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.     

Effect of sensor modelling methods on computation of 3-D coordinates from Cartosat-1 stereo data

The orbital and the rational polynomial coefficients (RPC) models are the two most commonly used models to compute a three-dimensional coordinates from an image stereo-pair. But it is still confusing that with the identical user provided inputs, which one of these two models provides more accurate digital elevation model (DEM), especially for mountainous terrain. This study aimed to find out the answer by evaluating the impact of used models on the vertical accuracy of DEM extracted from Cartosat-1 stereo data. We used high-accuracy photogrammetric DEM as the reference DEM. Apart from general variations in statistics, surprisingly in a few instances, both the DEMs provided contrasting results, thus proving the significance of this study. The computed root mean square errors and linear error at 90% (LE90) were lower in case of RPC DEM for various classes of slope, aspect and land cover, thus suggesting its better relative accuracy.     

深水等深流沉积中记录的米兰科维奇特性——以陕西富平地区上奥陶统赵老峪组为例

陕西富平地区上奥陶统赵老峪组为深水盆地边缘至深水斜坡沉积环境,发育深水原地沉积、等深流沉积及重力流沉积。以野外实测剖面、岩相特征等资料为基础,结合米兰科维奇理论、天文地层学、古海洋学以及古气候学,系统研究该地区等深流强度与古气候、海平面、古盐度的关系。结果表明:Fischer图解可以客观、准确地反映深水沉积地层相对海平面变化;深水沉积及等深流沉积中不同级次旋回垂向组合关系记录了米兰科维奇特性,即小级别旋回在垂向上有序地按照1∶4或者1∶5的形式叠加构成较大级别旋回;等深流强度受米兰科维奇旋回影响,呈多周期弱→强→弱递变;等深流强化周期约为0.1Ma。