Difference Of Longitude Research Articles

Cовершенствование математических моделей проекции Гаусса – Крюгера для вычисления плоских прямоугольных координат по геодезическим координатам

Algorithms with improved convergence for the calculation of rectangular coordinates in the Gauss – Kruger coordinate system according to the parameters of any ellipsoid were designed. The approach of definition the spherical components in the classic series defined variables x, y, represented by the difference between the degrees of longitude l, followed by the replacement of their sums by formulas of spherical trigonometry. For definition of the amounts of spherical components of the relevant decompositions patterns of transverse-cylindrical sphere plane projection in the condition of the initial data equality on the ellipsoid and sphere radius N were used. Analysis of othertransformation methods of classical expansions in series, used in derivation of both logarithmical and non-logarithmical working formulas is carried outfor comparison with developed algorithms. The technique of algorithms development with usage of hyperbolic tangent function, applied by L. Kruger, Yu. Karelin, A. Schödlbauer is considered and their analysis is carried out. Advantages of Krasovskii – Isotov formulas for six-degree strips are pointed out. The usage of the spherical function sin τ in the expansion made it possible not only to obtain a rapidly convergent series, but also to represent the spherical part of the solution of the problem with the help of trigonometric identities in different types. It is proved that derived for the calculation algorithms with the proposed estimates of their accuracy, are optimal in removing points from the central meridian to l ≤ 6°. For the difference of longitudes l > 6°, the expansions of the unknown quantities into Fourier series should be applied. An example of the calculation of coordinates in the system SK-2011 is given. Theoretical studies have been carried out and shortened formulas with a reliability estimate for the determination of coordinates in the area l ≤ 3° have been proposed.

Анализ математических моделей вычисления прямоугольных координат в расширенных зонах проекции Гаусса – Крюгера

This article contains analysis of mathematical models built depending on longitude difference degree, that are used for calculating planimetric rectangular coordinates in accordance with geodesic coordinates in the longitudinally expanded zones of Gauss Kruger conformal projection. Coefficients of these expansions are measured by successive differentiation or by recurrence formula. Disadvantages of performed coordinate mathematical transformations using schemes recommended by Federal Agency on Technical Regulating and Metrology and Euro-Asian Council for Standardization, Metrology and Certification GOST 32543-2013 for calculations in18 grade meridian zones with millimetric degree of accuracy are pointed out. Two optimal schemes with high convergence rate are suggested for calculating meridian arc length. Ineffectiveness of using formal power series for large grid zones is proved. Practical necessity of efficient schemes’ creation for calculating coordinates in accordance with any ellipsoid’s characteristics.

Using the WSA Model to Test the Parker Spiral Approximation for SEP Event Magnetic Connections

In studies of solar energetic ( $E > 10~\mbox{MeV}$ ) particle (SEP) events the Parker spiral (PS) field approximation, based only on the measured 1 AU solar wind (SW) speed $V$ sw, is nearly always used to determine the coronal or photospheric source locations of the 1 AU magnetic fields. There is no objective way to validate that approximation, but here we seek guidelines for optimizing its application. We first review recent SEP studies showing the extensive use of the PS approximation with various assumptions about coronal and photospheric source fields. We then run the Wang–Sheeley–Arge (WSA) model over selected Carrington rotations (CRs) to track both the photospheric and $5~\mbox{R}_{\odot}$ source locations of the forecasted 1 AU SW, allowing us to compare those WSA sources with the PS sources inferred from the WSA $V$ sw forecast. We compile statistics of the longitude differences (WSA–PS) for all the CRs and discuss the limitations of using the WSA model to validate the PS approximation. Over nearly all of each CR the PS and WSA source longitudes agree to within several degrees. The agreement is poor only in the slow–fast SW interaction regions characterized by high-speed events (HSEs), where the longitude differences can reach several tens of degrees. This result implies that SEP studies should limit use of the PS approximation around HSEs and use magnetic field polarities as an additional check of solar source connections.

Impulsive Ground-Track Adjustment for Assigned Final Orbit

This paper provides analytical approximate solutions to the impulsive coplanar ground-track adjustment problem for an assigned final orbit (e.g., repeated ground-track orbit) whose ground track passes over a user-specified Earth site. A three-impulse method associated with bielliptical transfer and four-impulse methods based on the optimal slewing of the apse line are proposed for coplanar circular and noncoaxial elliptical orbits, respectively. All impulses are required to be tangential. A semi-analytical method is proposed to obtain the longitude difference for the assigned ground-site latitude. Then, approximate solutions are obtained by solving a quartic equation in a high-fidelity model. Numerical examples with both circular and elliptical orbits are provided to validate this approach for one-day repeated ground-track final orbits.

