LNEXT-SYS-DESC-0018 LNext WRS-3 Rev A 20230406.pdf

DOORS EXPORT

National Aeronautics and Space Administration

Goddard Space Flight Center Greenbelt, Maryland

LNEXT-SYS-DESC-0018, Revision A Landsat Next, Code 426

Landsat Next Worldwide Reference System-3 (WRS-3) Definition

4/6/2023

Landsat WRS-3 Definition LNEXT-SYS-DESC-0018 Revision A iii

Electronic Signatures available online at: https://ipdtdms.gsfc.nasa.gov iv

CM Foreword This document is a Landsat Next Project Configuration Management (CM)-controlled document.

Changes to this document require prior approval of the applicable Configuration Control Board (CCB) Chairperson or designee. Proposed changes shall be submitted to the Landsat Next CM Office (CMO), along with supportive material justifying the proposed change. Changes to this document will be made by complete revision.

Questions or comments concerning this document should be addressed to:

NASA/Goddard Space Flight Center Landsat Next Project Office, Code 426 Attention: Configuration Management Office Greenbelt, Maryland 20771 v

Change History Log vi

Table of Contents SIGNATURE/APPROVAL PAGE ................................................................................................ II

CM FOREWORD ......................................................................................................................... IV

CHANGE HISTORY LOG ............................................................................................................ V

TABLE OF CONTENTS .............................................................................................................. VI

LIST OF FIGURES ...................................................................................................................... VI

LIST OF TABLES ........................................................................................................................ VI

1.0 PURPOSE

1.1 WRS-3 Scene Definition

1.2 WRS-3 Path Definition

1.3 WRS-3 Row Definition

2.0 MATHEMATICAL DEFINITION OF THE WRS-3 GRID

2.1 WRS-3 Nominal Scene Center Computation Algorithm

3.0 REFERENCES

APPENDIX A: SCENE CENTER TABLE

APPENDIX B: ABBREVIATIONS AND ACRONYMS

List of Figures Figure 1.1-1 Image Interval Figure 2.1-1 WRS-3 Scene Center Calculations

List of Tables

Table 1.2-1 WRS-3 Path Time Sequence Table 2-1 WRS-3 Input Parameters

1.0 PURPOSE

The Landsat Worldwide Reference System-3 (WRS-3) provides an indexing scheme for the repeating pattern of orbital ground tracks traversed by the Landsat Next spacecrafts over their 18-day orbital repeat cycle. The previous two WRS grids (WRS-1 and WRS-2) were designed for the Landsat 1-9 missions which flew in a higher orbit. The current WRS-3 was designed for the 653-km orbit used by the later missions.

1.1 WRS-3 SCENE DEFINITION

Although the Landsat Next Instrument Suite (LandIS) imagers collect continuous along-track swaths of data while operating, the data are cataloged and distributed as fixed-size along-track image segments referred to as scenes. Standard Landsat scenes are extracted around nominal scene-center coordinates and are sized to provide along-track overlap between adjacent scenes.

Figure 1.1-1 shows how a continuous Landsat interval of data is segmented into overlapping scenes, based on the WRS grid, for cataloging and distribution. Using the WRS-3 orbital parameters listed in Table 2-1 and the LandIS instrument field of view requirement definition, for scenes the nominal along and across track dimensions are 168-km and 164-km respectively.

Figure 1.1-1 Image Interval

A continuous interval of imagery is logically subdivided into overlapping scenes.

1.2 WRS-3 PATH DEFINITION

The WRS indexes orbits (paths) and scene centers (rows) into a global grid system comprising 265 paths by 248 rows. Since adjacent Landsat scenes overlap, indexing the location of an acquisition by latitude/longitude can be ambiguous and, in any event, provides little insight into where the scene falls in the 18-day acquisition cycle. The path/row notation provides a standard designator for every nominal scene center that can be readily related to both the 18-day acquisition cycle and longitude and latitude coordinates. Like the previous Landsat WRS definitions WRS-3 also provides a target data collection pattern ensuring that nominal Earth targets are observed using common viewing geometry, independent of the collecting spacecraft.

The Landsat orbital altitude and repeat cycle dictate that the 18-day acquisition cycle is completed in 265 orbits. The repeating ground tracks corresponding to the 265 orbits that make up a complete acquisition cycle are numbered sequentially with the numbers increasing to the west. The number of unique ground tracks means that adjacent ground tracks are approximately 151-km apart at the equator. The Earth’s rotation during each revolution of the spacecraft in its sun-synchronous orbit causes consecutive orbits to be approximately 2719-km apart at the equator. Thus, each orbit advances 18 paths (2719/151), causing each WRS path to be traversed once per 18-day cycle in an interleaved pattern. Table 1.2-1 shows the time sequence of WRS-3 paths over an 18-day acquisition cycle.

