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NASA NTRS2002

Dynamical Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations

This report summarizes the activities of NASA grant NAG5-11068, "Dynamicai Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations." The High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS) has been providing direct measurements of the Earth's horizontal wind field in the stratosphere, mesosphere and lower thermosphere. Mesospheric temperatures, ozone, and O((sup 1) D) densities, and stratospheric aerosol extinctions coefficients, are also retrieved. The goal of HRDI is to measure the vector winds in the stratosphere (10-40 km), mesosphere, and lower thermosphere (approximately 50-120 km) during the day, and the lower thermosphere at night (approximately 95 km) to an accuracy of 5 m/s. The horizontal wind vector is measured by observing the Doppler shift of rotational lines of molecular oxygen along two lines of sight. In addition to winds, temperatures and volume emission rates are determined in the mesosphere and lower thermosphere, from which ozone and O((sup 1) D) concentrations can be derived, and aerosol scattering coefficients are determined in the stratosphere. UARS was launched on September 12, 1991, into a 585-km circular orbit inclined 57 degrees to the equator HRDI was activated September 28, 1991 and following a period of checkout and adjustment of the instrument parameters, scientific observations began November 2, 199 1. HRDI operated nearly continuously from launch until April 1995. At that time the UARS solar array drive failed, forcing the instruments to time-share the available power. From July 1995 to July 1996 HRDI operated approximately 50% of the time. At that point, one of the three spacecraft batteries failed and from then until September 1998 the duty cycle was less than 20% per month, At that time it was determined that HRDI could operate during each daytime pass, which increased the daytime duty cycle to close to l00%, while nighttime operations were limited to about a week per month. In the fall of 1999, the second tape recorder failed requiring a real time contact with a TRDSS satellite to retrieve that data. This resulted in about 60% data collection efficiency. Finally, in the summer of 2000, the second star sensor failed requiring the spacecraft attitude to be controlled by a three axis magnetometer and sun sensor. This resulted in a loss of attitude knowledge but operations continue with the anticipation of correcting the attitude. A new method for determining the tide and mean structure from satellite data in conjunction with a new tidal model has been devised. For brevity, it shall be referred to as the TMAT or Tide-Mean Assimilation Technique. Most previous methods of tidal analysis are based on various ways of slicing the data set.

Skinner, Wilbert↗

NASA NTRS2022

Vertical Coupling by Solar Semidiurnal Tides in the Thermosphere From ICON/MIGHTI Measurements

Wind measurements from the Michelson Interferometer for Global High-resolution Ther-23mospheric Imaging (MIGHTI) instrument on the Ionospheric CONnections (ICON) mis-24sion provide new insights into the semidiurnal tidal spectrum in the thermosphere, cov-25ering latitudes 9◦S-39◦N and altitudes 100-280 km altitude throughout 2020. Latitude26versus day of year (DOY) variability of solar semidiurnal tides SE2, S0, SW1, SW2, SW327and SW4 at 250 km are presented for the first time, and evaluated relative to similar re-28sults at 106 km. Using daytime-only data, height versus latitude and height versus DOY29variability of SE2, S0, SW1. SW3 and SW4 amplitudes and phases are depicted for the30first time, revealing the effects of a dissipative thermosphere on the vertical evolutions31of these tidal structures. SW2 is absent from these depictions due to potential aliasing32by zonal mean winds. The above results are considered in light of the Climatological Tidal33Model of the Thermosphere (CTMT), which is based on fits to tidal winds and temper-34atures from the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED)35mission between 80 and 120 km during 2002-2008, and extrapolated to an altitude of 40036km based on modeled tidal structures propagating in a dissipative thermosphere, but with-37out in-situ sources of excitation due to tide-tide or tide-ion drag nonlinear interactions.38On the basis of comparisons with the CTMT and other characteristics revealed in the39MIGHTI tidal structures, it is concluded that in-situ sources exist for S0, SW1, SW2 and40SW3 in the thermosphere above about 200 km.

