On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

On the orbits and masses of the satellites of the Pluto-Charon system

Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400-500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future.     

On the calculation of perturbations in the radial position of satellites

With the aim of analyzing the errors in the radial position of satellites, we give in this paper the expressions for the radial perturbation which include the complete zeroth- and first-order terms in the orbital eccentricity. A simpler and faster method of calculating the perturbation is given.     

Celestial-mechanical peculiarities of Uranus’s satellite system

We consider the structural peculiarities of Uranus’s satellite system associated with its separation into two groups: inner equatorial satellites moving in nearly circular orbits and distant irregular satellites with retrograde motion in highly elliptical orbits. The intermediate region is free from satellites in a wide range of semimajor axes. By analyzing the evolution of satellite orbits under the combined effect of solar attraction and Uranus’s oblateness, we offer a celestial-mechanical explanation for the absence of equatorial satellites in this region. M.L. Lidov’s studies during 1961–1963 have served as a basis for our analysis.     

Numerical Stabilization of Orbital Motion

Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders.     

Periodicities in natural remanent magnetization and palaeoclimatic records detected by walsh spectra

The time series consisting of nonsinusoidal Natural Remanent Magnetization (NRM) and palaeoclimatic variations for the past two million years have been spectrally examined by using a new Walsh transform technique. The results show statistically significant periodicities (at 95% confidence level) of approximately 92,000 years; 43,000 years and 21,000 years in the ensemble spectra of the NRM intensity (mineralogic) variations. These NRM periodicities are remarkably close to the well-known Milankovitch cycles. The ensemble spectra of palaeoclimatic records reveal only 41,000 years statistically significant (95%) periodicity corresponding to the obliquity cycle. The study suggests that NRM variations in deep sea sediments probably are more sensitive recorders of palaeoclimatic memory than the oxygen isotope variations.     

Ar/Ar ages of tephras intercalated in astronomically tuned Neogene sedimentary sequences in the eastern Mediterranean

We present new ⁴⁰Ar/³⁹Ar data for sanidine and biotite derived from volcanic ash layers that are intercalated in Pliocene and late Miocene astronomically dated sequences in the Mediterranean with the aim to solve existing inconsistencies in the intercalibration between the two independent absolute dating methods. ⁴⁰Ar/³⁹Ar sanidine ages are systematically younger by 0.7-2.3% than the astronomical ages for the same ash layers. The significance of the discrepancy disappears except for the upper Ptolemais ashes, which reveal the largest difference, if an improved full error propagation method is applied to calculate the absolute error in the ⁴⁰Ar/³⁹Ar ages. The total variance is dominated by that of the activity of the decay of ⁴⁰K to ⁴⁰Ar (∼70%) and that the amount of radiogenic ⁴⁰Ar_p in the primary standard GA1550 biotite (∼15%). If the ⁴⁰Ar/³⁹Ar ages are calculated relative to an astronomically dated standard, the influence of these parameters is greatly reduced, resulting in a more reliable age and in a significant reduction of the error in ⁴⁰Ar/³⁹Ar dating.Astronomically calibrated ages for Taylor Creek Rhyolite (TCR) and Fish Canyon Tuff (FCT) sanidine are 28.53±0.02 and 28.21±0.04 Ma (±1 S.E.), respectively, if we start from the more reliable results of the Cretan A1 ash layer. The most likely explanation for the large discrepancy found for the younger Ptolemais ash layers (equivalent to FCT of 28.61 Ma) is an error in the tuning of this part of the sequence.     

Precessional forcing of tropical vegetation carbon storage

Since the Mid Pleistocene Revolution, which occurred about one million years ago, global temperatures have fluctuated with a quasi‐periodicity of ca. 100 ka. The pattern of past change in the extent of woodlands, and therefore by inference vegetation carbon storage, has been demonstrated to have a strong positive link with this global temperature change at high and mid latitudes. However, understanding of climate systems and ecosystem function indicates that the pattern of woodland change at low latitudes may follow a fundamentally different pattern. We present output from the intermediate complexity model GENIE‐1, comprising a single transient simulation over the last 800 ka and a 174‐member ensemble of 130 ka transient simulations over the last glacial cycle. These simulations suggest that while vegetation carbon storage in mid–high northern latitudes robustly follows the characteristic ca. 100 ka cycle, this signal is not a robust feature of tropical vegetation, which is subject to stronger direct forcing by the precessional (21 ka) orbital cycle (albeit with a highly uncertain response). We conclude that the correlation of palaeoenvironmental records from low latitudes with global temperature change must be done with caution. Copyright © 2011 John Wiley & Sons, Ltd.     

Drivers of ecosystem and climate change in tropical West Africa over the past ∼540 000 years

A paucity of empirical non‐marine data means that uncertainty surrounds the impact of climate change on terrestrial ecosystems in tropical regions beyond the last glacial period. The sedimentary fill of the Bosumtwi impact crater (Ghana) provides the longest continuous Quaternary terrestrial archive of environmental change in West Africa, spanning the last ～1.08 million years. Here we explore the drivers of change in ecosystem and climate in tropical West Africa for the past ～540 000 years using pollen analysis and the nitrogen isotope composition of bulk organic matter preserved in sediments from Lake Bosumtwi. Variations in grass pollen abundance (0?99%) indicate transitions between grassland and forest. Coeval variations in the nitrogen isotopic composition of organic matter indicate that intervals of grassland expansion coincided with minimum lake levels and low regional moisture availability. The observed changes responded to orbitally paced global climate variations on both glacial–interglacial and shorter timescales. Importantly, the magnitude of ecosystem change revealed by our data exceeds that previously determined from marine records, demonstrating for the first time the high sensitivity of tropical lowland ecosystems to Quaternary climate change.

     

A timescale decomposed threshold regression downscaling approach to forecasting South China early summer rainfall

A timescale decomposed threshold regression(TSDTR) downscaling approach to forecasting South China early summer rainfall(SCESR) is described by using long-term observed station rainfall data and NOAA ERSST data. It makes use of two distinct regression downscaling models corresponding to the interannual and interdecadal rainfall variability of SCESR.The two models are developed based on the partial least squares(PLS) regression technique, linking SCESR to SST modes in preceding months on both interannual and interdecadal timescales. Specifically, using the datasets in the calibration period 1915–84, the variability of SCESR and SST are decomposed into interannual and interdecadal components. On the interannual timescale, a threshold PLS regression model is fitted to interannual components of SCESR and March SST patterns by taking account of the modulation of negative and positive phases of the Pacific Decadal Oscillation(PDO). On the interdecadal timescale, a standard PLS regression model is fitted to the relationship between SCESR and preceding November SST patterns. The total rainfall prediction is obtained by the sum of the outputs from both the interannual and interdecadal models. Results show that the TSDTR downscaling approach achieves reasonable skill in predicting the observed rainfall in the validation period 1985–2006, compared to other simpler approaches. This study suggests that the TSDTR approach,considering different interannual SCESR-SST relationships under the modulation of PDO phases, as well as the interdecadal variability of SCESR associated with SST patterns, may provide a new perspective to improve climate predictions.