Table 1.2-1 WRS-3 Path Time Sequence

1.3 WRS-3 ROW DEFINITION

Segmenting each Landsat orbit into 248 equally spaced scenes, covering both the day and night sides of the Earth, leads to a set of scene centers separated by just under 162-km along track.

This definition leads to approximately 3% of the scene in the along track dimension overlapping between adjacent scenes. This 3% represents a total overlap between adjacent scenes, including the scene acquired prior and after a given scene’s path and row. The WRS row system is indexed so that the scene center at the orbital descending node is row 60, with the row numbers increasing in the along-track direction. Note that unlike the path numbers which, being fixed to the orbital ground tracks, must be integers, fractional row numbers are possible by shifting the scene window along-track relative to the fixed WRS-3 scene centers.

2.0 MATHEMATICAL DEFINITION OF THE WRS-3 GRID

The WRS-3 grid is related to WGS84 geodetic latitude/longitude coordinates using the nominal Landsat orbital parameters listed in Table 2-1. The procedure for computing the WRS scene center is described below. Table 2-1 shows the input parameters used in the subsequent WRS scene center computations.

Table 2-1 WRS-3 Input Parameters

Parameter Value Earth Parameters Semi-Major Axis (WGS84) 6378137.0 m Semi-Minor Axis (WGS84) 6356752.314 m Orbit Parameters Inclination 97.9835 degrees WRS Parameters Number of Paths 265 Number of Rows 248 WRS Repeat Cycle 18 days Descending Node Row 60 Longitude of Path 001, Row 060 -65.2 degrees (65.2 West) Scene Parameters Path Integer 1-265 Row Float 0.5 < R < 248.5

The unknown values to be computed are:

WRS Scene Center Latitude (θd ) WRS Scene Center Longitude (λd)

2.1 WRS-3 NOMINAL SCENE CENTER COMPUTATION ALGORITHM

Figure 2.1-1 WRS-3 Scene Center Calculations

Convert input angles to radians:

ξ = π / 180 * ξ λ001 = π / 180 * λ001 Compute the Earth’s angular rotation rate:

Note: These computations use the solar rotation rate, rather than the sidereal rate as called for in the General Electric Landsat D Program Information Release (PIR) that was first described the Worldwide Reference System-2, in order to account for the orbital precession which is designed to make the orbit sun synchronous. Thus, the apparent Earth angular velocity is the inertial (sidereal) angular velocity plus the mean precession rate which, by design, is equal to the solar angular rate.

Compute the spacecraft’s angular rotation rate:

Compute the central travel angle from the descending node:

Compute the WRS geocentric latitude:

Compute the longitude of Row 60 for this Path:

Compute the WRS longitude:

Make sure the longitude is in the range +/-π:

While ( λd > π ) λd = λd - 2 π

While ( λd < - π ) λd = λd + 2 π Convert the WRS geocentric latitude to geodetic latitude:

Convert angles to degrees:

θd = θd * 180 / π λd = λd * 180 / π Round WRS lat/long off to the nearest whole arc minute:

θd = round( θd*60 ) / 60 λd = round( λd*60 ) / 60 Return the results:

WRS Latitude θd WRS Longitude λd

3.0 REFERENCES

Landsat 8 Science Data Users Handbook, https://www.usgs.gov/landsat-missions/landsat- 8-data-users-handbook. Accessed April 18, 2022.

Landsat 8 Level Zero Reformatted Data Format Control Book.

https://www.usgs.gov/media/files/landsat-8-level-0-reformatted-data-format-control-book. Accessed April 18, 2022.

DMA TR 8350.2-A, DMA Technical Report, Supplement to Department of Defense World Geodetic System 1984 Technical Report, prepared by the Defense Mapping Agency WGS84 Development Committee, dated December 1, 1987.

https://apps.dtic.mil/sti/pdfs/ADA280358.pdf. Accessed April 18, 2022.

Landsat 8-9 Calibration Validation Algorithm Description Document.

https://www.usgs.gov/media/files/landsat-8-9-calibration-validation-algorithm-description-document. Accessed April 18, 2022.

https://www.usgs.gov/landsat-missions/landsat-8-data-users-handbook https://www.usgs.gov/landsat-missions/landsat-8-data-users-handbook https://www.usgs.gov/media/files/landsat-8-level-0-reformatted-data-format-control-book https://www.usgs.gov/media/files/landsat-8-level-0-reformatted-data-format-control-book https://apps.dtic.mil/sti/pdfs/ADA280358.pdf https://www.usgs.gov/media/files/landsat-8-9-calibration-validation-algorithm-description-document https://www.usgs.gov/media/files/landsat-8-9-calibration-validation-algorithm-description-document

Appendix A: Scene Center Table

The Scene Center Table is attached to this document.

