Topography of the Lunar Poles and Application to Geodesy with the Lunar Reconnaissance Orbiter

The Lunar Orbiter Laser Altimeter (LOLA) [1] onboard the Lunar Reconnaissance Orbiter (LRO) [2] has been operating continuously since July 2009 [3], accumulating approx.5.4 billion measurements from 2 billion on-orbit laser shots. LRO s near-polar orbit results in very high data density in the immediate vicinity of the lunar poles, which are each sampled every ~2h. With more than 10,000 orbits, high-resolution maps can be constructed [4] and studied [5]. However, this requires careful processing of the raw data, as subtle errors in the spacecraft position and pointing can lead to visible artifacts in the final map. In other locations on the Moon, ground tracks are subparallel and longitudinal separations are typically a few hundred meters. Near the poles, the track intersection angles can be large and the inter-track spacing is small (above 80 latitude, the effective resolution is better than 50m). Precision Orbit Determination (POD) of the LRO spacecraft [6] was performed to satisfy the LOLA and LRO mission requirements, which lead to a significant improvement in the orbit position knowledge over the short-release navigation products. However, with pixel resolutions of 10 to 25 meters, artifacts due to orbit reconstruction still exist. Here, we show how the complete LOLA dataset at both poles can be adjusted geometrically to produce a high-accuracy, high-resolution maps with minimal track artifacts. We also describe how those maps can then feedback to the POD work, by providing topographic base maps with which individual LOLA altimetric measurements can be contributing to orbit changes. These direct altimetry constraints improve accuracy and can be used more simply than the altimetric crossovers [6]

High-resolution Local Gravity Model of the South Pole of the Moon from GRAIL Extended Mission Data

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6deg by 1/6deg (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40deg. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models

The Effect of Geocenter Motion on Jason-2 and Jason-1 Orbits and the Mean Sea Level

We have investigated the impact of geocenter motion on Jason-2 orbits. This was accomplished by computing a series of Jason-1, Jason-2 GPS-based and SLR/DORIS-based orbits using ITRF2008 and the IGS repro1 framework based on the most recent GSFC standards. From these orbits, we extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. The fitted annual and seasonal terms of these time-series are compared to two different geocenter motion models. Subsequently, we included the geocenter motion corrections in the POD process as a degree-1 loading displacement correction to the tracking network. The analysis suggested that the GSFC's Jason-2 std0905 GPS-based orbits are closely tied to the center of mass (CM) of the Earth whereas the SLR/DORIS std0905 orbits are tied to the center of figure (CF) of the ITRF2005 (Melachroinos et al., 2012). In this study we extend the investigation to the centering of the GPS constellation and the way those are tied in the Jason-1 and Jason-2 POD process. With a new set of standards, we quantify the GPS and SLR/DORIS-based orbit centering during the Jason-1 and Jason-2 inter-calibration period and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the full term of the geocenter motion correction

Time Variable Gravity modeling for Precise Orbits Across the TOPEX/Poseidon, Jason-l and Jason-2 Missions

Modeling of the Time Variable Gravity (TVG) is believed to constitute one of the the largest remaining source of orbit error for altimeter satellite POD. The GSFC operational TVG model consists of forward modeling the atmospheric gravity using ECMWF 6-hour pressure data, a GRACE derived 20x20 annual field to account for changes in the hydrology and ocean water mass, and linear rates for C20, C30, C40, based on 17 years of SLR data analysis (IERS 2003) using the EIGEN-GL04S1 (a GRACE+Lageos-based geopotential solution). Although the GSFC Operational model can be applied from 1987, there may be long-term variations not captured by these linear models, and more importantly the linear models may not be consistent with more recent surface mass trends due to global climate change, We have evaluated the impact of TVG in two different wavs: (1) by using the more recent EIGEN-6S gravity model developed by the GFZ/GRGS tearm, which consists of annual, semi-annual and secular changes in the coefficients to 50x50 determined over 8(?) years of GRACE+Lageos+GOCE data (2003-200?): (2) Application of 4x4 solutions developed from a multi satellite SLR+DORIS solution based on GGM03S that span the period from 1993 to 2011. We have evaluated the recently released EIGEN6s static and time-varying gravity field for Jason-2 (J2). Jason-I (J1), and TOPEX/Posiedon (TP) Precise Orbit Determination (POD) spanning 1993-2011. Although EIGEN6s shows significant improvement for J2POD spanning 2008 - 2011, it also shows significant degradation for TP POD from 1992. The GSFC 4x4 time SLR+DORIS-based series spans 1993 to mid 2011, and shows promise for POD. We evaluate the performance of the different TVG models based on analysis of tracking data residuals use of independent data such as altimeter crossovers, and through analysis of differences with internally-generated and externally generated orbits

