Lunar gravity field modeling critical analysis and challenges

This paper summarizes and provides a critical analysis of the historical developments of lunar gravitational models from the earliest use of ground based tracking systems of the Lunar Orbiter to the Lunar Prospector mission. This encompasses a comprehensive and critical analysis of the various methods used in the estimation of the gravity coefficients and the processing of large batches of diverse measurements and data types. It has been shown that weakness exists in the current models of the lunar gravity field, which is primarily due to the lack of far side lunar tracking data information, which makes the lunar potential modeling difficult but expected to be overcome as data from SELENE satellite-to-satellite tracking becomes available. Comparisons of various lunar models reveal an agreement in the low order coefficients of the spherical harmonics. However, substantial differences in the models exist in the higher-order harmonics. A numerical comparison has been presented showing the performance of all the contemporary lunar gravitational models used within the astrodynamics community and available in public domain. Improvements to the current models are part of a continuing process and the recent model improvements and future possibilities in lunar gravity modeling are discussed. A brief review of the recent missions has been presented. It is hoped that this critical review will benefit the researchers by presenting the historical as well as state of the art in this field.     

Venus Atmospheric Thermal Structure and Radiative Balance

From the discovery that Venus has an atmosphere during the 1761 transit by M. Lomonosov to the current exploration of the planet by the Akatsuki orbiter, we continue to learn about the planet’s extreme climate and weather. This chapter attempts to provide a comprehensive but by no means exhaustive review of the results of the atmospheric thermal structure and radiative balance since the earlier works published in Venus and Venus II books from recent spacecraft and Earth based investigations and summarizes the gaps in our current knowledge. There have been no in-situ measurements of the deep Venus atmosphere since the flights of the two VeGa balloons and landers in 1985 (Sagdeev et al., Science 231:1411–1414, 1986). Thus, most of the new information about the atmospheric thermal structure has come from different remote sensing (Earth based and spacecraft) techniques using occultations (solar infrared, stellar ultraviolet and orbiter radio occultations), spectroscopy and microwave, short wave and thermal infrared emissions. The results are restricted to altitudes higher than about 40 km, except for one investigation of the near surface static stability inferred by Meadows and Crisp (J. Geophys. Res. 101:4595–4622, 1996) from 1 \(\upmu\)m observations from Earth. Little information about the lower atmospheric structure is possible below about 40 km altitude from radio occultations due to large bending angles. The gaps in our knowledge include spectral albedo variations over time, vertical variation of the bulk composition of the atmosphere (mean molecular weight), the identity, properties and abundances of absorbers of incident solar radiation in the clouds. The causes of opacity variations in the nightside cloud cover and vertical gradients in the deep atmosphere bulk composition and its impact on static stability are also in need of critical studies. The knowledge gaps and questions about Venus and its atmosphere provide the incentive for obtaining the necessary measurements to understand the planet, which can provide some clues to learn about terrestrial exoplanets.     

Water and Volatile Inventories of Mercury,Venus, the Moon,and Mars

We review the geochemical observations of water, \(\mbox{D}/\mbox{H}\) and volatile element abundances of the inner Solar System bodies, Mercury, Venus, the Moon, and Mars. We focus primarily on the inventories of water in these bodies, but also consider other volatiles when they can inform us about water. For Mercury, we have no data for internal water, but the reducing nature of the surface of Mercury would suggest that some hydrogen may be retained in its core. We evaluate the current knowledge and understanding of venusian water and volatiles and conclude that the venusian mantle was likely endowed with as much water as Earth of which it retains a small but non-negligible fraction. Estimates of the abundance of the Moon’s internal water vary from Earth-like to one to two orders of magnitude more depleted. Cl, K, and Zn isotope anomalies for lunar samples argue that the giant impact left a unique geochemical fingerprint on the Moon, but not the Earth. For Mars, an early magma ocean likely generated a thick crust; this combined with a lack of crustal recycling mechanisms would have led to early isolation of the Martian mantle from later delivery of water and volatiles from surface reservoirs or late accretion. The abundance estimates of Martian mantle water are similar to those of the terrestrial mantle, suggesting some similarities in the water and volatile inventories for the terrestrial planets and the Moon.     