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Appendix B: Abbreviations and Acronyms Acronym/Abbreviation Definition in Inches km Kilometer LandIS Landsat Next Instrument Suite m Meter PIR Program Information Release TR Technical Report WGS84 World Geodetic System 1984, as defined by NIMA TR8350.2 WRS Worldwide Reference System WRS-1 Worldwide Reference System-1 WRS-2 Worldwide Reference System-2 WRS-3 Worldwide Reference System-3 This Acronyms List was Generated from the Landsat Next Acronym List (LNEXT-MGMT-DESC-0006) Rev -

wrs_path,wrs_row,ID,LandPercent,ul_lat,ul_lon,ur_lat,ur_lon,ll_lat,ll_lon,lr_lat,lr_lon,center_lat,center_lon 1,1,1001,0,81.967581,4.12398,80.626028,8.082583,81.210236,-4.719565,79.966466,0.065955,80.94257775,1.88823825 1,2,1002,0,81.234826,-4.483646,79.988242,0.283972,80.314109,-11.859332,79.169312,-6.686754,80.17662225,-5.68644 1,3,1003,0,80.3428,-11.663917,79.195258,-6.499059,79.299586,-17.75011,78.249254,-12.473558,79.2717245,-12.096661 1,4,1004,0.164543114,79.33133,-17.588864,78.278489,-12.313508,78.197102,-22.612403,77.232784,-17.405696,78.25992625,-17.48011775 1,5,1005,0.84967309,78.231115,-22.478771,77.264589,-17.269524,77.029006,-26.652125,76.141046,-21.611576,77.166439,-22.002999 1,6,1006,1,77.064719,-26.540414,76.174859,-21.495433,75.811428,-30.040673,74.990398,-25.213228,76.010351,-25.822437 1,7,1007,1,75.848432,-29.946296,75.025786,-25.113644,74.556,-32.9137,73.79332,-28.31685,74.8058845,-29.0726225 1,8,1008,1,74.593998,-32.833076,73.829957,-28.230886,73.27117,-35.376349,72.559309,-31.010875,73.5636085,-31.8627965 1,9,1009,1,73.309948,-35.306717,72.596943,-30.936117,71.963152,-37.509635,71.295609,-33.367346,72.291413,-34.27995375 1,10,1010,1,72.002548,-37.448868,71.334049,-33.30184,70.636571,-39.376103,70.007783,-35.444385,70.99523775,-36.392799 1,11,1011,1,70.676466,-39.322552,70.046881,-35.386557,69.294925,-41.024327,68.700141,-37.288761,69.67960325,-38.25554925 1,12,1012,1,69.335228,-40.976711,68.739783,-37.237345,67.94089,-42.492347,67.376054,-38.938165,68.34798875,-39.911142 1,13,1013,1,67.98153,-42.449655,67.41615,-38.892138,66.576543,-43.810216,66.038183,-40.423093,67.0031015,-41.3937755 1,14,1014,1,66.617465,-43.771647,66.07866,-40.381623,65.203516,-45.001906,64.688647,-41.768347,65.647072,-42.73088075 1,15,1015,1,65.244678,-44.966818,64.729449,-41.730759,63.823106,-46.086713,63.329153,-42.994227,64.2815965,-43.94462925 1,16,1016,1,63.864472,-46.054588,63.370233,-42.959965,62.436352,-47.080312,61.961087,-44.117451,62.908036,-45.053079 1,17,1017,0.992471909,62.477895,-47.050726,62.002407,-44.086056,61.044099,-47.995542,60.585581,-45.15188,61.5274955,-46.071051 1,18,1018,0.078681794,61.085796,-47.968147,60.62711,-45.122968,59.647038,-48.843008,59.203571,-46.109076,60.14087875,-47.01079975 1,19,1019,0,59.68887,-48.817516,59.245283,-46.082329,58.245739,-49.631539,57.815837,-46.99875,58.74893225,-47.8825335 1,20,1020,0,58.28769,-49.607708,57.85771,-46.973897,56.840676,-50.368534,56.423028,-47.829103,57.352276,-48.6948105 1,21,1021,0,56.882734,-50.346162,56.465045,-47.805915,55.432247,-51.060239,55.025696,-48.607102,55.9514305,-49.4548545 1,22,1022,0,55.474401,-51.039155,55.06784,-48.585385,54.02079,-51.711963,53.624306,-49.338703,54.54683425,-50.1688015 1,23,1023,0,54.063031,-51.69202,53.666565,-49.318289,52.60659,-52.328239,52.219258,-50.029019,53.138861,-50.84189175 