Citation Context

...e Session k2 = 0.0257±0.0025 as reported by Williams et al. [2003]. There is a concordant determination of k2 = 0.026±0.003 based on gravity field variations detected by spacecraft orbiting the Moon [=-=Konopliv et al., 2001-=-]. The Love numbers depend on the radial distribution of the elastic properties, most strongly on the rigidity, or shear modulus, or the related S-wave speed. By themselves the second-degree Love numb...

Citation Context

...enting the Moon, appropriate for mean Earth and mean rotation axes, is given in (Seidelmann et al., 2000). A 2comparison of the series and numerically integrated physical librations is presented in (=-=Konopliv et al., 2001-=-). The LLR reflector coordinates, along with VLBI determined ALSEP transmitter locations (King, Counselman, and Shapiro, 1976), serve as control points for a lunar geodetic network (Davies, Colvin, an...

Citation Context

...omputational resources required for model evaluation. Additionally, orbits about bodies with irregular mass distributions, such as the moon, require a high-degree model to properly propagate an orbit =-=[1]-=-. Unfortunately, an increase in the degree and order of the model by a factor of 10 results in computation time increasing by a factor of 100 [2]. Interpolation models have been developed tomake evalu...

Citation Context

...he spacecraft to the earth Qe = diag ([ 2.82 · 1020 ρ8 , 2.82 · 1020 ρ8 , 7.34 · 1020 ρ8 ]) km2 s4 . The same has been done for the Moon gravitational field asymmetry, by considering the model LP-150 =-=[27]-=-. The standard deviations of the modeled disturbance as a function of ρsm has been estimated, giving a covariance matrix Qm = 1018 ρ8sm I3×3 km2 s4 , where I3×3 is the identity matrix of order 3. The ...

Citation Context

...sed to determine the required control accelerations. However, as discussed later in the paper, due to the physical inability to control the line of nodes during equatorial crossings a switch is made between two controllers in these regions. This leads to suboptimal (but still effective) trajectories. The dynamic model used in this study includes the three primary perturbations that a low-altitude lunar orbiter would experience: the perturbations due to the Earth and Sun’s gravity and due to the nonspherical lunar gravity field. The lunar gravity field is modeled using the LP165P gravity model [2] obtained from the NASA PDS Geosciences Node. Previous Studies Lunar Mapping Missions Some of the first lunar mapping missions date back to the 1960s. As the United States and Russia were competing to be the first to perform a manned mission to land on the Moon, both countries began conducting unmanned scientific missions to the Moon in order to study the lunar surface and test soft landing approaches. NASA began its first set of unmanned lunar missions in the early 1960s with the Ranger program [3]. The goal of each of the Ranger missions was to take high resolution images of the Moon and ret...

Citation Context

...8·1010 ρ4 , 1.68·10 10 ρ4 , 2.71·10 10 ρ4 ]) and ωe ∈ R3 is an independent white noise with standard normal distribution N (0, I). The same has been done for the Moon by considering the model LP-150 (=-=Konopliv et al., 2001-=-). The standard deviations of the modelled disturbance as a function of ρs$, reported in Fig. 2(b), can be approximated by ω$ =G$ωm, whereG$ = 109 ρ4 s$ I and ωm ∈ R3 is an independent white noise wit...