Mean Longitude Research Articles

Are there spurious precipitation trends in the United States Climate Division database?

The United States Climate Division datasets (CDD) may contain spurious precipitation trends, induced by the method in which climate divisional data are created. This study investigated how the redistribution of stations within a climate division has affected purported annual trends in precipitation. CDD were compared to USHCN data for the 15 climate divisions of New England. Results showed that trends in the datasets are not always the same. We conclude that changing mean latitude, longitude, and elevation of stations within a division through time can affect, and even induce, trends in the time series. Trends found here were mostly increasing through time, but rates of change differed dramatically in some cases. Two climate divisions did have opposing trends between datasets. It appears that other factors, such as distance from the coast and changing slope direction (aspect) of stations, may also influence these trends.

Elevation changes measured on Svalbard glaciers and ice caps from airborne laser data

AbstractPrecise airborne laser surveys were conducted during spring in 1996 and 2002 on 17 ice caps and glaciers in the Svalbard archipelago covering the islands of Spitsbergen and Nordaustlandet. We present the derived elevation changes. Lower-elevation glaciers in south Spitsbergen show the largest thinning rates of ∼ 0.5 m a-1, while some of the higher, more northerly ice caps appear to be close to balance. The pattern of elevation change is complex, however, due to several factors including glacier aspect, microclimatological influences and the high natural annual variability in local accumulation and ablation rates. Anomalous changes were observed on Fridtjovbreen, which started surging in 1996, at the start of the measurement period. On this glacier, thinning (of > 0.6 m a-1) was observed in the accumulation area, coincident with thickening at lower elevations. Asymmetric thinning was found on two ice caps on Nordaustlandet, with the largest values on the eastern side of Vestfonna but the western slopes of Vegafonna. The mean elevation change for all ice masses was -0.19 m a-1 w.e., which is 1.6 times the net mass-balance value determined for the last 30 years. Using mass-balance sensitivity estimates for Svalbard suggests that the implied increase in negative balance is linked to warmer air temperatures in the late 1990s. Multiple linear regression suggests that mass balance is most closely correlated with latitude, rather than mean altitude or longitude.

On the possibility of measuring the gravitomagnetic clock effect in an Earth space-based experiment

In this paper the effect of the post-Newtonian gravitomagnetic force on the mean longitudes l of a pair of counter-rotating Earth artificial satellites following almost identical circular equatorial orbits is investigated and the possibility of measuring it is examined. The observable is the difference of the times required for l to pass from 0 to 2π for both senses of motion. Such a gravitomagnetic time shift, which is independent of the orbital parameters of the satellites, amounts to 5×10−7 s for the Earth; it is cumulative and should be measurable after a sufficiently high number of revolutions. The major limiting factors are the unavoidable imperfect cancellation of the Keplerian periods, which yields a constraint of 10−2 cm in knowing the difference between the semimajor axes a of the satellites, and the difference I of the inclinations i of the orbital planes which, for i ∼ 0.01°, should be less than 0.006°. A pair of spacecraft endowed with a sophisticated intersatellite tracking apparatus and drag-free control down to 10-9 cm s-2 Hz-1/2 level might allow us to meet the stringent requirements posed by such a mission.

Efficient Integration of Highly Eccentric Orbits by Quadruple Scaling for Kustaanheimo-Stiefel Regularization

We have extended the single scaling method for Kustaanheimo-Stiefel (K-S) regularization by applying different scaling factors to each component of the four-dimensional harmonic oscillator associated with the regularization. This is achieved by monitoring the time development of the total energy of each component of the harmonic oscillator and rescaling the magnitude of the position and velocity of the corresponding component so as to satisfy the defining relation for the harmonic energy. To perform the monitoring increases the number of variables to be integrated per celestial body from 10 to 13; however, the extra cost of computation is still negligible compared with that of the perturbing acceleration. The resulting method of quadruple scaling significantly enhances the numerical stability of orbit integrations. In the case of unperturbed orbits, the new method when applied at every integration step reduces to the machine-epsilon level the errors in all the orbital elements except the mean longitude at epoch, if sufficiently high order integrators are used with sufficiently small step sizes. This remarkable feature is lost when the scaling is applied at every apocenter. In the case of perturbed orbits, we confirm the superiority of the quadruple scaling method applied at every integration step over the other scaling methods for K-S regularized orbital motions unless round-off plays the key role in the accumulation of integration error.