1,24,1024,0,52.648909,-52.309313,52.261621,-50.009765,51.189891,-52.912967,50.810894,-50.682465,51.72782875,-51.4786275 1,25,1025,0,51.232283,-52.894951,50.853351,-50.664246,49.770907,-53.469517,49.399512,-51.302872,50.31401325,-52.0828965 1,26,1026,0.133145224,49.813366,-53.452317,49.442054,-51.285579,48.349821,-54.000816,47.985369,-51.893577,48.8976525,-52.65807225 1,27,1027,0.597375088,48.392341,-53.98435,48.027988,-51.877116,46.926792,-54.509417,46.56869,-52.457503,47.47895275,-53.2070965 1,28,1028,0.047572505,46.96937,-54.493615,46.61138,-52.441791,45.501963,-54.997562,45.149674,-52.997217,46.05809675,-53.73254625 1,29,1029,0,45.544594,-54.982361,45.19243,-52.982181,44.075458,-55.467224,43.728498,-53.514988,44.635245,-54.2366885 1,30,1030,0,44.118139,-55.45257,43.771314,-53.500562,42.64739,-55.920148,42.305317,-54.012824,43.21054,-54.721526 1,31,1031,0,42.690118,-55.905992,42.348189,-53.99895,41.217857,-56.357885,40.880272,-54.492511,41.784109,-55.1888345 1,32,1032,0,41.26063,-56.344182,40.923195,-54.479138,39.786952,-56.781815,39.453488,-54.955643,40.35606625,-55.6401945 1,33,1033,0,39.829767,-56.768529,39.496459,-54.942725,38.354756,-57.193175,38.02508,-55.403648,38.9265155,-56.07701925 1,34,1034,0,38.397611,-57.180271,38.068095,-55.391144,36.921346,-57.593078,36.595152,-55.837808,37.495551,-56.50057525 1,35,1035,0,36.964238,-57.580524,36.638209,-55.825681,35.48679,-57.982523,35.1638,-56.259282,36.06325925,-56.9120025 1,36,1036,0,35.529719,-57.970292,35.206894,-56.247497,34.051155,-58.362417,33.73111,-56.669114,34.6297195,-57.31233 1,37,1037,0,34.094118,-58.350483,33.77424,-56.657642,32.6145,-58.733582,32.297165,-57.068253,33.19500575,-57.70249 1,38,1038,0,32.657496,-58.721922,32.340328,-57.057066,31.176884,-59.096767,30.862041,-57.457564,31.75918725,-58.08332975 1,39,1039,0,31.219911,-59.085361,30.905234,-57.446636,29.738361,-59.452657,29.425808,-57.837835,30.3223285,-58.45562225 1,40,1040,0,29.781418,-59.441485,29.469029,-57.827143,28.298982,-59.801879,27.988533,-58.209788,28.8844905,-58.82007375 1,41,1041,0,28.342068,-59.790923,28.03178,-58.199311,26.858798,-60.145011,26.550281,-58.574086,27.44573175,-59.17733275 1,42,1042,0,26.901911,-60.134256,26.593551,-58.563804,25.417857,-60.482587,25.111111,-58.931339,26.0061075,-59.5279965 1,43,1043,0,25.460996,-60.472017,25.154404,-58.921234,23.976206,-60.815101,23.671081,-59.282113,24.56567175,-59.87261625 1,44,1044,0,24.01937,-60.804702,23.714394,-59.272168,22.53389,-61.143013,22.230248,-59.626929,23.1244755,-60.211703 1,45,1045,0,22.577078,-61.132773,22.27358,-59.61713,21.090955,-61.466752,20.788665,-59.966276,21.6825695,-60.54573275 1,46,1046,0,21.134165,-61.456658,20.832013,-59.956607,19.647443,-61.78672,19.346384,-60.300607,20.24000125,-60.875148 1,47,1047,0,19.690675,-61.776761,19.389747,-60.291054,18.203398,-62.103295,17.903456,-60.630345,18.796819,-61.20036375 1,48,1048,0,18.246651,-62.093461,17.946832,-60.620897,16.758864,-62.416834,16.459929,-60.955891,17.353069,-61.52177075 1,49,1049,0,16.802136,-62.407114,16.503317,-60.946536,15.313882,-62.727675,15.015854,-61.277621,15.90879725,-61.8397365 1,50,1050,0,15.357172,-62.71806,15.059251,-61.268346,13.868496,-63.036141,13.571276,-61.595889,14.46404875,-62.154609 1,51,1051,0,13.911802,-63.026621,13.614682,-61.586685,12.422746,-63.342539,12.126243,-61.911034,13.01886825,-62.46671975 1,52,1052,0.001014306,12.466068,-63.333106,12.169656,-61.90189,10.976675,-63.647165,10.680801,-62.223377,11.5733,-62.7763845 