Recovery of Bennu's Orientation for the OSIRIS-REx Mission: Implications for the Spin State Accuracy and Geolocation Errors

The goal of the OSIRIS-REx mission is to return a sample of asteroid material from Near-Earth Asteroid (101955) Bennu. The role of the navigation and fight dynamics team is critical for the spacecraft to execute a precisely planned sampling maneuver over a specifically-selected landing site. In particular, the orientation of Bennu needs to be recovered with good accuracy during orbital operations to contribute as small an error as possible to the landing error budget. Although Bennu is well characterized from Earth-based radar observations, its orientation dynamics are not sufficiently known to exclude the presence of a small wobble. To better understand this contingency and evaluate how well the orientation can be recovered in the presence of a large 1 degree wobble, we conduct a comprehensive simulation with the NASA GSFC GEODYN orbit determination and geodetic parameter estimation software. We describe the dynamic orientation modeling implemented in GEODYN in support of OSIRIS-REx operations, and show how both altimetry and imagery data can be used as either undifferenced (landmark, direct altimetry) or differenced (image crossover, altimetry crossover) measurements. We find that these two different types of data contribute differently to the recovery of instrument pointing or planetary orientation. When upweighted, the absolute measurements help reduce the geolocation errors, despite poorer astrometric (inertial) performance. We find that with no wobble present, all the geolocation requirements are met. While the presence of a large wobble is detrimental, the recovery is still reliable thanks to the combined use of altimetry and imagery data

GSFC OSTM, Jason-l and TOPEX POD Update

The OSTM (Jason-2) has been in orbit for three years (since June 2008), and the full suite of altimeter data from TOPEX/Poseidon, Jason-I and Jason-2 now span nearly twenty years since the launch of TOPEX in 1992. Issues that affect the stability of the orbits through time and the orbit accuracy include the reference frame, the radiation pressure models for the altimeter satellites and the fidelity of the dynamic force model, including time-variable gravity, as well as the performance of the individual tracking systems. We have conducted detailed analyses of the new ITRF2008 reference frame and find only a small effect on global mean sea level compared to ITRF2005, although we note an improvement in POD quality over the most recent time periods for Jason-2. In the past year we have developed a new time series of orbits for TOPEX/Poseidon, Jason-I, and Jason-2 based on the ITRF2008 reference frame using SLR and DORIS data and for Jason-2 using GPS data. In addition, we have continued to experiment with improvements to the radiation pressure model for the altimeter satellites in particular the Jason satellites since these nonconservative force model errors now rank as the most outstanding source of error on altimeter satellite POD. In the previous (ITRF2005-based) and current (ITRF2008-based) orbits we have relied on a simplified time-variable gravity (TVG) model, derived from GRACE solutions. We have recently experimented with improvements using higher fidelity TVG models (both temporally and spatially) and report on the results. We have computed a time series of GPS-only reduced-dynamic orbits at GSFC, and used these in conjunction with the SLR-DORIS dynamic and reduced-dynamic orbits to assess reference fiame stability with respect to the different tracking systems for both ITRF2005 and ITRF2008. We show through internal (GSFConly) and external comparisons (with other analysis centers) that the radial orbit accuracy for Jason-2 remains at I cm

