On the free rotation of a rigid body

It is well known that the equations governing the motion of a freely-rotating rigid body possess an exact analytical solution, involving Jacobi's elliptic functions. Andoyer (1923) and Deprit (1967) have shown that the problem may be very usefully reduced to a one-degree-of-freedom Hamiltonian system. When two of the body's principal moments of inertia are very nearly equal, the Hamiltonian system has the same form as the Ideal Resonance Problem. In earlier publications (Jupp, 1969, 1972, 1973), the author has constructed formal power-series solutions of the latter problem.In this article, the general solution of the Ideal Resonance Problem is employed to formulate a second-order formal series solution of the problem of a freely-rotating rigid body which has two of its principal moments of inertia differing by a small quantity. This solution is firstly expressed in terms of the mean elements, and then in terms of the initial conditions. The latter solution is global in nature being applicable over the whole phase plane. It is demonstrated that the exact solution and the second-order formal series solution, written in terms of the initial conditions, differ by terms of at most third order in the small parameter, over the whole domain of possible motions. This serves as an important check on the general results published in the earlier articles.     

In the other 90%: phytoplankton responses to enhanced nutrient availability in the Great Barrier Reef Lagoon

Our view of how water quality effects ecosystems of the Great Barrier Reef (GBR) is largely framed by observed or expected responses of large benthic organisms (corals, algae, seagrasses) to enhanced levels of dissolved nutrients, sediments and other pollutants in reef waters. In the case of nutrients, however, benthic organisms and communities are largely responding to materials which have cycled through and been transformed by pelagic communities dominated by micro-algae (phytoplankton), protozoa, flagellates and bacteria. Because GBR waters are characterised by high ambient light intensities and water temperatures, inputs of nutrients from both internal and external sources are rapidly taken up and converted to organic matter in inter-reefal waters. Phytoplankton growth, pelagic grazing and remineralisation rates are very rapid. Dominant phytoplankton species in GBR waters have in situ growth rates which range from approximately 1 to several doublings per day. To a first approximation, phytoplankton communities and their constituent nutrient content turn over on a daily basis. Relative abundances of dissolved nutrient species strongly indicate N limitation of new biomass formation. Direct ((15)N) and indirect ((14)C) estimates of N demand by phytoplankton indicate dissolved inorganic N pools have turnover times on the order of hours to days. Turnover times for inorganic phosphorus in the water column range from hours to weeks. Because of the rapid assimilation of nutrients by plankton communities, biological responses in benthic communities to changed water quality are more likely driven (at several ecological levels) by organic matter derived from pelagic primary production than by dissolved nutrient stocks alone.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Minor constituents in the atmosphere of Jupiter

New spectra of Jupiter in the region 0.93–1.63 are presented. Laboratory comparisons of spectra of NH₃ and CH₄ permit estimates of the absorbing pathlength for various bands of these two gases. Abundances in a single transmission through the Jupiter atmosphere, above the mean reflecting level, vary from 10 to 100 m-atm for CH₄ and from 0.2–5 m-atm for NH₃, depending on the bands considered. Upper limits for other gases are derived from new laboratory spectra and comparison with the Jupiter spectra presented herein. These are as follows: C₂H₂<2 m-atm, H₂S<0.25 m-atm, HCN<0.05 m-atm, CH₃NH₂<0.02 m-atm. A table summarizing the chemical composition of Jupiter's atmosphere is presented.     

The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2

The emergence of low-frequency, high-amplitude, quasi-periodic (100-kyr) glacial variability during the middle Pleistocene in the absence of any significant change in orbital forcing indicates a fundamental change internal to the climate system. This middle Pleistocene transition (MPT) began 1250 ka and was complete by 700 ka. Its onset was accompanied by decreases in sea surface temperatures (SSTs) in the North Atlantic and tropical-ocean upwelling regions and by an increase in African and Asian aridity and monsoonal intensity. During the MPT, long-term average ice volume gradually increased by 50 m sea-level equivalent, whereas low-frequency ice-volume variability experienced a 100-kyr lull centered on 1000 ka followed by its reappearance 900 ka, although as a broad band of power rather than a narrow, persistent 100-kyr cycle. Additional changes at 900 ka indicate this to be an important time during the MPT, beginning with an 80-kyr event of extreme SST cooling followed by the partial recovery and subsequent stabilization of long-term North Atlantic and tropical ocean SSTs, increasing Southern Ocean SST variability primarily associated with warmer interglacials, the loss of permanent subpolar sea-ice cover, and the emergence of low-frequency variability in Pacific SSTs and global deep-ocean circulation. Since 900 ka, ice sheets have been the only component of the climate system to exhibit consistent low-frequency variability. With the exception of a near-universal organization of low-frequency power associated with marine isotope stages 11 and 12, all other components show an inconsistent distribution of power in frequency-time space, suggesting a highly nonlinear system response to orbital and ice-sheet forcing.Most hypotheses for the origin of the MPT invoke a response to a long-term cooling, possibly induced by decreasing atmospheric pCO₂. None of these hypotheses, however, accounts for the geological constraint that the earliest Northern Hemisphere ice sheets covered a similar or larger area than those that followed the MPT. Given that the MPT was associated with an increase in ice volume, this constraint requires that post-MPT ice sheets were substantially thicker than pre-MPT ice sheets, indicating a change in subglacial conditions that influence ice dynamics. We review evidence in support of the hypothesis that such an increase in ice thickness occurred as crystalline Precambrian Shield bedrock became exposed by glacial erosion of a thick mantle of regolith. This exposure of a high-friction substrate caused thicker ice sheets, with an attendant change in their response to the orbital forcing. Marine carbon isotope data indicate a rapid transfer of organic carbon to inorganic carbon in the ocean system during the MPT. If this carbon came from terrigenous sources, an increase in atmospheric pCO₂ would be likely, which is inconsistent with evidence for widespread cooling, Apparently rapid carbon transfer from terrestrial sources is difficult to reconcile with gradual erosion of regolith. A more likely source of organic carbon and nutrients (which would mitigate pCO₂ rise) is from shelf and upper slope marine sediments, which were fully exposed for the first time in millions of years in response to thickening ice sheets and falling sealevels during the MPT. Modeling indicates that regolith erosion and resulting exposure of crystalline bedrock would cause an increase in long-term silicate weathering rates, in good agreement with marine Sr and Os isotopic records. We use a carbon cycle model to show that a post-MPT increase in silicate weathering rates would lower atmospheric pCO₂ by 7–12 ppm, suggesting that the attendant cooling may have been an important feedback in causing the MPT.     