Investigation of ionospheric TEC over China based on GNSS data

In this paper, the ionospheric total electron content (TEC) is derived from 250 Global Navigation Satellite Systems (GNSS) receivers over China. The GNSS TEC data are utilized to study the diurnal and day-to-day variability of ionosphere, ionospheric east–west differences and to construct regional ionospheric map. The GNSS–TEC curves clearly show sunrise and sunset enhancements in the diurnal variation. The peak value of TEC is lower in January 2015 than in May 2014. There is 2h difference in the occurrence time of TEC maximum/minimum between May and January. Compared with the observations of Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS), the measurements from the Geostationary Earth Orbit (GEO) satellites of BeiDou Navigation Satellite System (BDS) clearly present the ionospheric day-to-day variability and east–west differences in a region with small longitude differences (3.52–11.31°). The east–west differences in TEC are more obvious in larger longitude differences at 11:30 local time on 23 January 2015. The maximum east–west difference in TEC is about 7 total electron content unit (TECU, 1 TECU=1016el m−2) in longitude difference of 11.31°. Our analysis shows that the TEC for east–west small longitude differences may be associated with the east–west gradient of geomagnetic declination. Based on 250 GNSS stations, a regional TEC map constructed by Kriging method can well capture the main spatial structure of ionosphere in China. A comparison between TEC maps obtained by Kriging method and provided by Jet Propulsion Laboratory displays that there are large deviations in the North of China, which is mainly caused by the difference in the number of used GNSS stations. In addition, comprehensive investigation presents that GNSS has more advantages over GPS and GLONASS in the ionosphere research over China.

Vegetation changes in the agricultural-pastoral areas of northern China from 2001 to 2013

Climate change and human activity have resulted in increasing change of vegetation growth globally. Numerous studies have been conducted on extreme climate events and analyses of ecological environment evolution. However, such studies have placed little emphasis on vegetation change and spatial variation in this type of ecotone. Accordingly, this study analyzed the changes in vegetation type and growth using the 16-d composite MOD13A1 product with 1-km resolution and MOD12Q1 product with 1-km resolution. We used the mean, maximum, standard deviation normalized-difference vegetation index (NDVI) values, and the rate of change (ROC) of NDVI value to explain vegetation changes within the studied ecotone. Our results showed that significant vegetation type and growth changes have occurred in the study area. From 2001 to 2013, for example, with the exception of 2001, 2004 and 2009, a certain extent of grassland area was converted to cropland. Drought severity index (DSI) results indicate that there exists drought in 2001, 2004 and 2009. Such temporal changes in cropland and grassland area confirmed the ecological vulnerability of the ecotone. At the same time, vegetation varied spatially from west to east and from south to north. The mean, maximum and standard deviation NDVI values were all sorted in descending order based on differences in latitude and longitude, as follows: NDVI2013>NDVI2009>NDVI2004>NDVI2001

Quasi-satellite dynamics in formation flight

The quasi-satellite (QS) phenomenon makes two celestial bodies to fly near each other (Mikkola et al. 2006) and that effect can be used also to make artificial satellites move in tandem. We consider formation flight of two or three satellites in low eccentricity near Earth orbits. With the help of weak ion thrusters it is possible to accomplish tandem flight. With ion thrusters it is also possible to mimic many kinds of mutual force laws between the satellites. We found that both a constant repulsive force or an attractive force that decreases with the distance are able to preserve the formation in which the eccentricities cause the actual relative motion and the weak thrusters keep the mean longitude difference small. Initial values are important for the formation flight but very exact adjustment of orbital elements is not important. Simplicity is one of our goals in this study and this result is achieved at least in the way that, when constant force thrusters are used, the satellites only need to detect the directions of the other ones to fly in tandem. A repulsive acceleration of the order of 10^-6 times the Earth attraction, is enough to effectively eliminate the disruptive effects of all the perturbations at least for a timescale of years.

Coplanar ground-track adjustment using time difference

The coplanar ground track adjustment problem is studied for both impulsive and continuous low-thrust maneuvers considering the J2 perturbation. For the initial orbit, semi-analytical solutions of the flight time and the longitude difference are obtained for an assigned ground-site latitude. Based on the time difference, the flight time for the two-body model is derived. This avoids directly solving the transfer orbit with the J2 effect. Then two methods including single-impulse method for free final orbit and shape-based low-thrust method for an assigned final orbit are proposed. For the single-impulse method, the analytical approximate solution is obtained by solving a cubic equation. For the low-thrust method, the shape-based approach is used with a combined inverse polynomial and trigonometric function. The results of several numerical examples show that the final longitude errors of the proposed methods are less than 0.04 deg for the nonlinear J2 model.