Secular Trends in the Mean Longitudes of Planets Derived from Optical Observations

About 240,000 worldwide optical observations of the Sun, Mercury, and Venus, accumulated during the entire era of classical astrometry from James Bradley up to the present, are used to analyze the secular longitude variations of the innermost planets. A reduction method relating historical planetary observations to the Hipparcos reference frame is presented. Secular trends in the longitudes of the Sun, Mercury, and Venus with respect to the ephemeris DE405 are estimated for the time span 1750–2000.

Transient co-orbital asteroids

We analyze the orbital behavior of four new co-orbital NEOs and the Earth horseshoe object 2002 AA29. The new objects are 2001 CK32, a 3753 Cruithne-like co-orbital of Venus, 2001 GO2 and 2003 YN107, two objects with motion similar to 2002 AA29. 2001 CK32 is on a compound orbit. The asteroid reverses its path when the mean longitude difference is −50°. Its motion is chaotic. 2001 GO2 is an Earth HS orbiter with repeated transitions to the QS phase, the next occurring 200 years from now. The HS libration period is 190 years and the QS phases last 45 years. For 2002 AA29, our simulations permit us to find useful theoretical insights into the HS–QS transitions. Its orbit can be simulated with adequate accuracy for 4400 years into the future and 1483 years into the past. The new co-orbital 2003 YN107 is at present an Earth QS. It has entered this phase in 1997 and will leave it again in 2006, completing one QS cycle. Like 2002 AA29, it has frequent transitions between HS and QS. One HS cycle takes 133 years.

Efficient Orbit Integration by Linear Transformation for Consistency of Kepler Energy, Full Laplace Integral, and Angular Momentum Vector

By adopting a general linear transformation as the method of manifold correction, we modify our dual scaling method to integrate quasi-Keplerian orbits numerically. The new method adjusts the integrated position and velocity at each integration step in order to exactly satisfy the relations for the Kepler energy, angular momentum vector, and the full Laplace vector. In the case of no perturbation, the integration errors in all the orbital elements except the mean longitude at the epoch, which grows linearly with time, are reduced to the level of the machine epsilon throughout the integration. For perturbed orbits, the integration errors in position are smaller than with the previous methods of manifold correction. Since its wide applicability is unchanged and the cost of additional computation is similarly negligible, we recommend the new method as the best of our methods of manifold correction.

Dynamical Influences on the Orbits of Prometheus and Pandora

We present the results of a numerical and analytical study of the orbits of the Saturnian satellites Prometheus and Pandora, including the perturbing effects of other moons. The full equations of motion have been integrated numerically between 1980 and 2010, taking into account Saturn's oblateness up to terms in J6. Included in the simulations are the effects of the eight major satellites of Saturn, together with the co-orbital satellites, Janus and Epimetheus. The results show that the anticorrelation in the temporal variation of the mean longitudes of Prometheus and Pandora, demonstrated in previously published two-satellite simulations, survives the addition of the other satellites to the model. Chaos is apparent through sensitivity to initial conditions and a positive value for the maximum Lyapunov characteristic exponent. There is evidence that the other satellites also contribute to the chaotic motion on a longer timescale. The effects of the nearby Mimas 3 : 2 resonance on the orbit of Pandora are clearly detectable. We find evidence that Janus and Epimetheus have a secondary role in the dynamical evolution of Prometheus and Pandora and discuss possible mechanisms. We show from theory that two independent sets of second-order resonances due to Epimetheus sweep across the orbits of Prometheus and Pandora every 4 years, when the orbit of Epimetheus switches position with its co-orbital companion. However, no effects related to this have so far been identified. Comparison of integrated results with extrapolations of current published ephemerides suggest uncertainties on the order of 104 km in the down-track positions of Prometheus and Pandora, equivalent to 4° in mean longitude, during the Cassini tour.