Preparing for climate change in Washington State

Climate change is expected to bring potentially significant changes to Washington State’s natural, institutional, cultural, and economic landscape. Addressing climate change impacts will require a sustained commitment to integrating climate information into the day-to-day governance and management of infrastructure, programs, and services that may be affected by climate change. This paper discusses fundamental concepts for planning for climate change and identifies options for adapting to the climate impacts evaluated in the Washington Climate Change Impacts Assessment. Additionally, the paper highlights potential avenues for increasing flexibility in the policies and regulations used to govern human and natural systems in Washington.     

Ejecta exchange and satellite color evolution in the Pluto system, with implications for KBOs and asteroids with satellites

In this Note, I present first-order scaling calculations to examine the efficacy of impacts by Kuiper Belt debris in causing regolith exchange between objects in the Pluto system. It is found that ejecta can escape Nix and Hydra with sufficient velocity to reach one another, as well as Charon, and even Pluto. The degree of ejecta exchanged between Nix and Hydra is sufficient to cover these bodies with much more material than is required for photometrically change. In specific, Nix and Hydra may have exchanged as up to 10s of meters of regolith, and may have covered Charon to depths up to 14 cm with their ejecta. Pluto is likely unaffected by most Nix and Hydra ejecta by virtue of a combination of dynamical shielding from Charon and Pluto's own annual atmospheric frost deposition cycle. As a result of ejecta exchange between Nix, Hydra, and Charon, these bodies are expected to evolve their colors, albedos, and other photometric properties to be self similar. These are testable predictions of this model, as is the prediction that Nix and Hydra will have diameters near 50 km, owing to having a Charon-like albedo induced by ejecta exchange. As I discuss, this ejecta exchange process can also be effective in many KBOs and asteroids with satellites, and may be the reason that very many KBO and asteroid satellite systems have like colors.     

A survey of Karin cluster asteroids with the Spitzer Space Telescope

The Karin cluster is one of the youngest known families of main-belt asteroids, dating back to a collisional event only 5.8±0.2 Myr ago. Using the Spitzer Space Telescope we have photometrically sampled the thermal continua (3.5-22 μm) of 17 Karin cluster asteroids of different sizes, down to the smallest members discovered so far, in order to make the first direct measurements of their sizes and albedos and study the physical properties of their surfaces. Our targets are also amongst the smallest main-belt asteroids observed to date in the mid-infrared. The derived diameters range from 17.3 km for 832 Karin to 1.5 km for 75176, with typical uncertainties of 10%. The mean albedo is pv=0.215±0.015, compared to 0.20±0.07 for 832 Karin itself (for H=11.2±0.3), consistent with the view that the Karin asteroids are closely related physically as well as dynamically. The albedo distribution (0.12?pv?0.32) is consistent with the range associated with S-type asteroids but the variation from one object to another appears to be significant. Contrary to the case for near-Earth asteroids, our data show no evidence of an albedo dependence on size. However, the mean albedo is lower than expected for young, fresh “S-type” surfaces, suggesting that space weathering can darken main-belt asteroid surfaces on very short timescales. Our data are also suggestive of a connection between surface roughness and albedo, which may reflect rejuvenation of weathered surfaces by impact gardening. While the available data allow only estimates of lower limits for thermal inertia, we find no evidence for the relatively high values of thermal inertia reported for some similarly sized near-Earth asteroids. Our results constitute the first observational confirmation of the legitimacy of assumptions made in recent modeling of the formation of the Karin cluster via a single catastrophic collision 5.8±0.2 Myr ago.     

Spectral properties and composition of potentially hazardous Asteroid (99942) Apophis

The known close approach of Asteroid (99942) Apophis in April 2029 provides the opportunity for the case study of a potentially hazardous asteroid in advance of its encounter. The visible to near-infrared (0.55 to 2.45 μm) reflectance spectrum of Apophis is compared and modeled with respect to the spectral and mineralogical characteristics of likely meteorite analogs. Apophis is found to be an Sq-class asteroid that most closely resembles LL ordinary chondrite meteorites in terms of spectral characteristics and interpreted olivine and pyroxene abundances, although we cannot rule out some degree of partial melting. A meteorite analog allows some estimates and conjectures of Apophis' possible range of physical properties such as the grain density and micro-porosity of its constituent material. Composition and size similarities of Apophis with (25143) Itokawa suggest a total porosity of 40% as a “current best guess” for Apophis. Applying these parameters to Apophis yields a mass estimate of 2×¹⁰¹⁰ kg with a corresponding energy estimate of 375 Mt for its potential hazard. Substantial unknowns, most notably the total porosity, allow uncertainties in these mass and energy estimates to be as large as factors of two or three.