Hemispheric asymmetry of subauroral ion drifts: Statistical results

AbstractA large database of more than 18,000 subauroral ion drift (SAID) events from DMSP observations from 1987 to 2012 is used to systematically investigate the features of SAID. SAID occurs mostly at ~62°/−60° magnetic latitude (MLAT) and ~22:15/22:45 magnetic local time (MLT) for geomagnetically quiet conditions and at ~58°/−56° MLAT and ~22:15/22:45 MLT for geomagnetically disturbed conditions in the North Hemisphere (NH)/South Hemisphere (SH), respectively. Significant north‐south asymmetries in SAID occurrence, shape, and geomagnetic activity variations are found in this statistical study. The latitudinal width of a SAID is larger in the NH than in the SH. An interesting finding of this work is that the SAID occurrence probability peaks have an ~180° difference in longitude between the two hemispheres in the geographic coordinates for both geomagnetically quiet and disturbed conditions. The SAID width peaks in almost the same geomagnetic meridian zone with a geomagnetic longitude of ~80°–120° in both hemispheres. Significant hemispheric asymmetries and spike signatures with sharp dips are found in all the latitudinal profiles of the horizontal velocities of SAIDs. The SAID is highly correlated to geomagnetic activity, indicating that the location and evolution of the SAID might be influenced by global geomagnetic activity, auroral dynamics, and the dynamics of ring currents.

ALMA and VLA measurements of frequency-dependent time lags in Sagittarius A*: evidence for a relativistic outflow

Radio and mm-wavelength observations of Sagittarius A* (Sgr A*), the radio source associated with the supermassive black hole at the center of our Galaxy, show that it behaves as a partially self-absorbed synchrotron-emitting source. The measured size of Sgr A* shows that the mm-wavelength emission comes from a small region and consists of the inner accretion flow and a possible collimated outflow. Existing observations of Sgr A* have revealed a time lag between light curves at 43 GHz and 22 GHz, which is consistent with a rapidly expanding plasma flow and supports the presence of a collimated outflow from the environment of an accreting black hole. Here we wish to measure simultaneous frequency-dependent time lags in the light curves of Sgr A* across a broad frequency range to constrain direction and speed of the radio-emitting plasma in the vicinity of the black hole. Light curves of Sgr A* were taken in May 2012 using ALMA at 100 GHz using the VLA at 48, 39, 37, 27, 25.5, and 19 GHz. As a result of elevation limits and the longitude difference between the stations, the usable overlap in the light curves is approximately four hours. Although Sgr A* was in a relatively quiet phase, the high sensitivity of ALMA and the VLA allowed us to detect and fit maxima of an observed minor flare where flux density varied by ~10%. The fitted times of flux density maxima at frequencies from 100 GHz to 19 GHz, as well as a cross-correlation analysis, reveal a simple frequency-dependent time lag relation where maxima at higher frequencies lead those at lower frequencies. Taking the observed size-frequency relation of Sgr A* into account, these time lags suggest a moderately relativistic (lower estimates: 0.5c for two-sided, 0.77c for one-sided) collimated outflow.

An Assessment to Relationships between the Yellowfin Tuna and the Spotted Dolphin in Eastern Pacific Ocean (EPO) from 1998 to 2006

Database belong to the Programa Nacional de Aprovechamiento del Atún y Protección de los Delfines (PNAAPD) from México. The area covers from latitude 5 to 20 N and longitude 90 to 125 W, Eastern Pacific Ocean (EPO), for 1998, 2001, 2002, 2005 and 2006 includes date, geographical position, sea surface temperature, tuna’s catch, yellowfin tuna’s size and dolphin’s number. 5 degress squares of latitude and longitude, each year were made. Yellowfin tuna number was normally distributed (KSd = 0.02, P > 0.20). The problem to solve is the relationship of the spotted dolphin and yellowfin tuna, that may analyze in the background of a non linear generalized model. Considering the array of latitude and longitude over the years that the abundance of yellowfin tuna is a dependent variable and the spotted dolphin abundance is the covariance continuous variable, the interaction and covariance, indicates a significant contribution to variability. The tuna abundance index does produce significative differences in latitude and longitude. Considering the dolphin as a dependent variable and the yellowfin tuna as a covariance continuous variable, the dolphin abundance index produced significative differences in latitude and longitude.