1,53,1053,0.816801502,11.020012,-63.637811,10.72422,-62.214283,9.530324,-63.950304,9.234994,-62.533227,10.1273875,-63.08390625 1,54,1054,1,9.573675,-63.941019,9.278418,-62.524174,8.083737,-64.252233,7.788869,-62.840878,8.68117475,-63.389576 1,55,1055,1,8.1271,-64.24301,7.832295,-62.831858,6.636953,-64.553219,6.34247,-63.146617,7.2347045,-63.693676 1,56,1056,1,6.680328,-64.54405,6.385897,-63.13762,5.190017,-64.853527,4.89584,-63.450719,5.7880205,-63.996479 1,57,1057,1,5.233401,-64.844404,4.939267,-63.441738,3.742968,-65.153415,3.449023,-63.753456,4.34116475,-64.29825325 1,58,1058,1,3.786362,-65.144331,3.492449,-63.744482,2.295851,-65.453138,2.002063,-64.055089,2.89418125,-64.59926 1,59,1059,1,2.339252,-65.444085,2.045486,-64.046115,0.848706,-65.75295,0.555003,-64.355878,1.44711175,-64.899757 1,60,1060,1,0.892114,-65.743921,0.598422,-64.346895,-0.598422,-66.053105,-0.892114,-64.656079,2.77556E-17,-65.2 1,61,1061,1,-0.555009,-66.044092,-0.8487,-64.64708,-2.045493,-66.353855,-2.339246,-64.955945,-1.447112,-65.500243 1,62,1062,1,-2.002076,-66.344851,-2.295838,-64.946922,-3.492461,-66.655458,-3.786349,-65.255729,-2.894181,-65.80074 1,63,1063,1,-3.449042,-66.646454,-3.742949,-65.246675,-4.939286,-66.958172,-5.233382,-65.555686,-4.34116475,-66.10174675 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1,186,1186,0.80841863,2.295838,102.826663,2.002076,101.428734,3.786349,102.517856,3.492461,101.118127,2.894181,101.972845 1,187,1187,1,3.742949,102.52691,3.449042,101.127131,5.233382,102.217899,4.939286,100.815413,4.34116475,101.6718383 1,188,1188,0.986243891,5.189991,102.226992,4.895865,100.824424,6.680303,101.917515,6.385922,100.511325,5.78802025,101.370064 1,189,1189,0.336115959,6.636922,101.926654,6.342501,100.520351,8.127069,101.616444,7.832327,100.205592,7.23470475,101.0672603 1,190,1190,0.067043027,8.083699,101.625638,7.788907,100.214642,9.573638,101.314424,9.278455,99.897939,8.68117475,100.7631608 1,191,1191,0,9.530281,101.32368,9.235038,99.90702,11.019969,101.011186,10.724264,99.588078,10.127388,100.457491 1,192,1192,0.20822097,10.976626,101.020512,10.680851,99.5972,12.466019,100.706452,12.169706,99.275714,11.5733005,100.1499695 1,193,1193,0.734826686,12.422691,100.715857,12.126299,99.284886,13.911748,100.399937,13.614738,98.960538,13.018869,99.8403045 1,194,1194,1,13.868435,100.40943,13.571338,98.96977,15.357112,100.091347,15.059314,98.642228,14.46404975,99.52819375 1,195,1195,1,15.313817,100.100935,15.015921,98.65153,16.80207,99.780372,16.503385,98.320447,15.90879825,99.213321 1,196,1196,1,16.758793,99.790065,16.460003,98.329829,18.24658,99.466689,17.946905,97.994837,17.35307025,98.895355 1,197,1197,1,18.203322,99.476498,17.903535,98.004311,19.690599,99.149961,19.389826,97.665023,18.7968205,98.57394825 1,198,1198,1,19.647362,99.159895,19.346469,97.674599,21.134084,98.82983,20.832098,97.330604,20.24000325,98.248732 1,199,1199,1,21.090869,98.839899,20.788755,97.340296,22.576992,98.505916,22.27367,96.991155,21.6825715,97.9193165 1,200,1200,1,22.5338,98.516133,22.230343,97.000977,24.019279,98.177818,23.71449,96.646221,23.124478,97.58528725 1,201,1201,1,23.976111,98.188194,23.671181,96.656187,25.460901,97.845105,25.154504,96.295314,24.56567425,97.2462 1,202,1202,1,25.417758,97.855654,25.111216,96.305439,26.901811,97.507316,26.593657,95.93791,26.0061105,96.90157975 1,203,1203,1,26.858695,97.518052,26.55039,95.948211,28.341964,97.163957,28.03189,95.573444,27.44573475,96.550916 