition, the Lunar Orbiters and
Apollo spacecraft were placed in orbits whose periapses were close to the lunar equator - so
that even knowledge of the higher latitude regions of the lunar near side is less detailed.
Clementine, in contrast was inserted into an elliptical lunar orbit, with a mean periapse
altitude of 415 km. Clementine now provides a powerful constraint on the low degree and
order field, through degree and order twenty, whereas the historical data provide
distributed regions of high resolution coverage ± 30° of the lunar equator.
The earliest models of the lunar potential were derived from radiometric tracking of the
Lunar Orbiters. Because of the primitive nature of the computers available at the time,
investigators were limited in the size of the models that they could develop. So, alternate
methods, other than decomposition of the gravity field into spherical harmonics, were
employed. Muller and Sjogren [1968], Wong et al. [1971], Sjogren et al. [1972, 1974a,
1974b, 1974c], for instance, mapped the line of sight accelerations or estimated discrete
masses over the lunar surface. Liu and Laing [1971] developed an eighth degree and order
model, with zonals complete through degree fifteen, and Michael and Blackshear [1972]
developed a 13th degree and order model. However these models have a maximum
resolution of 26 degrees (780 km) on the lunar surface - woefully inadequate given the
altitudes from which much of the satellite tracking data have been acquired. Ferrari [1977]
and Ananda [1977] developed gravity solutions using the long periodic variations in the
orbital elements of the Apollo 15 and 16 subsatellites and the Lunar Orbiter 5 spacecraft
This method has the merit of implicitly accounting for the effects of the gravity field on the
lunar far side. Bills and Ferrari [1980] combined the data of Wong et al. [1971], the data
of Ananda [1977], and incorporated lunar laser ranging. Lunar laser ranging is sensitive
to the low degree and order harmonics through their influence on the lunar librations
[Dickey et al., 1994], and provides a complimentary and independent means to determine
the low degree and order field.
Konoplivet al. [1993] reanalyzed the available Lunar Orbiter and Apollo data, and derived
a 60th degree and order model. Taking advantage of the high speed and memory capacity
of modem computers, the field of Konopliv et al. [1993], known as Lun6Od, was the first
serious attempt to exhaust the available signal in the tracking data in a spherical harmonic
model. Their work was also of great value for the scientific community, since they
undoubtedly rescued the historic tracking data from almost certain oblivion. Although the
model fits the satellite data admirably, the coefficients have excessive power. When the
anomalies are evaluated on the lunar surface, striping is apparent over the entire planet -
which vanishes when the anomalies are evaluated at an altitude of 100 kIn.
Therefore in our analysis, our objective was to derive a high degree and order spherical
harmonic model useful for geophysical analyses. This field should have the following
characteristics: (1) it should attenuate the power of the high degree tenns compared to
Lun6Od, to avoid the excessive striping apparent in that model; (2) it must fit the data at
least as well as Lun6Od; (3) the model should incorporate Clementine tracking data.
DATA
The data used in GLGM-2 consist of Doppler tracking of the U. S. Lunar Orbiters 1 to 5,
the Apollo 15 and 16 subsatellites, and the Clementine spacecraft. The orbits of these
spacecraft are reviewed in Konopliv et al. [1993] and Lemoine et al. [1995]. Lunar
Orbiters 1 to 3 had low inclinations (11 ° to 21°). Lunar Orbiters 4 and 5 had near polar
inclinations of 85°. The Apollo subsatellites were deployed in retrograde, near-circular
177