Jeffrey M Forbes↗

NASA NTRS1995

A numerical model of nonmigrating diurnal tides between the surface and 65 km

Observations of surface pressure and middle atmosphere temperatures and winds indicate that a substantial nonmigrating component is present in the diurnal tide. The nonmigrating tides, which propagate with a zonal phase speed that is different from the earth's rotation, are attributed to the diurnal heating of geographically fixed sources. In this study we utilize a classical tidal model to examine the propagation characteristics of diurnal tides. The global fields of tropospheric sensible, radiative, and latent heating used to drive the model are supplied from summer and winter diurnal climatologies of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM2). A novel aspect of this study is the focus on the relative importance of the nonmigrating components. The classical model successfully reproduces many observed features of the low-latitude diurnal surface pressure tides. In the middle atmosphere, the simulated migrating (or sun-synchronous) tide shows qualitative agreement with November-March Limb Infrared Monitor of the Stratosphere (LIMS) observations. Tropospheric solar heating is clearly the dominant driving force for the migrating tide, with secondary contributions from boundary-layer sensible heating and tropospheric latent heat release. The leading modes of the zonal mean tide are also driven chiefly by tropospheric solar heating. The higher-order modes of the zonal mean and eastward propagating tides may be attributed to the joint effects of tropospheric solar heating, sensible heating, and latent heat release. The LIMS and other data reveal features that cannot be explained or examined within the context of the classical model used in the present study. These include upward phase propagation, vertical attenuation, and temporal variations in the migrating diurnal tide.

Lieberman, Ruth S.↗

NASA NTRS1979

Tides and the midnight temperature anomally in the thermosphere

Spectral analysis of the midnight temperature anomaly observed on Atmosphere Explorer-E indicates that the phenomenon can be adequately represented with wave numbers between 1 and 5. Results from a multiconstituent circulation model suggest that this feature and associated variations in composition are the result of a complex interaction between the semidiurnal tide generated in the lower atmosphere and ion-neutral momentum coupling associated with the diurnal variation of the ion density which, in turn, also generates higher order tidal models.

Mayr, H. G.↗

DOE OSTI2025

Marine Toxicity, Biodegradability, and Rolling-Sliding Tribological Performance of Ionic Liquid-Enhanced Environmentally-Acceptable Lubricants for Tidal Turbomachinery

Environmentally acceptable lubricants (EALs) are increasingly being recognized in many fields including waterpower, hydraulics, water transport, agricultural machinery, offshore wind turbines, etc. Specifically, high-performance EALs are demanded for tidal turbomachinery to ensure high efficiency and reliability and avoid the significant risk of direct contamination of the marine ecosystem upon leaks. Here we report a new development of ionic liquid (IL)-enhanced EALs for tidal energy. One short-chain phosphonium phosphate and one short-chain ammonium phosphate ILs were used as the candidate additives and the IL-containing EALs demonstrated significantly improved lubricating performance, much lower toxicity, and increased biodegradability compared with commercial baselines. Specifically, in a rolling-sliding test simulating the operation of a model tidal turbine gearbox bearing, an EAL containing the ILs at a 0.5 wt % concentration demonstrated 40% lower friction, 45% less wear loss, substantially reduced rolling contact fatigue-induced surface damage, and one order of magnitude lower vibration noise compared with a commercial gear oil. In an EPA standard toxicity test, 90 and 70% survival of marine biota was observed when exposed to an EAL containing 5 wt % of the short-chain phosphonium phosphate and ammonium phosphate ILs, respectively, while the selected commercial gear oil and bioderived additive killed all marine biota. In a standard biodegradability test, 2 wt % addition of the phosphonium phosphate IL not only retained the EAL’s ready biodegradability but further boosted the oil decomposition from a range of 60–80% to a higher level of 80–95%. Conversely, adding the commercial bioderived additive downgraded the EAL from readily to inherently biodegradable. Furthermore, this work offers scientific insights for development of ILs as potential EAL additives for marine energy and broader applications.

additives↗

NASA NTRS2012

Simulation Study of a Follow-on Gravity Mission to GRACE

The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth's time-variable gravity field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude errors, orbit errors, and temporal aliasing caused by unmodeled high-frequency variations in the gravity signal. Recent work by Ball Aerospace and Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging system improves the range-rate measurement precision to approximately 0.6 nm/s as compared to approx. 0.2 micro-seconds for the GRACE K-band microwave ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two different altitudes. The first pair of simulated missions is flown at GRACE altitude (approx. 480 km) assuming on-board accelerometers with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude of approx. 250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude, the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE, even when time-varying background models are not included. This study also shows that only modest improvement is realized for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission design or data processing could reduce the effects of temporal aliasing.

