Gravity Recovery and Interior Laboratory (GRAIL): Mapping the Lunar Interior from Crust to Core

The Gravity Recovery and Interior Laboratory (GRAIL) is a spacecraft-to-spacecraft tracking mission that was developed to map the structure of the lunar interior by producing a detailed map of the gravity field. The resulting model of the interior will be used to address outstanding questions regarding the Moon’s thermal evolution, and will be applicable more generally to the evolution of all terrestrial planets. Each GRAIL orbiter contains a Lunar Gravity Ranging System instrument that conducts dual-one-way ranging measurements to measure precisely the relative motion between them, which in turn are used to develop the lunar gravity field map. Each orbiter also carries an Education/Public Outreach payload, Moon Knowledge Acquired by Middle-School Students (MoonKAM), in which middle school students target images of the Moon for subsequent classroom analysis. Subsequent to a successful launch on September 10, 2011, the twin GRAIL orbiters embarked on independent trajectories on a 3.5-month-long cruise to the Moon via the EL-1 Lagrange point. The spacecraft were inserted into polar orbits on December 31, 2011 and January 1, 2012. After a succession of 19 maneuvers the two orbiters settled into precision formation to begin science operations in March 1, 2012 with an average altitude of 55 km. The Primary Mission, which consisted of three 27.3-day mapping cycles, was successfully completed in June 2012. The extended mission will permit a second three-month mapping phase at an average altitude of 23 km. This paper provides an overview of the mission: science objectives and measurements, spacecraft and instruments, mission development and design, and data flow and data products.     

The Scientific Measurement System of the Gravity Recovery and Interior Laboratory (GRAIL) Mission

The Gravity Recovery and Interior Laboratory (GRAIL) mission to the Moon utilized an integrated scientific measurement system comprised of flight, ground, mission, and data system elements in order to meet the end-to-end performance required to achieve its scientific objectives. Modeling and simulation efforts were carried out early in the mission that influenced and optimized the design, implementation, and testing of these elements. Because the two prime scientific observables, range between the two spacecraft and range rates between each spacecraft and ground stations, can be affected by the performance of any element of the mission, we treated every element as part of an extended science instrument, a science system. All simulations and modeling took into account the design and configuration of each element to compute the expected performance and error budgets. In the process, scientific requirements were converted to engineering specifications that became the primary drivers for development and testing. Extensive simulations demonstrated that the scientific objectives could in most cases be met with significant margin. Errors are grouped into dynamic or kinematic sources and the largest source of non-gravitational error comes from spacecraft thermal radiation. With all error models included, the baseline solution shows that estimation of the lunar gravity field is robust against both dynamic and kinematic errors and a nominal field of degree 300 or better could be achieved according to the scaled Kaula rule for the Moon. The core signature is more sensitive to modeling errors and can be recovered with a small margin.     

The Juno Gravity Science Instrument

The Juno mission’s primary science objectives include the investigation of Jupiter interior structure via the determination of its gravitational field. Juno will provide more accurate determination of Jupiter’s gravity harmonics that will provide new constraints on interior structure models. Juno will also measure the gravitational response from tides raised on Jupiter by Galilean satellites. This is accomplished by utilizing Gravity Science instrumentation to support measurements of the Doppler shift of the Juno radio signal by NASA’s Deep Space Network at two radio frequencies. The Doppler data measure the changes in the spacecraft velocity in the direction to Earth caused by the Jupiter gravity field. Doppler measurements at X-band (\(\sim 8\) GHz) are supported by the spacecraft telecommunications subsystem for command and telemetry and are used for spacecraft navigation as well as Gravity Science. The spacecraft also includes a Ka-band (\(\sim 32\) GHz) translator and amplifier specifically for the Gravity Science investigation contributed by the Italian Space Agency. The use of two radio frequencies allows for improved accuracy by removal of noise due to charged particles along the radio signal path.     

月球重力场模型误差对CE-5T1探测器定轨的影响

利用嫦娥五号再入返回飞行试验拓展任务期间获取的探测器(CE-5T1)实测数据,采用内符合方法比较了3种重力场模型的实测数据定轨结果,发现采用GRAIL(Gravity Recovery And Interior Laboratory,重力恢复与内部实验室)重力场模型进行定轨的结果最优。相比于之前的嫦娥系列探测器定轨常用的LP(Lunar Prospector,月球勘探者)重力场模型,采用GRAIL重力场模型定轨后测距数据的残差降低了1个量级。进一步采用不同重力场模型进行轨道外推,定量分析重力场模型对不同类型轨道的影响,结果表明,对于倾角为90°的环月极轨道,不同重力场模型的轨道外推结果差异较小;而对于倾角为20°和40°的环月轨道,不同重力场模型的外推星历的偏差均方根可达到2km,大于当前环月探测器的定轨精度。为此,建议在后续探月任务中使用GRAIL重力场模型进行轨道确定。     