1,204,1204,1,28.298875,97.174894,27.988647,95.583939,29.78131,96.814492,29.469143,95.201302,28.88449375,96.19365675 1,205,1205,1,29.738249,96.825647,29.425926,95.212011,31.219799,96.458342,30.905353,94.820821,30.32233175,95.82920525 1,206,1206,1,31.176769,96.469733,30.862163,94.831764,32.657381,96.094878,32.340451,94.431276,31.759191,95.45691275 1,207,1207,1,32.614382,96.106523,32.297292,94.442477,34.093999,95.723414,33.774368,94.031876,33.19501025,95.0760725 1,208,1208,1,34.051034,95.735335,33.731241,94.043361,35.529597,95.343198,35.207026,93.621756,34.6297245,94.6859125 1,209,1209,1,35.486666,95.355418,35.163934,93.633552,36.964113,94.953406,36.638344,93.199963,36.06326425,94.28558475 1,210,1210,1,36.921219,94.96595,36.59529,93.2121,38.397483,94.553129,38.068234,92.765449,37.4955565,93.874157 1,211,1211,1,38.354627,94.566025,38.025221,92.777961,39.829636,94.141364,39.496601,92.317053,38.92652125,93.45060075 1,212,1212,1,39.786821,94.154643,39.453631,92.329977,41.260497,93.716995,40.92334,91.853488,40.35607225,93.01377575 1,213,1213,1,41.217724,93.730693,40.880418,91.866865,42.689983,93.278782,42.348337,91.373321,41.7841155,92.56241525 1,214,1214,1,42.647254,93.292937,42.305466,91.387197,44.118002,92.825339,43.771465,90.874953,43.21054675,92.0951065 1,215,1215,1,44.075321,92.839993,43.728649,90.88938,45.544455,92.35511,45.192584,90.356592,44.63525225,91.61026875 1,216,1216,1,45.501824,92.370313,45.149827,90.371627,46.969229,91.866343,46.611536,89.816221,46.058104,91.106126 1,217,1217,1,46.926652,91.88215,46.568845,89.831928,48.392199,91.357059,48.028146,89.251564,47.4789605,90.58067525 1,218,1218,1,48.349679,91.373532,47.985526,89.268019,49.813222,90.825007,49.442214,88.660045,48.89766025,90.03165075 1,219,1219,1,49.770765,90.842217,49.399671,88.677328,51.232139,90.267624,50.853513,88.038728,50.314022,89.45647425 1,220,1220,1,51.189748,90.285652,50.811055,88.056935,52.648763,89.68197,52.261785,87.384262,51.72783775,88.85220475 1,221,1221,1,52.606446,89.70091,52.219419,87.403502,54.062884,89.064661,53.666731,86.692801,53.13887,88.2154685 1,222,1222,1,54.020646,89.084621,53.624468,86.713198,55.474253,88.411781,55.068007,85.95991,54.5468435,87.5423775 1,223,1223,1,55.432103,88.432886,55.025859,85.981607,56.882585,87.718774,56.465213,85.180451,55.95144,86.8284295 1,224,1224,1,56.840531,87.741169,56.423192,85.203616,58.287541,86.980308,57.857879,84.348444,57.35228575,86.06838425 1,225,1225,1,58.245594,87.004165,57.816001,84.373271,59.68872,86.190104,59.245453,83.456885,58.748942,85.25610625 1,226,1226,1,59.646893,86.215627,59.203736,83.483602,61.085646,85.340725,60.62728,82.497531,60.14088875,84.38437125 1,227,1227,1,61.043955,85.368154,60.585745,82.526409,62.477745,84.423296,62.002577,81.460624,61.5275055,83.44462075 1,228,1228,1,62.436208,84.45292,61.961251,81.491982,63.864322,83.427152,63.370404,80.334537,62.90804625,82.42664775 1,229,1229,1,63.822963,83.45932,63.329317,80.368757,65.244529,82.339377,64.72962,79.105332,64.28160725,81.3181965 1,230,1230,1,65.203374,82.374512,64.68881,79.142873,66.617317,81.144204,66.078831,77.756193,65.647083,80.1044455 1,231,1231,1,66.576402,81.182825,66.038345,77.797612,67.981381,79.822212,67.41632,76.266702,67.003112,78.76733775 1,232,1232,0.998854155,67.940749,79.864962,67.376215,76.312675,69.33508,78.349273,68.739953,74.611899,68.34799925,77.28470225 