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.     

The Preboreal climate reversal and a subsequent solar‐forced climate shift

Accurate chronologies are essential for linking palaeoclimate archives. Carbon‐14 wiggle‐match dating was used to produce an accurate chronology for part of an early Holocene peat sequence from the Borchert (The Netherlands). Following the Younger Dryas–Preboreal transition, two climatic shifts could be inferred. Around 11 400 cal. yr BP the expansion of birch (Betula) forest was interrupted by a dry continental phase with dominantly open grassland vegetation, coeval with the PBO (Preboreal Oscillation), as observed in the GRIP ice core. At 11 250 cal. yr BP a sudden shift to a humid climate occurred. This second change appears to be contemporaneous with: (i) a sharp increase of atmospheric ¹⁴C; (ii) a temporary decline of atmospheric CO₂; and (iii) an increase in the GRIP ¹⁰Be flux. The close correspondence with excursions of cosmogenic nuclides points to a decline in solar activity, which may have forced the changes in climate and vegetation at around 11 250 cal. yr BP. Copyright © 2004 John Wiley & Sons, Ltd.     

Wind-driven interannual variability over the northeast Pacific Ocean

Interannual variability of the sea surface height (SSH) over the northeast Pacific Ocean is hindcast with a reduced-gravity, quasi-geostrophic model that includes linear damping. The model is forced with monthly Ekman pumping fields derived from the NCEP reanalysis wind stresses. The numerical solution is compared with SSH observations derived from satellite altimeter data and gridded at a lateral resolution of 1 degree. Provided that the reduced gravity parameter is chosen appropriately, the results demonstrate that the model has significant hindcast skill over interior regions of the basin, away from continental boundaries. A damping time scale of 2 to 3 years is close to optimal, although the hindcast skill is not strongly dependent on this parameter.A simplification of the quasi-geostrophic model is considered in which Rossby waves are eliminated, yielding a Markov model driven by local Ekman pumping. The results approximately reproduce the hindcast skill of the more complete quasi-geostrophic model and indicate that the interannual SSH variability is dominated by the local response to wind forcing. There is a close correspondence the two leading empirical orthogonal modes of the local model and those of the observed SSH anomalies. The latter account for over half of the variance of the interannual signal over the region.     

潮汐对瞬态气候响应模拟的影响研究

In this study, the impact of oceanic processes on the sensitivity of transient climate change is investigated using two sets of coupled experiments with and without tidal forcing, which are termed Exp_Tide and Exp_Control,respectively. After introducing tidal forcing, the transient climate response(TCR) decreases from 2.32 K to 1.90 K,and the surface air temperature warming at high latitudes decreases by 29%. Large ocean heat uptake efficiency and heat storage can explain the low TCR in Exp_Tide. Approximately 21% more heat is stored in the ocean in Exp_Tide(1.10×10~(24) J) than in Exp_Control(0.91×10~(24) J). Most of the large ocean warming occurs in the upper 1 000 m between 60°S and 60°N, primarily in the Atlantic and Southern Oceans. This ocean warming is closely related to the Atlantic Meridional Overturning Circulation(AMOC). The initial transport at mid-and high latitudes and the decline in the AMOC observed in Exp_Tide are both larger than those observed in Exp_Control. The spatial structures of AMOC are also different with and without tidal forcing in present experiments. The AMOC in Exp_Tide has a large northward extension. We also investigated the relationship between AMOC and TCR suggested by previous studies using the present experiments.     

一种准确通用的台风路径预报模式

应用天气学理论,对台风云图的晴空区轴线制约台风移动的规律进行物理解释。根据台风云团与晴空区之间存在的干、湿梯度力和推动台风前进的惯性力的互相关系,建立台风移向预报方程和轨迹预报方程,分析论证了台风移向变化的物理过程,把影响台风移动的复杂因子转化为单一的预报因子。