Ion Composition of the Earth’s Radiation Belts in the Range from 100 keV to $100\mbox{ MeV}/\mbox{nucleon}$: Fifty Years of Research

Spatial, energy and angular distributions of ion fluxes in the Earth’s radiation belts (ERB) near the equatorial plane, at middle geomagnetic latitudes and at low altitudes are systematically reviewed herein. Distributions of all main ion components, from protons to Fe (including hydrogen and helium isotopes), and their variations under the action of solar and geomagnetic activity are considered. For ions with \(Z\geq 2\) and especially for ions with \(Z \geq 9\), these variations are much more than for protons, and these have no direct connection with the intensity of magnetic storms (\(Z\) is the charge of the atomic nucleus with respect to the charge of the proton). The main physical mechanisms for the generation of ion fluxes in the ERB and the losses of these ions are considered. Solar wind, Solar Cosmic Rays (SCR), Galactic Cosmic Rays (GCR), and Anomalous component of Cosmic Rays (ACR) as sources of ions in the ERB are considered.     

Daytime O/N<Subscript>2</Subscript> Retrieval Algorithm for the Ionospheric Connection Explorer (ICON)

The NASA Ionospheric Connection Explorer Far-Ultraviolet spectrometer, ICON FUV, will measure altitude profiles of the daytime far-ultraviolet (FUV) OI 135.6 nm and N₂ Lyman-Birge-Hopfield (LBH) band emissions that are used to determine thermospheric density profiles and state parameters related to thermospheric composition; specifically the thermospheric column O/N₂ ratio (symbolized as \(\Sigma\)O/N₂). This paper describes the algorithm concept that has been adapted and updated from one previously applied with success to limb data from the Global Ultraviolet Imager (GUVI) on the NASA Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) mission. We also describe the requirements that are imposed on the ICON FUV to measure \(\Sigma\)O/N₂ over any 500-km sample in daytime with a precision of better than 8.7%. We present results from orbit-simulation testing that demonstrates that the ICON FUV and our thermospheric composition retrieval algorithm can meet these requirements and provide the measurements necessary to address ICON science objectives.     

Pulsar Timing and Its Application for Navigation and Gravitational Wave Detection

Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from testing theories of gravity to detecting gravitational waves. Also an external reference system suitable for autonomous space navigation can be defined by pulsars, using them as natural navigation beacons, not unlike the use of GPS satellites for navigation on Earth. By comparing pulse arrival times measured on-board a spacecraft with predicted pulse arrivals at a reference location (e.g. the solar system barycenter), the spacecraft position can be determined autonomously and with high accuracy everywhere in the solar system and beyond. We describe the unique properties of pulsars that suggest that such a navigation system will certainly have its application in future astronautics. We also describe the on-going experiments to use the clock-like nature of pulsars to “construct” a galactic-sized gravitational wave detector for low-frequency (\(f_{GW}\sim 10^{-9} \text{--} 10^{-7}\) Hz) gravitational waves. We present the current status and provide an outlook for the future.     

A Pre-Landing Assessment of Regolith Properties at the InSight Landing Site

This article discusses relevant physical properties of the regolith at the Mars InSight landing site as understood prior to landing of the spacecraft. InSight will land in the northern lowland plains of Mars, close to the equator, where the regolith is estimated to be \(\geq3\mbox{--}5~\mbox{m}\) thick. These investigations of physical properties have relied on data collected from Mars orbital measurements, previously collected lander and rover data, results of studies of data and samples from Apollo lunar missions, laboratory measurements on regolith simulants, and theoretical studies. The investigations include changes in properties with depth and temperature. Mechanical properties investigated include density, grain-size distribution, cohesion, and angle of internal friction. Thermophysical properties include thermal inertia, surface emissivity and albedo, thermal conductivity and diffusivity, and specific heat. Regolith elastic properties not only include parameters that control seismic wave velocities in the immediate vicinity of the Insight lander but also coupling of the lander and other potential noise sources to the InSight broadband seismometer. The related properties include Poisson’s ratio, P- and S-wave velocities, Young’s modulus, and seismic attenuation. Finally, mass diffusivity was investigated to estimate gas movements in the regolith driven by atmospheric pressure changes. Physical properties presented here are all to some degree speculative. However, they form a basis for interpretation of the early data to be returned from the InSight mission.     

