Kinetic modeling of sodium in the lunar exosphere

Our knowledge about the lunar environment is based on a large volume of ground-based, remote, and in situ observations. These observations have been conducted at different times and sampled different pieces of such a complex system as the surface-bound exosphere of the Moon. Numerical modeling is the tool that can link results of these separate observations into a single picture. Being validated against previous measurements, models can be used for predictions and interpretation of future observations results. In this paper we present a kinetic model of the sodium exosphere of the Moon as well as results of its validation against a set of ground-based and remote observations. The unique characteristic of the model is that it takes the orbital motion of the Moon and the Earth into consideration and simulates both the exosphere as well as the sodium tail self-consistently. The extended computational domain covers the part of the Earth’s orbit at new Moon, which allows us to study the effect of Earth’s gravity on the lunar sodium tail. The model is fitted to a set of ground-based and remote observations by tuning sodium source rate as well as values of sticking, and accommodation coefficients. The best agreement of the model results with the observations is reached when all sodium atoms returning from the exosphere stick to the surface and the net sodium escape rate is about 5.3 × 1022 s−1.

Improved star camera attitude data and their effect on the gravity field

Efforts are ongoing to decrease the noise of the GRACE gravity field models and hence to arrive closer to the GRACE baseline. The most significant error sources belong the untreated errors in the observation data and the imperfections in the background models. The recent study (Bandikova&Flury,2014) revealed that the current release of the star camera attitude data (SCA1B RL02) contain noise systematically higher than expected by about a factor 3-4. This is due to an incorrect implementation of the algorithms for quaternion combination in the JPL processing routines. Generating improved SCA data requires that valid data from both star camera heads are available which is not always the case because the Sun and Moon at times blind one camera. In the gravity field modeling, the attitude data are needed for the KBR antenna offset correction and to orient the non-gravitational linear accelerations sensed by the accelerometer. Hence any improvement in the SCA data is expected to be reflected in the gravity field models. In order to quantify the effect on the gravity field, we processed one month of observation data using two different approaches: the celestial mechanics approach (AIUB) and the variational equations approach (ITSG). We show that the noise in the KBR observations and the linear accelerations has effectively decreased. However, the effect on the gravity field on a global scale is hardly evident. We conclude that, at the current level of accuracy, the errors seen in the temporal gravity fields are dominated by errors coming from sources other than the attitude data.

Time variable Earth’s gravity field from SLR satellites

The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 %. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.