Dynamics and Control Modeling for Gravity Probe B

A generic drag-free simulator has been developed to aid in the design, on-orbit and post-mission data analysis phases of increasingly complex future missions such as Gaia and STEP. Adaptation to the recent science mission Gravity Probe B (GP-B) has been carried out for a first simulator verification with actual flight data. Lessons learned from GP-B have shown that the controls simulator, developed concurrently with GP-B, has been invaluable to test flight control design and furthermore to resolve on-orbit anomalies in a time-saving manner. A complete mission software simulator including controls, full-body dynamics and comprehensive spacecraft environment disturbances has been established for Gravity Probe B. This simulator provides a reference and development platform for future mission design. The importance of this effort lies in the challenge to meet rising science requirements for future missions in the area of maximum disturbance rejection.     

Monitoring Changes in Continental Water Storage with GRACE

The Gravity Recovery and Climate Experiment, GRACE , will enable the recovery of monthly estimates of changes in water storage, on land and in the ocean, averaged over arbitrary regions having length scales of a few hundred km and larger. These data will allow the examination of changes in the distribution of water in the ocean, in snow and ice on polar ice sheets, and in continental water and snow storage. Extracting changes in water storage from the GRACE dataset requires the use of averaging kernels which can isolate a particular region. To estimate the accuracy to which continental water storage changes in a few representative regions may be recovered, we construct a synthetic GRACE dataset from global, gridded models of surface-mass variability. We find that regional changes in water storage can be recovered with rms error less than 1 cm of equivalent water thickness, for regions having areas of 4 × 10⁵ km² and larger. Signals in smaller regions may also be recovered; however, interpretations of such results require a careful consideration of model resolution, as well as the nature of the averaging kernel. This revised version was published online in August 2006 with corrections to the Cover Date.     

Lunar Magnetic Field Observation and Initial Global Mapping of Lunar Magnetic Anomalies by MAP-LMAG Onboard SELENE (Kaguya)

The magnetic field around the Moon has been successfully observed at a nominal altitude of ～100 km by the lunar magnetometer (LMAG) on the SELENE (Kaguya) spacecraft in a polar orbit since October 29, 2007. The LMAG mission has three main objectives: (1) mapping the magnetic anomaly of the Moon, (2) measuring the electromagnetic and plasma environment around the Moon and (3) estimating the electrical conductivity structure of the Moon. Here we review the instrumentation and calibration of LMAG and report the initial global mapping of the lunar magnetic anomaly at the nominal altitude. We have applied a new de-trending technique of the Bayesian procedure to multiple-orbit datasets observed in the tail lobe and in the lunar wake. Based on the nominal observation of 14 months, global maps of lunar magnetic anomalies are obtained with 95% coverage of the lunar surface. After altitude normalization and interpolation of the magnetic anomaly field by an inverse boundary value problem, we obtained full-coverage maps of the vector magnetic field at 100 km altitude and the radial component distribution on the surface. Relatively strong anomalies are identified in several basin-antipode regions and several near-basin and near-crater regions, while the youngest basin on the Moon, the Orientale basin, has no magnetic anomaly. These features well agree with characteristics of previous maps based on the Lunar Prospector observation. Relatively weak anomalies are distributed over most of the lunar surface. The surface radial-component distribution estimated from the inverse boundary value problem in the present study shows a good correlation with the radial component distribution at 30 km altitude by Lunar Prospector. Thus these weak anomalies over the lunar surface are not artifacts but likely to be originated from the lunar crustal magnetism, suggesting possible existence of an ancient global magnetic field such as a dynamo field of the early Moon. The possibility of the early lunar dynamo and the mechanism of magnetization acquisition will be investigated by a further study using the low-altitude data of the magnetic field by Kaguya.     

The Kaguya Mission Overview

The Japanese lunar orbiter Kaguya (SELENE) was successfully launched by an H2A rocket on September 14, 2007. On October 4, 2007, after passing through a phasing orbit 2.5 times around the Earth, Kaguya was inserted into a large elliptical orbit circling the Moon. After the apolune altitude was lowered, Kaguya reached its nominal 100 km circular polar observation orbit on October 19. During the process of realizing the nominal orbit, two subsatellites Okina (Rstar) and Ouna (Vstar) were released into elliptical orbits with 2400 km and 800 km apolune, respectively; both elliptical orbits had 100 km perilunes. After the functionality of bus system was verified, four radar antennas and a magnetometer boom were extended, and a plasma imager was deployed. Acquisition of scientific data was carried out for 10 months of nominal mission that began in mid-December 2007. During the 8-month extended mission, magnetic fields and gamma-rays from lower orbits were measured; in addition to this, low-altitude observations were carried out using a Terrain Camera, a Multiband Imager, and an HDTV camera. New data pertaining to an intense magnetic anomaly and GRS data with higher spatial resolution were acquired to study magnetism and the elemental distribution of the Moon. After some orbital maneuvers were performed by using the saved fuel, the Kaguya spacecraft finally impacted on the southeast part of the Moon. The Kaguya team has archived the initial science data, and since November 2, 2009, the data has been made available to public, and can be accessed at the Kaguya homepage of JAXA. The team continues to also study and publish initial results in international journals. Science purposes of the mission and onboard instruments including initial science results are described in this overview.     