Estimations of the Seismic Pressure Noise on Mars Determined from Large Eddy Simulations and Demonstration of Pressure Decorrelation Techniques for the Insight Mission

The atmospheric pressure fluctuations on Mars induce an elastic response in the ground that creates a ground tilt, detectable as a seismic signal on the InSight seismometer SEIS. The seismic pressure noise is modeled using Large Eddy Simulations (LES) of the wind and surface pressure at the InSight landing site and a Green’s function ground deformation approach that is subsequently validated via a detailed comparison with two other methods: a spectral approach, and an approach based on Sorrells’ theory (Sorrells, Geophys. J. Int. 26:71–82, 1971; Sorrells et al., Nat. Phys. Sci. 229:14–16, 1971). The horizontal accelerations as a result of the ground tilt due to the LES turbulence-induced pressure fluctuations are found to be typically \(\sim 2 \mbox{--} 40~\mbox{nm}/\mbox{s}^{2}\) in amplitude, whereas the direct horizontal acceleration is two orders of magnitude smaller and is thus negligible in comparison. The vertical accelerations are found to be \(\sim 0.1\mbox{--}6~\mbox{nm}/\mbox{s}^{2}\) in amplitude. These are expected to be worst-case estimates for the seismic noise as we use a half-space approximation; the presence at some (shallow) depth of a harder layer would significantly reduce quasi-static displacement and tilt effects.We show that under calm conditions, a single-pressure measurement is representative of the large-scale pressure field (to a distance of several kilometers), particularly in the prevailing wind direction. However, during windy conditions, small-scale turbulence results in a reduced correlation between the pressure signals, and the single-pressure measurement becomes less representative of the pressure field. The correlation between the seismic signal and the pressure signal is found to be higher for the windiest period because the seismic pressure noise reflects the atmospheric structure close to the seismometer.In the same way that we reduce the atmospheric seismic signal by making use of a pressure sensor that is part of the InSight Auxiliary Payload Sensor Suite, we also the use the synthetic noise data obtained from the LES pressure field to demonstrate a decorrelation strategy. We show that our decorrelation approach is efficient, resulting in a reduction by a factor of \(\sim 5\) in the observed horizontal tilt noise (in the wind direction) and the vertical noise. This technique can, therefore, be used to remove the pressure signal from the seismic data obtained on Mars during the InSight mission.     

Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles,Cosmic Rays,and Magnetic Fields

This paper summarizes the results obtained by the team “Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields” supported by the International Space Science Institute (ISSI) in Bern, Switzerland. We focus on the physical processes occurring in the outer heliosphere, especially at its boundary called the heliopause, and in the local interstellar medium. The importance of magnetic field, charge exchange between neutral atoms and ions, and solar cycle on the heliopause topology and observed heliocentric distances to different heliospheric discontinuities are discussed. It is shown that time-dependent, data-driven boundary conditions are necessary to describe the heliospheric asymmetries detected by the Voyager spacecraft. We also discuss the structure of the heliopause, especially due to its instability and magnetic reconnection. It is demonstrated that the Rayleigh–Taylor instability of the nose of the heliopause creates consecutive layers of the interstellar and heliospheric plasma which are magnetically connected to different sources. This may be a possible explanation of abrupt changes in the galactic and anomalous cosmic ray fluxes observed by Voyager 1 when it was crossing the heliopause structure for a period of about one month in the summer of 2012. This paper also discusses the plausibility of fitting simulation results to a number of observational data sets obtained by in situ and remote measurements. The distribution of magnetic field in the vicinity of the heliopause is discussed in the context of Voyager measurements. It is argued that a classical heliospheric current sheet formed due to the Sun’s rotation is not observed by in situ measurements and should not be expected to exist in numerical simulations extending to the boundary of the heliosphere. Furthermore, we discuss the transport of energetic particles in the inner and outer heliosheath, concentrating on the anisotropic spatial diffusion diffusion tensor and the pitch-angle dependence of perpendicular diffusion and demonstrate that the latter can explain the observed pitch-angle anisotropies of both the anomalous and galactic cosmic rays in the outer heliosheath.