Loomis, Bryant D.↗

NASA NTRS1995

Atmospheric response in aurora experiment: Observations of E and F region neutral winds in a region of postmidnight diffuse aurora

The goal of the Atmospheric Response in Aurora (ARIA) experiment carried out at Poker Flat, Alaska, on March 3, 1992, was to determine the response of the neutral atmosphere to the long-lived, large-scale forcing that is characteristic of the diffuse aurora in the post midnight sector. A combination of chemical release rocket wind measurements, instrumented rocket composition measurements, and ground-based optical measurements were used to characterize the response of the neutral atmosphere. The rocket measurements were made at the end of a 90-min period of strong Joule heating. We focus on the neutral wind measurements made with the rocket. The forcing was determined by running the assimilated mapping of ionospheric electrodynamics (AMIE) analysis procedure developed at the National Center for Atmospheric Research. The winds expected at the latitude and longitude of the experiment were calculated using the spectral thermospheric general circulation model developed at the Danish Meteorological Institute. Comparisons of the observations and the model suggest that the neutral winds responded strongly in two height ranges. An eastward wind perturbation of approximately 100 m/s developed between 140 and 200 km altitude with a peak near 160 km. A southwestward wind with peak magnitude of approximately 150 m/s developed near 115 km altitude. The large amplitude winds at the lower altitude are particularly surprising. They appear to be associated with the upward propagating semidiurnal tide. However, the amplitude is much larger than predicted by any of the tidal models, and the shear found just below the peak in the winds was nominally unstable with a Richardson number of approximately 0.08.

Larsen, M. F.↗

NASA NTRS1989

On the diurnal variation of noctilucent clouds

The relationship between nuctilucent clouds (NLC), which are observed from the ground usually within 2 or 3 hrs of local midnight, and the polar mesospheric clouds (PMC), which are observed by satellites in full daylight, as well as the reason for the differences in their optical properties and their observed heights are investigated. Based on a suggestion that these differences can be attributed to a diurnal variation in the properties of a single type of cloud, two published models of the diurnal and semidiurnal variations of temperature, vertical wind speed, and eddy diffusion coefficient at high latitude to simulate the evolution of ice clouds over a 24-hr period. The results show that the minimum in temperature at about 2000 hours LT causes a sharp maximum in scattered brightness to occur about 1 hour before local midnight, with up to a factor of 7 variation in cloud brightness between noon and midnight. It is noted, however, that considerable uncertainties exist in these tidal models.

Jensen, Eric↗

NASA NTRS1993

A Simulation Atlas of Tidal Features in Galaxies

Detailed simulations of tidally induced structure in disk galaxies have either concentrated on specific systems or consisted of a few encounters with relatively small numbers of particles and no self-gravity. Observers need a 'dictionary' of simulations that covers many encounter parameters with fine morphological resolution and includes effects of self-gravitation. Observers can then search the dictionary for the parameters that best match a particular observed morphology. Alternatively, the dictionary can be used with observational samples for statistical studies of system parameters. To fill this need, we present a survey of model tidal encounters using a self-gravitating, 180,000 particle, two-component ('stars' and 'gas') disk. A wide variety of fascinating morphologies results. There are 86 different encounters that vary orbit tilt, perigalacticon distance, galaxy to companion mass ratio, and the amount of halo dark matter relative to the disk. For morphological comparisons, over 1700 images of the entire survey are available in video form. While there is a rich variety of tidal structure covering much of this parameter space, some general patterns may be remarked. There is a strong orbital inclination dependence of the symmetry of tidal patterns, most symmetric for planar orbits and nearly one-sided for polar encounters. Retrograde encounters produce only broad fanlike global patterns, but rich small-scale internal structure. In both kinds of encounter, our numerical resolution allows us to track internal spiral structure driven by the outer material arms, especially in the lighter halo simulations. We note also that polar encounters generate series of expanding, essentially non-rotating loops resembling shell structures in some respects.