One to One Resonance at High Inclination

We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L5 point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 109 periods in two cases and for 106 periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (φ, ω) plane, with φ being the mean longitude difference and ω the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.

The lunar theory ELP revisited. Introduction of new planetary perturbations

On the basis of the semi-analytical theory ELP, a new solution has been built that makes use of the planetary perturbations MPP01 constructed by P. Bidart. This new solution, called ELP/MPP02, is an analytical solution that contains all the perturbations to represent the lunar motion. The level of truncation for the series is the centimeter. This limit induces analytical developments of a reasonable dimension. ELP/MPP02 is compared to the JPL ephemerides DE405 and DE406. After fitting the constants and the reference frame to DE405, over a few centuries, numerical comparisons with DE405 show a significant improvement in precision, in particular for the radius vector. Over the long range of several millennia, comparisons with DE406 show an improvement in the long periodic perturbations due to planets. On the time interval of one century around J2000 we added to ELP/MPP02 numerical complements based on the differences with DE405 in such a way that ELP/MPP02+ has the precision of the numerical integration. Using this new ephemeris to analyse LLR data provided since 1970, we build the solution ELP/MPP02(LLR) fitted to LLR observations. Various approximations have been also tested on the residuals DE406 - ELP/MPP02. We first determined corrections to the secular variations of the mean longitude, longitudes of the node and perigee under a simple polynomial form; they reduce the differences between ELP/MPP02 and DE406 to less than 3 arcsec in longitude and latitude and 2 km in distance over the whole time interval of DE406 [ -3000; +3000] . Next, the differences themselves between the two solutions are approximated over 2 millennia with Poisson series in a pseudo analytical form similar to ELP/MPP02. We reduce the residuals to less than 0.03 arcsec in longitude and latitude and 30 m in distance.

Adaptive optics observations of small moons of saturn

We report near-infrared observations of Prometheus and Janus taken on 9 and 13 November 2000 (UT) with the Palomar Adaptive Optics System on the 5-m Hale telescope at Palomar Observatory. Dione, Rhea, and Tethys were used as guide “stars” for the adaptive optics system, and, though they were outside the isoplanatic patch of the region of interest, they allowed significant correction of the atmospheric turbulence. Prometheus, which is usually impossible to observe from the ground due to scattered light from the A ring, was imaged at superior conjunction with Saturn. At the time of the observations, the rings of Saturn were blocked by the southern limb of the planet while the moon passed just 0.35″ below the planet’s south pole. A K filter, in a methane absorption band, was used to suppress light from the disk of the planet, and template subtraction removed much of the scattered light from the A ring. Prometheus was found to be 21.9 ± 0.1° of mean longitude behind the position predicted by Voyager-era ephemerides, consistent with the orbital lag discovered during the 1995 ring-plane crossing.

Ecogeographical analysis of the distribution of six Trifolium species in Sardinia

Collections of six species of Trifolium (Fabaceae) were made at 16 sites across the island of Sardinia in June/July 1998 and detailed ecogeographic information was recorded at each site. The six species collected were the inbreeding T. glomeratum, T. subterraneum and T. tomentosum, and the outcrossing T. nigrescens, T. michelianum and T. resupinatum. A principal components analysis and canonical variate analysis were conducted to group the sites, using the ecogeographical variables collected at each site. The variables that were found to be most important in grouping the sites were: mean January and July temperature, mean annual rainfall, latitude, longitude and soil pH. None of the six species were limited to only one ecogeographical group. However, it was often found to be only one or two variables that were determining their distribution. It is suggested that more detailed analysis of ecogeographic data of collection sites will become vital for improved planning of future collection missions, as the cost of collections and genetic erosion increases.

The joint effect of relativistic and direct solar radiation pressure on an axially symmetric spacecraft.: II. The solution and the elements of transformation.