Science Objectives and Rationale for the Radiation Belt Storm Probes Mission

The NASA Radiation Belt Storm Probes (RBSP) mission addresses how populations of high energy charged particles are created, vary, and evolve in space environments, and specifically within Earth’s magnetically trapped radiation belts. RBSP, with a nominal launch date of August 2012, comprises two spacecraft making in situ measurements for at least 2 years in nearly the same highly elliptical, low inclination orbits (1.1×5.8 RE, 10^°). The orbits are slightly different so that 1 spacecraft laps the other spacecraft about every 2.5 months, allowing separation of spatial from temporal effects over spatial scales ranging from ～0.1 to 5 RE. The uniquely comprehensive suite of instruments, identical on the two spacecraft, measures all of the particle (electrons, ions, ion composition), fields (E and B), and wave distributions (d E and d B) that are needed to resolve the most critical science questions. Here we summarize the high level science objectives for the RBSP mission, provide historical background on studies of Earth and planetary radiation belts, present examples of the most compelling scientific mysteries of the radiation belts, present the mission design of the RBSP mission that targets these mysteries and objectives, present the observation and measurement requirements for the mission, and introduce the instrumentation that will deliver these measurements. This paper references and is followed by a number of companion papers that describe the details of the RBSP mission, spacecraft, and instruments.     

Geochemical Constraints on the Origin of the Moon and Preservation of Ancient Terrestrial Heterogeneities

Space Science Reviews - Chang’E 4 is the first mission to the far side of the Moon and consists of a lander, a rover, and a relay spacecraft. Lander and rover were launched at 18:23...     

Measuring the Distribution of Ocean Mass Using GRACE

The Gravity Recovery and Climate Experiment (GRACE), which was successfully launched March 17, 2002, has the potential to create a new paradigm in satellite oceanography with an impact perhaps as large as was observed with the arrival of precision satellite altimetry via TOPEX/Poseidon (T/P) in 1992. The simulations presented here suggest that GRACE will be able to monitor non-secular changes in ocean mass on a global basis with a spatial resolution of ≈500 km and an accuracy of ≈3 mm water equivalent. It should be possible to recover global mean ocean mass variations to an accuracy of ≈1 mm, possibly much better if the atmospheric pressure modeling errors can be reduced. We have not considered the possibly significant errors that may arise due to temporal aliasing and secular gravity variations. Secular signals from glacial isostatic adjustment and the melting of polar ice mass are expected to be quite large, and will complicate the recovery of secular ocean mass variations. Nevertheless, GRACE will provide unprecedented insight into the mass components of sea level change, especially when combined with coincident satellite altimeter measurements. Progress on these issues would provide new insight into the response of sea level to climate change. This revised version was published online in August 2006 with corrections to the Cover Date.     

国内外深空探测器精密定轨软件研究综述及WUDOGS简介

深空探测器精密定轨软件系统的研制在深空探测活动中是一个非常重要的环节,一直受到各大航天机构的重视。针对国内外深空探测器精密定轨软件平台的研究现状,重点介绍了具有代表性的美国JPL(Jet Propulsion Laboratory,喷气推进实验室)的DPTRAJ/ODP(Double Precision TRAJectory program/Orbit Determination Program,双精度轨道程序/定轨程序)和MONTE(Mission analysis,Operations,and Navigation Toolkit Environment,任务分析、操作和导航工具箱环境),GSFC(Goddard Space Flight Center,戈达德航天飞行中心)的GEODYN-II以及法国CNES(Centre National dEtudes Spatiales,国家空间研究中心)的GINS(Géodésie par Intégrations Numériques Simultanées,同步数值积分大地测量)软件系统,对这些软件的结构与功能进行了总结。之后对武汉大学自主研制的深空探测器精密定轨软件系统WUDOGS(Wuhan University Deep space Orbit determination and Gravity recovery System,武汉大学深空探测器精密定轨与重力场解算软件系统)的主要模块与功能进行了介绍,通过与GEODYN-II的交叉对比验证,表明:对于探测器的轨道预报,WUDOGS与GEODYN-II的1个月位置差异小于0.3mm,2d位置差值小于5×10~(-3) mm;双程测距、双程测速的理论计算值和GEODYN-II的差值RMS(Root Mean Square,均方根)分别在0.06mm,0.002mm/s的水平;WUDOGS目前已初步具备了月球和火星探测器精密定轨能力。最后对WUDOGS的下一步发展方向进行了展望。     