Howard, Sethanne↗

DOE OSTI2023

LANL Institutional Computing Close-out Report for Project t22_ocean_time_step

This year, my team made a very productive use of LANL IC time. Four papers were published that used IC resources, and two more are under review. These publications fall into three categories: 1.) Improving tide modeling in the global ocean by adding self attraction and loading (Barton et. al. 2022), ice shelf cavities (Pal et al. 2023), and local time stepping (Lilly et al. 2023). 2.) A new sea ice numerical formulation (Capodaglio 2023). 3.) Performance comparisons, methods, and test cases for ocean model development, This includes a verification suite for ocean models (Bishnu, submitted) and a comparison between Julia and Fortran (Strauss, submitted). A new time-stepping method was introduced in Calandrini et al. (2022). These publications, and the use of LANL IC resources, go hand-in-hand with our mentoring efforts to train young scientists. Two of the lead authors are graduate students who are conducting their PhD research: Kristin Barton at the University of Michigan and Jeremy Lilly at Oregon State. These are both their first publications, and they both have DOE funding and DOE mentors. In addition, Bishnu is a post-doctoral researcher at LANL; Strauss conducted his research as a senior in high school; and Capodaglio, Calandrini and Pal are all early-career scientists who were converted to staff in 2021 or 2022. Here we highlight two publications on improvements in tidal modeling: Barton et al. 2022 and Lilly et al. 2023.

58 GEOSCIENCES↗

NASA NTRS1994

Preliminary assessment of the accuracy and precision of TOPEX/POSEIDON altimeter data with respect to the large-scale ocean circulation

TOPEX/POSEIDON sea surface height measurements are examined for quantitative consistency with known elements of the oceanic general circulation and its variability. Project-provided corrections were accepted but are at tested as part of the overall results. The ocean was treated as static over each 10-day repeat cycle and maps constructed of the absolute sea surface topography from simple averages in 2 deg x 2 deg bins. A hybrid geoid model formed from a combination of the recent Joint Gravity Model-2 and the project-provided Ohio State University geoid was used to estimate the absolute topography in each 10-day period. Results are examined in terms of the annual average, seasonal average, seasonal variations, and variations near the repeat period. Conclusion are as follows: the orbit error is now difficult to observe, having been reduced to a level at or below the level of other error sources; the geoid dominates the error budget of the estimates of the absolute topography; the estimated seasonal cycle is consistent with prior estimates; shorter-period variability is dominated on the largest scales by an oscillation near 50 days in spherical harmonics Y(sup m)(sub 1)(theta, lambda) with an amplitude near 10 cm, close to the simplest alias of the M(sub 2) tide. This spectral peak and others visible in the periodograms support the hypothesis that the largest remaining time-dependent errors lie in the tidal models. Though discrepancies attribute to the geoid are within the formal uncertainties of the good estimates, removal of them is urgent for circulation studies. Current gross accuracy of the TOPEX/POSEIDON mission is in the range of 5-10 cm, distributed overbroad band of frequencies and wavenumbers. In finite bands, accuracies approach the 1-cm level, and expected improvements arising from extended mission duration should reduce these numbers by nearly an order of magnitude.

Wunsch, Carl↗

NASA NTRS2011

The Kepler Light Curves of V1504 Cygni and V344 Lyrae: A Study of the Outburst Properties