1,233,1233,0.90955694,69.294786,78.396952,68.7003,74.663256,70.67632,76.695122,70.047049,72.761097,69.67961375,75.62910675 1,234,1234,0.650026758,70.636434,76.748742,70.007939,72.818859,72.002403,74.82145,71.334215,70.676359,70.99524775,73.7663525 1,235,1235,0.623625429,71.963017,74.882294,71.295762,70.741794,73.309804,72.679319,72.597107,68.310608,72.2914225,71.65350375 1,236,1236,0.031935446,73.271039,72.749034,72.559459,68.38529,74.593857,70.205706,73.830117,65.60534,73.563618,69.2363425 1,237,1237,0,74.555872,70.28642,73.793466,65.691222,75.848293,67.318964,75.025943,62.48805,74.8058935,66.446164 1,238,1238,0.514147083,75.811304,67.413439,74.990537,62.587547,77.064584,63.913133,76.17501,58.869777,76.01035875,63.195974 1,239,1239,0,77.028888,64.024949,76.141179,58.985829,78.230985,59.851559,77.264733,54.643791,77.16644625,59.376532 1,240,1240,0,78.196991,59.985303,77.232907,54.779868,79.331207,54.961744,78.278622,49.687679,78.25993175,54.8536485 1,241,1241,0.006130358,79.299484,55.123105,78.249365,49.847634,80.342687,49.036913,79.195379,43.873115,79.27172875,49.47019175 1,242,1242,0.075040773,80.314018,49.232444,79.16941,44.060719,81.234726,41.856785,79.988347,37.089956,80.17662525,43.059976 1,243,1243,0,81.210162,42.092814,79.966545,37.307889,81.9675,33.249321,80.626112,29.291212,80.94257975,35.485309 1,244,1244,0,81.948354,33.52927,80.609473,29.539387,82.494268,23.212926,81.075382,20.556169,81.53186925,26.709438 1,245,1245,0,82.481976,23.532845,81.064888,20.829747,82.769902,12.068714,81.306913,11.144362,81.90591975,16.893917 1,246,1246,0,82.765656,12.41333,81.30331,11.432736,82.765656,0.507424,81.30331,1.488019,82.034483,6.46037725 1,247,1247,0,82.769932,0.852018,81.306883,1.776409,82.482005,-10.612156,81.064858,-7.908945,81.9059195,-3.9731685 1,248,1248,0.379437272,82.494326,-10.292302,81.075323,-7.635322,81.948408,-20.608707,80.609417,-16.618492,81.5318685,-13.78870575 2,1,2001,0,81.967581,2.765489,80.626028,6.724092,81.210236,-6.078056,79.966466,-1.292536,80.94257775,0.52974725 2,2,2002,0,81.234826,-5.842136,79.988242,-1.074519,80.314109,-13.217823,79.169312,-8.045245,80.17662225,-7.04493075 2,3,2003,0.000161445,80.3428,-13.022407,79.195258,-7.857549,79.299586,-19.108601,78.249254,-13.832049,79.2717245,-13.4551515 2,4,2004,0.371099847,79.33133,-18.947355,78.278489,-13.671999,78.197102,-23.970894,77.232784,-18.764187,78.25992625,-18.83860875 2,5,2005,0.983388052,78.231115,-23.837261,77.264589,-18.628015,77.029006,-28.010616,76.141046,-22.970067,77.166439,-23.36148975 2,6,2006,1,77.064719,-27.898904,76.174859,-22.853923,75.811428,-31.399164,74.990398,-26.571719,76.010351,-27.1809275 2,7,2007,1,75.848432,-31.304786,75.025786,-26.472134,74.556,-34.27219,73.79332,-29.67534,74.8058845,-30.4311125 2,8,2008,1,74.593998,-34.191567,73.829957,-29.589377,73.27117,-36.73484,72.559309,-32.369365,73.5636085,-33.22128725 2,9,2009,1,73.309948,-36.665208,72.596943,-32.294608,71.963152,-38.868126,71.295609,-34.725836,72.291413,-35.6384445 2,10,2010,1,72.002548,-38.807358,71.334049,-34.66033,70.636571,-40.734593,70.007783,-36.802875,70.99523775,-37.751289 2,11,2011,1,70.676466,-40.681043,70.046881,-36.745047,69.294925,-42.382818,68.700141,-38.647252,69.67960325,-39.61404 2,12,2012,1,69.335228,-42.335202,68.739783,-38.595835,67.94089,-43.850837,67.376054,-40.296656,68.34798875,-41.2696325 2,13,2013,1,67.98153,-43.808145,67.41615,-40.250628,66.576543,-45.168707,66.038183,-41.781583,67.0031015,-42.75226575 