Enhanced baseline determination for formation flying LEOs by relative corrections of phase center and code residual variations

Formation flying Low Earth Orbiters(LEOs) are important for implementing new and advanced concepts in Earth observation missions. Precise Baseline Determination(PBD) is a prerequisite for LEOs to complete specified mission targets. PBD is usually performed based on space-borne GNSS data, the relative corrections of phase center and code residual variations play crucial roles in achieving the best relative orbit accuracy. Herein, the influences of antenna Relative Phase Centre Variations(RPCVs) a...     

交会对接任务天基双目标测控通信设计

针对交会对接任务对测控通信提出的高覆盖率和双目标测控等需求的问题,分析2颗中继卫星能够提供的覆盖率,设计双目标测控工作模式以及天地协同机制,计算中继链路的性能,分析表明,天基测控可提供约72%的测控覆盖率,能够支持双目标测控,链路余量满足要求;统计了任务中关键段落的测控通信工作情况,分析结果和实际任务情况验证了天基测控在交会对接任务测控通信中的重要作用;最后提出后续任务改进和完善的建议。     

The Lunar Orbiter Laser Altimeter Investigation on the Lunar Reconnaissance Orbiter Mission

The Lunar Orbiter Laser Altimeter (LOLA) is an instrument on the payload of NASA’s Lunar Reconnaissance Orbiter spacecraft (LRO) (Chin et al., in Space Sci. Rev. 129:391–419, 2007). The instrument is designed to measure the shape of the Moon by measuring precisely the range from the spacecraft to the lunar surface, and incorporating precision orbit determination of LRO, referencing surface ranges to the Moon’s center of mass. LOLA has 5 beams and operates at 28 Hz, with a nominal accuracy of 10 cm. Its primary objective is to produce a global geodetic grid for the Moon to which all other observations can be precisely referenced.     

Ocean Tides in GRACE Monthly Averaged Gravity Fields

The GRACE mission will map the Earth's gravity fields and its variations with unprecedented accuracy during its 5-year lifetime. Unless ocean tide signals and their load upon the solid earth are removed from the GRACE data, their long period aliases obscure more subtle climate signals which GRACE aims at. In this analysis the results of Knudsen and Andersen (2002) have been verified using actual post-launch orbit parameter of the GRACE mission. The current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower than 47. The accumulated tidal errors may affect the GRACE data up to harmonic degree 60. A study of the revised alias frequencies confirm that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields. The S₂ and the K₂ terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages. Those results have been verified using a simulated 30 days GRACE orbit. The results show that the magnitudes of the monthly averaged values are slightly higher than the previous values. This may be caused by insufficient sampling to fully resolve and reduce the tidal signals at short wavelengths and close to the poles. This revised version was published online in August 2006 with corrections to the Cover Date.     

Satellite Skin-Force Modelling for Atmospheric Drag Calculations

Satellites in low Earth orbits are influenced by the Earth’s atmosphere. The interactions between the molecules and the spacecraft cause the highest non-gravitational force, which in magnitude is comparable to planetary disturbances. Therefore the modelling of atmospheric drag effects is important for many missions with a scientific background like STEP (Satellite Test of Equivalence Principle). With the STEP mission variations between gravitational and inertial mass shall be measured with an accuracy of 10^?18. The results are of great interest for cosmological and gravitational theories. To achieve the aimed accuracy, a precise model of external disturbances is necessary. In this article the method of Ray-Tracing is used to quantify the atmospheric drag forces and torques for spacecrafts of arbitrary shape.     

Gravity Field Recovery from GRACE: Unique Aspects of the High Precision Inter-Satellite Data and Analysis Methods

The very high accuracy of the Doppler and range measurements between the two low-flying and co-orbiting spacecraft of the GRACE mission, which will be at the μm/sec and ≈10 μm levels respectively, requires that special procedures be applied in the processing of these data. Parts of the existing orbit determination and gravity field parameters retrieval methods and software must be modified in order to fully benefit from the capabilities of this mission. This is being done in the following areas: (i) numerical integration of the equations of motion (summed form, accuracy of the predictor-corrector loop, Encke's formulation): (ii) special inter-satellite dynamical parameterization for very short arcs; (iii) accurate solution of large least-squares problems (normal equations vs. orthogonal decomposition of observation equations); (iv) handling the observation equations with high accuracy. Theoretical concepts and first tests of some of the newly implemented algorithms are presented. This revised version was published online in August 2006 with corrections to the Cover Date.