We examine the Kepler light curves of V1504 Cyg and V344 Lyr, encompassing approximately 460 d at 1 min cadence. During this span each system exhibited approximately 40 outbursts, including four superoutbursts. We find that, in both systems, the normal outbursts lying between two superoutbursts increase in duration by a factor approximately 1.2 - 1.7, and then reset to a small value after the following superoutburst. In V344 Lyr the trend of quiescent intervals between normal outbursts is to increase to a local maximum about half way through the supercycle the interval from one superoutburst to the next - and then to decrease back to a small value by the time of the next superoutburst, whereas for V1504 Cyg the quiescent intervals are relatively constant during the supercycle. Both of these trends are inconsistent with the Osaki's thermal-tidal model, which robustly predicts a secular increase in the quiescent intervals between normal outbursts during a supercycle. Also, most of the normal outbursts have an asymmetric, fast-rise/slower-decline shape, which would be consistent with outbursts triggered at large radii. The exponential rate of decay of the plateau phase of the superoutbursts is 8 d mag(sup -1) for approximately 1504 Cyg and 12 d mag(sup -1) for V344 Lyr. This time scale gives a direct measure of the VISCOUS time scale III the outer accretion disk given the expectation that the entire disk is in the hot, viscous state during superoutburst. The resulting constraint on the Shakura-Sunyaev parameter, alpha(sub hot) approximately equal to 0.1, is consistent with the value inferred from the fast dwarf nova decays. By looking at the slow decay rate for superoutbursts, which occur in systems below the period gap, in combination with the slow decay rate in one long outburst above the period gap (in U Gem), we infer a steep dependence of the decay rate on orbital period for long outbursts. We argue that this relation implies a steep dependence of alpha(sub cold) on orbital period, which may be consistent with recent findings of Patterson, and is consistent with tidal torquing as being the dominant angular momentum transport mechanism in quiescent disks in interacting binary systems.

Cannizzo, John K.↗

DOE OSTI2023

Synchronous Rotation in the (136199) Eris–Dysnomia System

We combine photometry of Eris from a 6 month campaign on the Palomar 60 inch telescope in 2015, a 1 month Hubble Space Telescope WFC3 campaign in 2018, and Dark Energy Survey data spanning 2013–2018 to determine a light curve of definitive period 15.771 ± 0.008 days (1σ formal uncertainties), with nearly sinusoidal shape and peak-to-peak flux variation of 3%. This is consistent at part-per-thousand precision with the P = 15.785 90 ± 0.00005 day sidereal period of Dysnomia's orbit around Eris, strengthening the recent detection of synchronous rotation of Eris by Szakáts et al. with independent data. Photometry from Gaia are consistent with the same light curve. We detect a slope of 0.05 ± 0.01 mag per degree of Eris's brightness with respect to illumination phase averaged across g, V, and r bands, intermediate between Pluto's and Charon's values. Variations of 0.3 mag are detected in Dysnomia's brightness, plausibly consistent with a double-peaked light curve at the synchronous period. The synchronous rotation of Eris is consistent with simple tidal models initiated with a giant-impact origin of the binary, but is difficult to reconcile with gravitational capture of Dysnomia by Eris. The high albedo contrast between Eris and Dysnomia remains unexplained in the giant-impact scenario.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Intrinsic alignment as an RSD contaminant in the DESI survey

ABSTRACT We measure the tidal alignment of the major axes of luminous red galaxies (LRGs) from the Legacy Imaging Survey and use it to infer the artificial redshift-space distortion signature that will arise from an orientation-dependent, surface-brightness selection in the Dark Energy Spectroscopic Instrument (DESI) survey. Using photometric redshifts to downweight the shape–density correlations due to weak lensing, we measure the intrinsic tidal alignment of LRGs. Separately, we estimate the net polarization of LRG orientations from DESI’s fibre-magnitude target selection to be of order 10−2 along the line of sight. Using these measurements and a linear tidal model, we forecast a 0.5 per cent fractional decrease on the quadrupole of the two-point correlation function for projected separations of 40–80 h−1 Mpc. We also use a halo catalogue from the Abacussummit cosmological simulation suite to reproduce this false quadrupole.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Characterization of Low-mass Companions to Kepler Objects of Interest Observed with APOGEE-N