In this work we are concerned with the solution of a dynamical system that represents the coupling effects between the perturbing forces arising from the direct solar radiation pressure (S.R.P.) and Earth’s oblateness, limited to the principal term and the second zonal harmonic ( J 2), in the post Newtonian potential (P.N.). The Hamiltonian of the system, in terms of the Delaunay elements, is outlined. The phase space was augmented so as to remove the explicit time dependence, due to the mean longitude of the Sun. The second zonal harmonic of the geopotential, J 2 (considered to be the 1st order) was considered to be the small parameter of the problem. The solution is affected through two canonical transformations retaining, in successive, secular and periodic terms up to orders 4 and 3, respectively. The elements of the transformation and its inverse as well as a procedure for the computation of position and velocity are outlined.

The relativistic and direct solar radiation pressure effects on an axially symmetric spacecraft. I. The Hamiltonian and the canonical equations of motion

The effects of direct solar radiation pressure (SRP) and Earth oblateness in the post-Newtonian potential (PN) approximation on an Earth artificial satellite are investigated. The potential of the oblate Earth is limited to the principal term and the second zonal harmonic. The model of the satellite is adopted to be an axially symmetric body plus an axially symmetric antenna emitting or receiving radio beam. The attitude of the satellite is assumed stabilized such that the axis of the symmetric body is along the tangent to the orbit. The Hamiltonian of the system is developed in terms of the Delaunay elements augmented so as to remove the explicit time dependence, due to the mean longitude of the Sun. The canonical equations of motion are formed retaining terms up to O( J 2 4) so as to retain the terms arising from the coupling between SRP and the oblateness PN terms.

Analytical treatment of the Earth oblateness and solar radiation pressure effects on an artificial satellite I. The equations of motion

In this paper, the motion of the Earth artificial satellite problem including the solar radiation pressure force has been considered. The geopotential will be expressed in terms of both the zonal and tesseral harmonics up to J 4 and S 44 respectively. The solar radiation pressure force will be obtained to enable this effect to contribute in the Hamiltonian function corresponding to the motion of the satellite. The Hamiltonian function is then obtained in terms of the Delauny set of canonical variables, augmented so as to remove the explicit time dependence due to the mean longitude of the Sun and due to the motion of the Earth about its axis.

Equatorial Pacific Ocean Horizontal Velocity, Divergence, and Upwelling*

Upper-ocean horizontal velocity and divergence were estimated from shipboard observations taken from 1991 to 1999 in the equatorial Pacific between 170°W and 95°W. Mean transports were estimated for the zonal currents at the mean longitude of the sections, 136°W. Mean meridional currents for the entire longitude range included poleward surface flows reaching −0.09 m s−1 in the south and 0.13 m s−1 in the north as well as equatorward flow within the thermocline reaching 0.05 m s−1 in the south and −0.04 m s−1 in the north near 23°C (85 m). Vertical velocity was diagnosed by integrating horizontal divergence estimated for the entire region down from the surface. Equatorial upwelling velocities peaked at 1.9 (±0.9) × 10−5 m s−1 at 50 m. The upwelling transport in the area bounded by 3.6°S–5.2°N, 170°W–95°W was 62 (±18) × 106 m3 s−1 at 50 m. Strong downwelling was apparent within the North Equatorial Countercurrent. An asymmetry in the meridional flows suggested that on the order of 10 × 106 m3 s−1 of thermocline water from the Southern Hemisphere was upwelled at the equator and moved into the Northern Hemisphere as surface water. This interhemispheric exchange path could be part of the route for water from the Southern Hemisphere to supply the Indonesian Throughflow.

Removal of SO2 from the marine boundary layer over the Atlantic Ocean: A case study on the kinetics of the heterogeneous S(IV) oxidation on marine aerosols