The first measurement of the deflection of the vertical in longitude

During the summer of 1837 Christian Ludwig Gerling, a former student of Carl Friedrich Gauß’s, organized the world wide first determination of the deflection of the vertical in longitude. From a mobile observatory at the Frauenberg near Marburg (Hesse) he measured the astronomical longitude difference between C.F. Gauß’s observatory at Göttingen and F.G.B. Nicolai’s observatory at Mannheim within an error of 0.̋4. To achieve this precision he first used a series of light signals for synchronizing the observatory clocks and, second, he very carefully corrected for the varying reaction time of the observers. By comparing these astronomical results with the geodetic-determined longitude differences he had recently measured for the triangulation of Kurhessen, he was able to extract a combined value of the deflection of the vertical in longitude of Göttingen and Mannheim. His results closely agree with modern vertical deflection data.

'A thorn in the side of European geodesy': measuring Paris-Greenwich longitude by electric telegraph.

The difference in longitude between the observatories of Paris and Greenwich was long of fundamental importance to geodesy, navigation and timekeeping. Measured many times and by many different means since the seventeenth century, the preferred method of the later nineteenth and early twentieth centuries made use of the electric telegraph. I describe here for the first time the four Paris-Greenwich telegraphic longitude determinations made between 1854 and 1902. Despite contemporary faith in the new technique, the first was soon found to be inaccurate; the second was a failure, ending in Anglo-French dispute over whose result was to be trusted; the third failed in exactly the same way; and when eventually the fourth was presented as a success, the evidence for that success was far from clear-cut. I use this as a case study in precision measurement, showing how mutual grounding between different measurement techniques, in the search for agreement between them, was an important force for change and improvement. I also show that better precision had more to do with the gradually improving methods of astronomical, time determination than with the singular innovation of the telegraph, thus emphasizing the importance of what have been described as 'observatory techniques' to nineteenth-century practices of precision measurement.

Fundamental triangulation networks in Denmark

AbstractThe first triangulation activity on Danish ground was carried out by the astronomer Tycho Brahe who resided on the island Hven. He wanted to determine the longitude difference of his observatory Uraniborg to Copenhagen. A by-product was a map of his island made in 1579. In 1761 the Royal Danish Academy of Sciences and Letters initiated a mapping project which should be based on the principle of triangulation. Eventually 24 maps were printed in varying scales, predominantly in 1:120 000. The last map was engraved in 1842. The Danish GradeMeasurement initiated remeasurements and redesign of the fundamental triangulation network. This network served scientific as well as cartographic purposes in more than a century. Only in the 1960s all triangulation sides were measured electronically. A combined least-squares adjustment followed in the 1970s

Are Planetary Tides on the Sun and the Birthplace of Sunspots Related?

We study whether the birthplaces of sunspots (defined as the location of first appearance in the photosphere) are related to the planetary tides on the Sun. The heliocentric longitudes of newly emerging sunspots are statistically compared to the longitudes of tidal peaks caused by the tidal planets Mercury, Venus, Earth, and Jupiter. The longitude differences between new sunspots and tidal planets (and their conjugate locations) as well as the magnitudes of the vertical and horizontal tidal forces at the birthplace of new sunspots are calculated. The statistical distributions are compared with simulation results calculated using a random sunspot distribution. The results suggest that the birthplaces of sunspots (in the photosphere) are independent of the positions of tidal planets and the strength of tidal forces caused by them. However, since the sunspots actually originate near the tachocline (well below the photosphere) and it takes considerable time for the disturbances to reach photosphere, we hesitate to conclude that the formation of sunspots are not related to planetary positions.

Comprehensive assessment of the accuracy of the data from near space meteorological rocket sounding

We use the data obtained from empirical forecast model and satellite remote sensing to analyze and assess the accuracy of the data obtained from first near space meteorological rocket sounding in Jiuquan Satellite Launch Center (JSLC) in November 2004. Analysis shows that the data of empirical forecast model has great difference from meteorological rocket sounding data for the middle-upper stratosphere. Because the empirical forecast model has low spatial and temporal resolution, especially it lacks of the sounding data for the middle-upper stratosphere in China, the deviation between the data of meteorological rocket and the satellite data is obviouslly lower than the empirical forecast model gave. The deviation is caused by the systematic error between the two and the difference of time, latitude and longitude. Comprehensive comparison results show that the data of meteorological rocket is of high accuracy and credibility compared to the data of the empirical forecast model and satellite remote sensing. These data can be used to specify the probe’s results from other ways.