We report the characterization of 28 low-mass (0.02 M ⊙ ≤ M 2 ≤ 0.25 M ⊙ ) companions to Kepler objects of interest (KOIs), eight of which were previously designated confirmed planets. These objects were detected as transiting companions to Sunlike stars (G and F dwarfs) by the Kepler mission and are confirmed as single-lined spectroscopic binaries in the current work using the northern multiplexed Apache Point Observatory Galactic Evolution Experiment near-infrared spectrograph (APOGEE-N) as part of the third and fourth Sloan Digital Sky Surveys. We have observed hundreds of KOIs using APOGEE-N and collected a total of 43,175 spectra with a median of 19 visits and a median baseline of ~1.9 yr per target. We jointly model the Kepler photometry and APOGEE-N radial velocities to derive fundamental parameters for this subset of 28 transiting companions. The radii for most of these low-mass companions are overinflated (by ~10%) when compared to theoretical models. Tidally locked M dwarfs on short-period orbits show the largest amount of inflation, but inflation is also evident for companions that are well separated from the host star. We demonstrate that APOGEE-N data provide reliable radial velocities when compared to precise high-resolution spectrographs that enable detailed characterization of individual systems and the inference of orbital elements for faint (H > 12) KOIs. The data from the entire APOGEE-KOI program are public and present an opportunity to characterize an extensive subset of the binary population observed by Kepler.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

C/2014 UN 271 (Bernardinelli-Bernstein): The Nearly Spherical Cow of Comets

Abstract Comet C/2014 UN 271 (Bernardinelli-Bernstein), incoming from the Oort cloud, is remarkable in having the brightest (and presumably largest) nucleus of any well-measured comet and having been discovered at the heliocentric distance r h ≈ 29 au, farther than any Oort cloud comet. In this work, we describe the discovery process and observations and the properties that can be inferred from images recorded until the first reports of activity in 2021 June. The orbit has i = 95°, with a perihelion of 10.97 au to be reached in 2031 and a previous aphelion at 40,400 ± 260 au. Backward integration of the orbit under a standard Galactic tidal model and known stellar encounters suggests a perihelion of q ≈ 18 au on its previous perihelion passage 3.5 Myr ago; hence, the current data could be the first ever obtained of a comet that has not been inside Uranus’s orbit in 4 Gyr. The photometric data show an unresolved nucleus with absolute magnitude H r = 8.0, colors that are typical of comet nuclei or Damocloids, and no secular trend as it traversed the range 34–23 au. For the r -band geometric albedo p r , this implies a diameter of 150 ( p r / 0.04 ) − 0.5 km. There is strong evidence of brightness fluctuations at the ±0.2 mag level, but no rotation period can be discerned. A coma, nominally consistent with a “stationary” 1/ ρ surface brightness distribution, grew in scattering cross section at an exponential rate from A f ρ ≈ 1 to ≈150 m as the comet approached from 28 to 20 au. The activity rate is consistent with a very simple model of sublimation of a surface species in radiative equilibrium with the Sun. The inferred enthalpy of sublimation matches those of CO 2 and NH 3 . More volatile species, such as N 2 , CH 4 , and CO, must be far less abundant on the sublimating surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1974

Possible histories of the obliquity of Mercury

Possible evolutionary paths of the spin axis of Mercury are studied theoretically in terms of generalized Cassini's laws using the Hamiltonian approach. Three stable positions (Cassini states) of the spin axis are discerned. The Cassini states in which the spin axis remains fixed in the frame rotating with the orbit precession are extremes in the tide-free Hamiltonian under the condition of constant angular momentum. The stability of the 3/2 spin resonance for Mercury as a function of obliquity is discussed, and it is shown how control of the resonance is passed from one to another term in the averaged potential as the obliquity is increased with a corresponding loss of stability at each transfer. A sampling technique is used to infer the evolution due to tidal interaction. Two tidal models are used - one with a constant value of the specific dissipation function Q and the other with Q inversely proportional to frequency. An approximate analytic solution for precession trajectories very close to a Cassini state is developed.

Peale, S. J.↗

NASA NTRS1978

Tidal friction in the solid earth

The earth's imperfectly elastic response to body and loading tidal forces is discussed using complex Love numbers and complex mass loading coefficients. Exact analytical expressions were derived relating the energy dissipation within an inhomogeneous, compressible solid earth to the surface values of these complex characteristic numbers, thus relating the global dissipation function Q to the phase shifts in the potential, gravity, tilt, strain and displacement tides. Integration of a global ocean tidal model shows that energy dissipated in the solid earth due to ocean loading is at least 10% of that dissipated in the body tides.

Zschau, J.↗