Global and Local Gravity Field Models of the Moon Using GRAIL Primary and Extended Mission Data

The Gravity Recovery and Interior Laboratory (GRAIL) mission was designed to map the structure of the lunar interior from crust to core and to advance the understanding of the Moon's thermal evolution by producing a high-quality, high-resolution map of the gravitational field of the Moon. The mission consisted of two spacecraft, which were launched in September 2011 on a Discovery-class NASA mission. Ka-band tracking between the two satellites was the single science instrument, augmented by tracking from Earth using the Deep Space Network (DSN)

Serendipitous Geodesy from Bennu's Short-Lived Moonlets

The Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx; or OREx) spacecraft arrived at its target, near-Earth asteroid (101955) Bennu, on December 3, 2018. The OSIRIS-REx spacecraft has since collected a wealth of scientific information in order to select a suitable site for sampling. Shortly after insertion into orbit on December 31, 2018, particles were identified in starfield images taken by the navigation camera (NavCam 1). Several groups within the OSlRlS-REx team analyzed the particle data in an effort to better understand this newfound activity of Bennu and to investigate the potential sensitivity of the particles to Bennu's geophysical parameters. A number of particles were identified through automatic and manual methods in multiple images, which could be turned into short sequences of optical tracking observations. Here, we discuss the precision orbit determination (OD) effort focused on these particles at NASA GSFC, which involved members of the Independent Navigation Team (INT) in particular. The particle data are combined with other OSIRIS-REx tracking data (radiometric from OSN and optical landmark data) using the NASA GSFC GEODYN orbit determination and geodetic parameter estimation software. We present the results of our study, particularly those pertaining to the gravity field of Bennu. We describe the force modeling improvements made to GEODYN specifically for this work, e.g., with a raytracing-based modeling of solar radiation pressure. The short-lived, low-flying moonlets enable us to determine a gravity field model up to a relatively high degree and order: at least degree 6 without constraints, and up to degree 10 when applying Kaula-like regularization. We can backward- and forward-integrate the trajectory of these particles to the ejection and landing sites on Bennu. We assess the recovered field by its impact on the OSIRIS-REx trajectory reconstruction and prediction quality in the various mission phases (e.g., Orbital A, Detailed Survey, and Orbital B)

The Functional DRD3 Ser9Gly Polymorphism (rs6280) Is Pleiotropic, Affecting Reward as Well as Movement

Abnormalities of motivation and behavior in the context of reward are a fundamental component of addiction and mood disorders. Here we test the effect of a functional missense mutation in the dopamine 3 receptor (DRD3) gene (ser9gly, rs6280) on reward-associated dopamine (DA) release in the striatum. Twenty-six healthy controls (HCs) and 10 unmedicated subjects with major depressive disorder (MDD) completed two positron emission tomography (PET) scans with [11C]raclopride using the bolus plus constant infusion method. On one occasion subjects completed a sensorimotor task (control condition) and on another occasion subjects completed a gambling task (reward condition). A linear regression analysis controlling for age, sex, diagnosis, and self-reported anhedonia indicated that during receipt of unpredictable monetary reward the glycine allele was associated with a greater reduction in D2/3 receptor binding (i.e., increased reward-related DA release) in the middle (anterior) caudate (p<0.01) and the ventral striatum (p<0.05). The possible functional effect of the ser9gly polymorphism on DA release is consistent with previous work demonstrating that the glycine allele yields D3 autoreceptors that have a higher affinity for DA and display more robust intracellular signaling. Preclinical evidence indicates that chronic stress and aversive stimulation induce activation of the DA system, raising the possibility that the glycine allele, by virtue of its facilitatory effect on striatal DA release, increases susceptibility to hyperdopaminergic responses that have previously been associated with stress, addiction, and psychosis