East‐west differences inF‐region electron density at midlatitude: Evidence from the Far East region

The global configuration of the geomagnetic field shows that the maximum east‐west difference in geomagnetic declination of northern middle latitude lies in the US region (~32°), which produces the significant ionospheric east‐west coast difference in terms of total electron content first revealed by Zhang et al. (2011). For verification, it is valuable to investigate this feature over the Far East area, which also shows significant geomagnetic declination east‐west gradient but smaller (~15°) than that of the US. The current study provides evidence of the longitudinal change supporting the thermospheric zonal wind mechanism by examining the climatology of peak electron density (NmF2), electron density (Ne) of different altitudes in the Far East regions with a longitude separation of up to 40–60° based on ground ionosonde and space‐based measurements. Although the east‐west difference (Rew) over the Far East area displays a clear diurnal variation similar to the US feature, that is negativeRew(West Ne > East Ne) in the noon and positive at evening‐night, the observational results reveal more differences including: (1) The noontime negativeRewis most pronounced in April–June while in the US during February–March. Thus, for the late spring and summer period negativeRewover the Far East region is more significant than that of the US. (2) The positiveRewat night is much less evident than in the US, especially without winter enhancement. (3) The magnitude of negativeRewtends to enhance toward solar maximum while in the US showing anticorrelation with the solar activity. The altitude distribution of pronounced negative difference (300–400 km) moves upward as the solar flux increases and hence produces the different solar activity dependence at different altitude. The result in the paper is not simply a comparison corresponding to the US results but raises some new features that are worth further studying and improve our current understanding of ionospheric longitude difference at midlatitude.

A simplified representation of the covariance structure of axially symmetric processes on the sphere

Spatial processes having covariance functions that depend solely on the distance between locations are known as homogeneous. Many random processes on the sphere are not homogeneous, especially in the latitudinal dimension. As a result, we study a class of statistical processes that exhibit axial symmetry, whereby their covariance function depends on differences in longitude alone. We develop a new and simplified representation for a valid axially symmetric process, reducing computational complexity considerably. In addition, we explore longitudinally reversible processes and the construction of parametric models for axially symmetric processes.

Evaluation of the positional difference between two common geocoding methods

Geocoding, the process of matching addresses to geographic coordinates, is a necessary first step when using geographical information systems (GIS) technology. However, different geocoding methodologies can result in different geographic coordinates. The objective of this study was to compare the positional (i.e. longitude/latitude) difference between two common geocoding methods, i.e. ArcGIS (Environmental System Research Institute, Redlands, CA, USA) and Batchgeo (freely available online at http://www.batchgeo.com). Address data came from the YMCA-Harvard After School Food and Fitness Project, an obesity prevention intervention involving children aged 5-11 years and their families participating in YMCA-administered, after-school programmes located in four geographically diverse metropolitan areas in the USA. Our analyses include baseline addresses (n = 748) collected from the parents of the children in the after school sites. Addresses were first geocoded to the street level and assigned longitude and latitude coordinates with ArcGIS, version 9.3, then the same addresses were geocoded with Batchgeo. For this analysis, the ArcGIS minimum match score was 80. The resulting geocodes were projected into state plane coordinates, and the difference in longitude and latitude coordinates were calculated in meters between the two methods for all data points in each of the four metropolitan areas. We also quantified the descriptions of the geocoding accuracy provided by Batchgeo with the match scores from ArcGIS. We found a 94% match rate (n = 705), 2% (n = 18) were tied and 3% (n = 25) were unmatched using ArcGIS. Forty-eight addresses (6.4%) were not matched in ArcGIS with a match score ≥80 (therefore only 700 addresses were included in our positional difference analysis). Six hundred thirteen (87.6%) of these addresses had a match score of 100. Batchgeo yielded a 100% match rate for the addresses that ArcGIS geocoded. The median for longitude and latitude coordinates for all the data was just over 25 m. Overall, the range for longitude was 0.04-12,911.8 m, and the range for latitude was 0.02-37,766.6 m. Comparisons show minimal differences in the median and minimum values, while there were slightly larger differences in the maximum values. The majority (>75%) of the geographic differences were within 50 m of each other; mostly <25 m from each other (about 49%). Only about 4% overall were ≥400 m apart. We also found geographic differences in the proportion of addresses that fell within certain meter ranges. The match-score range associated with the Batchgeo accuracy level "approximate" (least accurate) was 84-100 (mean = 92), while the "rooftop" Batchgeo accuracy level (most accurate) delivered a mean of 98.9 but the range was the same. Although future research should compare the positional difference of Batchgeo to criterion measures of longitude/latitude (e.g. with global positioning system measurement), this study suggests that Batchgeo is a good, free-of-charge option to geocode addresses.

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, where \sigma is the difference in mean longitudes and \Delta\omega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.