## 1. Introduction

[2] Direct tracking of the lunar-orbiting satellites from the Earth is not possible over the farside due to the synchronous rotation of the Moon about the Earth. Only the limb region of the farside is covered but with increased measurement noise [*Konopliv et al.*, 2001], which results in a lack of direct Doppler data over ∼40% of the entire lunar surface. Recently, the SELENE mission obtained 4-way Doppler data over the farside by indirectly tracking the main orbiter with a small relay satellite [*Namiki et al.*, 2009]. Those data improved the farside gravity to spherical harmonic degree ∼90. However, high-resolution gravity information still comes from satellites with lower orbiting altitudes such as Lunar Prospector [*Konopliv et al.*, 2001], for which no farside tracking data are available. The orthogonal sets of spherical harmonic functions are the candidates to parameterize the Newtonian potential fields since they satisfy the Laplace differential equations. However, not all of them are necessarily resolvable especially under the circumstance that the noisy data are not available uniformly over the globe. In order to overcome such problem, the power law, or Kaula's rule [*Kaula*, 1966], has been often used to obtain solutions of the gravitational fields of the planetary bodies from analysis of un-evenly sampled tracking data.

[3] The power law constraint, although it biases the solution, stabilizes a global gravity field parameterized with (non-localized) spherical harmonic functions, up to the spatial resolution corresponding to the orbiting altitude, by preventing high-degree terms from developing excessive power [e.g., *Marsh et al.*, 1990; *Lemoine et al.*, 1997; *Smith et al.*, 1999; *Konopliv et al.*, 2001]. The exploitation of Doppler tracking data over the nearside of the Moon, however, is limited due to the farside data gap, no matter how high a gravity field is modeled in degree and order, as noted by *Konopliv et al.* [2001]. Recently, *Han* [2008] proposed that the global gravity field can be modeled by implementing an alternative set of basis functions (both regionally-concentrated ones and their complements). The advantage over the ubiquitous spherical harmonic representation is that the nearside gravity field can be estimated without introducing the power law constraint. It is then also possible to simultaneously construct the nearside gravity field to a high resolution in order to fully exploit the low altitude measurements and the farside gravity field with a low resolution.

[4] In this study, we extend the work by *Han* [2008] discussing regional gravity fields with the line-of-sight acceleration measurements, but in a fully dynamic mode, to develop optimally-constrained global gravity models of the Moon. The innovation is to apply the power law constraint only over the farside and limb regions where direct observations are non-existent or the observational constraint is weak because of tracking geometry. The nearside gravity field is estimated based on the tracking data to degree and order 150. On the contrary, the farside gravity field is obtained by means of the nearside tracking data and the power law constraint.