2,14,2014,1,66.617465,-45.130138,66.07866,-41.740114,65.203516,-46.360397,64.688647,-43.126837,65.647072,-44.0893715 2,15,2015,1,65.244678,-46.325309,64.729449,-43.08925,63.823106,-47.445204,63.329153,-44.352717,64.2815965,-45.30312 2,16,2016,1,63.864472,-47.413079,63.370233,-44.318456,62.436352,-48.438802,61.961087,-45.475942,62.908036,-46.41156975 2,17,2017,0.904555083,62.477895,-48.409216,62.002407,-45.444546,61.044099,-49.354032,60.585581,-46.51037,61.5274955,-47.429541 2,18,2018,0.003093316,61.085796,-49.326637,60.62711,-46.481459,59.647038,-50.201499,59.203571,-47.467567,60.14087875,-48.3692905 2,19,2019,0,59.68887,-50.176006,59.245283,-47.440819,58.245739,-50.990029,57.815837,-48.357241,58.74893225,-49.24102375 2,20,2020,0,58.28769,-50.966199,57.85771,-48.332387,56.840676,-51.727024,56.423028,-49.187593,57.352276,-50.05330075 2,21,2021,0,56.882734,-51.704653,56.465045,-49.164405,55.432247,-52.41873,55.025696,-49.965593,55.9514305,-50.81334525 2,22,2022,0,55.474401,-52.397646,55.06784,-49.943876,54.02079,-53.070453,53.624306,-50.697194,54.54683425,-51.52729225 2,23,2023,0,54.063031,-53.050511,53.666565,-50.67678,52.60659,-53.68673,52.219258,-51.38751,53.138861,-52.20038275 2,24,2024,0,52.648909,-53.667804,52.261621,-51.368255,51.189891,-54.271458,50.810894,-52.040956,51.72782875,-52.83711825 2,25,2025,0,51.232283,-54.253441,50.853351,-52.022737,49.770907,-54.828008,49.399512,-52.661362,50.31401325,-53.441387 2,26,2026,0.665620845,49.813366,-54.810807,49.442054,-52.64407,48.349821,-55.359306,47.985369,-53.252067,48.8976525,-54.0165625 2,27,2027,0.692990015,48.392341,-55.34284,48.027988,-53.235607,46.926792,-55.867908,46.56869,-53.815993,47.47895275,-54.565587 2,28,2028,0.004788591,46.96937,-55.852105,46.61138,-53.800281,45.501963,-56.356053,45.149674,-54.355708,46.05809675,-55.09103675 2,29,2029,0,45.544594,-56.340852,45.19243,-54.340671,44.075458,-56.825715,43.728498,-54.873479,44.635245,-55.59517925 2,30,2030,0,44.118139,-56.81106,43.771314,-54.859053,42.64739,-57.278639,42.305317,-55.371315,43.21054,-56.08001675 2,31,2031,0,42.690118,-57.264482,42.348189,-55.357441,41.217857,-57.716375,40.880272,-55.851001,41.784109,-56.54732475 2,32,2032,0,41.26063,-57.702673,40.923195,-55.837629,39.786952,-58.140305,39.453488,-56.314133,40.35606625,-56.998685 2,33,2033,0,39.829767,-58.127019,39.496459,-56.301216,38.354756,-58.551666,38.02508,-56.762138,38.9265155,-57.43550975 2,34,2034,0,38.397611,-58.538762,38.068095,-56.749635,36.921346,-58.951568,36.595152,-57.196299,37.495551,-57.859066 2,35,2035,0,36.964238,-58.939015,36.638209,-57.184172,35.48679,-59.341014,35.1638,-57.617772,36.06325925,-58.27049325 2,36,2036,0,35.529719,-59.328782,35.206894,-57.605988,34.051155,-59.720908,33.73111,-58.027604,34.6297195,-58.6708205 2,37,2037,0,34.094118,-59.708974,33.77424,-58.016132,32.6145,-60.092073,32.297165,-58.426744,33.19500575,-59.06098075 2,38,2038,0,32.657496,-60.080413,32.340328,-58.415557,31.176884,-60.455258,30.862041,-58.816055,31.75918725,-59.44182075 2,39,2039,0,31.219911,-60.443851,30.905234,-58.805127,29.738361,-60.811147,29.425808,-59.196326,30.3223285,-59.81411275 2,40,2040,0,29.781418,-60.799975,29.469029,-59.185634,28.298982,-61.160369,27.988533,-59.568279,28.8844905,-60.17856425 2,41,2041,0,28.342068,-61.149414,28.03178,-59.557801,26.858798,-61.503501,26.550281,-59.932576,27.44573175,-60.535823 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