HIGH DEGREE AND ORDER SPHERICAL HARMONIC
MODELS FOR THE MOON FROM CLEMENTINE
AND HISTORIC S-BAND DATA
F. G. Lemoine 1 , D. E. Smithl, M. T. Zuber 1 ,2 and G. A. Neumann 3
1 Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center,
Greenbelt, MD 20771 U.S.A.
2 Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology
Cambridge, MA 02139-4307 U.S.A.
3 Department of Earth and Planetary Sciences, 10hns Hopkins University
Baltimore, MD 21218 U.S.A.
INTRODUCTION
A spherical harmonic model complete to degree and order seventy has been developed from
Doppler tracking of the Lunar Orbiters, the Apollo 15 and 16 subsatellites, and the
Clementine spacecraft. The model combines 361,000 observations from Clementine with
347,000 historical observations. The model was developed using the method of Lerch
[1991] in order to derive a more realistic realization of the uncertainties associated with this
model. An a priori power law of the form 15 x 10- 5 /12, where I is the spherical harmonic
degree, was applied in this model. The Clementine data provide a powerful constraint on
the low degree harmonics, and the sectoral terms through degree twenty, by virtue of the
spacecraft orbit geometry, and the excellent quality of the tracking data. The gravity
anomalies in our model, GLGM-2 (Goddard Lunar Gravity Model-2), have a dynamic
range of -294 to +358 mGals when evaluated on the lunar surface at a reference radius of
1738 km. The error predicted from the GLGM-2 covariance ranges from 14 mGals on the
equatorial near side to 44 mGals over the high latitude regions of the lunar far side. The
model resolves the mascon basins fIrst deduced from Lunar Orbiter tracking [Muller and
Sjogren, 1968]. Mare Orientale is resolved as a horseshoe-shaped low with an amplitude
of -225 mGals centered on the inner and outer Rook rings. Although direct tracking is not
available over substantial regions of the lunar farside, the model still resolves far side
basins such as South-Pole Aitken, Hertzsprung, Korolev, Moscoviens, and Tsiolkovsky.
REVIEW OF LUNAR GRAVITY FIELD DETERMINATION
The Clementine spacecraft became the fIrst US. spacecraft to return to lunar orbit in more
than twenty years, since the launch of the RAE-2 (Explorer 49) satellite: in 1974. Until the
launch of Clementine the primary sources of tracking data for use in gravity models were
the Lunar Orbiters and the Apollo spacecraft. The Lunar Orbiters were inserted into
elliptical orbits with periapses of 50 to 100 km. The Apollo spacecraft were inserted into
near-circular orbits at mean altitudes of 100 km, although some tracking was acquired from
altitudes as low as 10 to 20 km. Thus, the gravity fIeld of the Moon has been sampled at a
resolution unprecedented for other planetary orbiters, at either the Earth, Venus, or Mars.
However, the geographic extent of the coverage is incomplete. Since no lunar mission has
176
MODELS FOR THE MOON FROM CLEMENTINE
AND HISTORIC S-BAND DATA
F. G. Lemoine 1 , D. E. Smithl, M. T. Zuber 1 ,2 and G. A. Neumann 3
1 Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center,
Greenbelt, MD 20771 U.S.A.
2 Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology
Cambridge, MA 02139-4307 U.S.A.
3 Department of Earth and Planetary Sciences, 10hns Hopkins University
Baltimore, MD 21218 U.S.A.
INTRODUCTION
A spherical harmonic model complete to degree and order seventy has been developed from
Doppler tracking of the Lunar Orbiters, the Apollo 15 and 16 subsatellites, and the
Clementine spacecraft. The model combines 361,000 observations from Clementine with
347,000 historical observations. The model was developed using the method of Lerch
[1991] in order to derive a more realistic realization of the uncertainties associated with this
model. An a priori power law of the form 15 x 10- 5 /12, where I is the spherical harmonic
degree, was applied in this model. The Clementine data provide a powerful constraint on
the low degree harmonics, and the sectoral terms through degree twenty, by virtue of the
spacecraft orbit geometry, and the excellent quality of the tracking data. The gravity
anomalies in our model, GLGM-2 (Goddard Lunar Gravity Model-2), have a dynamic
range of -294 to +358 mGals when evaluated on the lunar surface at a reference radius of
1738 km. The error predicted from the GLGM-2 covariance ranges from 14 mGals on the
equatorial near side to 44 mGals over the high latitude regions of the lunar far side. The
model resolves the mascon basins fIrst deduced from Lunar Orbiter tracking [Muller and
Sjogren, 1968]. Mare Orientale is resolved as a horseshoe-shaped low with an amplitude
of -225 mGals centered on the inner and outer Rook rings. Although direct tracking is not
available over substantial regions of the lunar farside, the model still resolves far side
basins such as South-Pole Aitken, Hertzsprung, Korolev, Moscoviens, and Tsiolkovsky.
REVIEW OF LUNAR GRAVITY FIELD DETERMINATION
The Clementine spacecraft became the fIrst US. spacecraft to return to lunar orbit in more
than twenty years, since the launch of the RAE-2 (Explorer 49) satellite: in 1974. Until the
launch of Clementine the primary sources of tracking data for use in gravity models were
the Lunar Orbiters and the Apollo spacecraft. The Lunar Orbiters were inserted into
elliptical orbits with periapses of 50 to 100 km. The Apollo spacecraft were inserted into
near-circular orbits at mean altitudes of 100 km, although some tracking was acquired from
altitudes as low as 10 to 20 km. Thus, the gravity fIeld of the Moon has been sampled at a
resolution unprecedented for other planetary orbiters, at either the Earth, Venus, or Mars.
However, the geographic extent of the coverage is incomplete. Since no lunar mission has
176