Measurements of SO2 and NSS‐SO42− were made over the Atlantic Ocean on board the RV Polarstern from October 9 to November 2, 1996, as part of the ALBATROSS campaign. The measurements were performed between 66.7°N and 37.8°S with a mean longitude of approximately 30°W. The most frequent background values for SO2 were found to be 13 parts per trillion by volume (pptv) (0.54 nmol m−3 at standard ambient temperature and pressure (SATP)) in the Southern Hemisphere, and 15 pptv (0.62 nmol m−3 SATP) in the Northern Hemisphere. The mean values for total NSS‐SO42− in particles with a d>0.2 μm were (5.99±2.93) nmol m−3 (SATP) in the Southern Hemisphere, and (8.93±5.29) nmol m−3 (SATP) in the Northern Hemisphere. An analysis of the size‐fractionated aerosol samples (d >1 μm and 0.2 μm < d < 1 μm) of NSS‐SO42− shows that (34±13)% of the total NSS‐SO42− exists in coarse mode particles with d>1 μm. The main fraction of this NSS‐SO42− is most likely produced by the oxidation of dissolved SO2 via heterogeneous reactions occurring in the aqueous phase of coarse mode marine aerosols. A case study on the kinetics of this oxidation pathway was conducted during ALBATROSS. October 12, 1996, the ship sailed in the plume of a volcano on Iceland during its eruption from September 30 to October 13, 1996, as indicated by trajectory analysis and by the measurements of NSS‐SO42−, SO2, CO, and Hg. An empirical physicochemical approach considering the atmosphere as a natural flow reactor is used for the presented case study. The determined pseudo‐first‐order reaction rate constant for the oxidation of SO2 on marine aerosols is 3.31×10−4 s−1 at 25°C. Assuming that the occurrence of coarse mode marine aerosols is the rate‐limiting variable of the reaction, the second‐order reaction rate constant is found to be 1.32×10−6 cm3 s−1 particle−1 at 25°C. These values are in good agreement with results of previous field experiments as well as with the results of model studies.

The Prograde C7 Resonance for Earth and Mars Satellite Orbits

The resonance C7 is a 1:1 eccentricity (apsidal) resonance between the longitude of a satellite's pericentre and the mean longitude of the Sun. A previous paper by the author (Breiter, 1999) identified it as the strongest of the lunisolar apsidal resonances. After the reduction to a single degree of freedom, the problem is studied qualitatively for the prograde orbits around the Earth and Mars. Pitchfork, saddle-node, and saddle connection bifurcations give rise to a complicated phase flow, which may involve up to nine critical points.

The relationship between the Southern Oscillation Index and tropical cyclone tracks in the eastern North Pacific

Points of origin and downgradation of tropical cyclones in the eastern North Pacific (ENP) east of 160°W are related to the Southern Oscillation Index (SOI) during the hurricane season. All ENP tropical storms and hurricanes from 1966 through 1997 were grouped into three SOI‐based categories: those occurring during strong El Niño events (mean SOI < −0.6), strong La Niña events (mean SOI > 0.6), or near zero periods (−0.6 < mean SOI < 0.6). During El Niño storm seasons, ENP tropical cyclones originated approximately 5.7° (617 km) west and downgraded 7.5° (780 km) west of the long‐term mean longitudes for the positive SOI group. Near zero group storms also followed more northerly tracks than the negative SOI group storms. However, no significant differences in storm track are evident between the positive SOI and near zero groups, and the track length is not significantly different for any storm group.

Low-thrust trajectory optimization based on epoch eccentric longitude formulation

The mathematics of trajectory optimization based on the use of nonsingular orbit elements involving the eccentric longitude at epoch as the sixth element are fully derived. The epoch eccentric longitude and epoch mean longitude are fundamental nonsingular orbit elements, which stay constant in the absence of perturbations. These formulations constitute the basis from which the current time formulations are derived and, therefore, are important from a theoretical point of view. They are also beneficial in minimum-fuel problems during the natural coasting parts of the trajectory, where the adjoint equations need not be propagated by either analytical or numerical integration. The state and adjoint differential equations are explicit functions of time in this formulation that involves natural orbit elements with the optimal Hamiltonian, also varying in time. The mathematics of this epoch formulation provides added insight into the problem of trajectory optimization by relating the various assumptions used in generating the differential equations for the adjoint variables that correspond to various sets of orbital elements. Furthermore, the function that defines the transversality condition at the end time in minimum-time problems is shown to remain constant during the optimal transfer providing a further check in accepting a converged trajectory as truly optimal. This formulation is also related to the one that uses the current eccentric longitude as the sixth state variable, and the mathematical relationship between the Hamiltonian and the Lagrange multipliers of these two formulations is also shown. A pair of continuous constant acceleration minimum-time transfer examples are duplicated using this new formulation to validate the mathematical derivations.