820:
805:
55:
29:
1230:
1254:
1206:
1242:
1218:
689:
for a brass disk near Donner Summit, in
California. Given the dimensions of the ellipsoid, the conversion from lat/lon/height-above-ellipsoid coordinates to X-Y-Z is straightforward—calculate the X-Y-Z for the given lat-lon on the surface of the ellipsoid and add the X-Y-Z vector that is
690:
perpendicular to the ellipsoid there and has length equal to the point's height above the ellipsoid. The reverse conversion is harder: given X-Y-Z can immediately get longitude, but no closed formula for latitude and height exists. See "
624:
may also be used. Due to differences between datums, the ECEF coordinates for a location will be different for different datums, although the differences between most modern datums is relatively small, within a few meters.
932:
1118:
414:
1186:
and geocentric (ECEF) or local
Cartesian (ENU) coordinates. This provides accurate results for all inputs including points close to the center of the Earth.
236:
404:
372:
1279:
1163:
698:
the first iteration gives latitude correct within 10 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
382:
1173:
1018:
362:
983:
1150:
1274:
143:
442:
651:(IRP), which does not exactly coincide with the Earth's rotational axis The slight "wobbling" of the rotational axis is known as
589:
707:
819:
228:
804:
681:
is also in the plane of the equator, passing through extending from 90°W longitude (negative) to 90°E longitude (positive)
244:
1122:
776:
943:
772:
725:
468:
1196:
784:
780:
648:
506:
systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking
647:
is the line between the North and South Poles, with positive values increasing northward. In WGS 84, this is the
613:
207:
601:
471:
174:
20:
121:
921:
811:
729:
721:
671:
272:
292:
54:
1160:
938:
435:
352:
102:
1097:
968:
621:
503:
342:
312:
252:
202:
128:
1258:
788:
713:
552:
164:
112:
1246:
1234:
752:
612:
that binds the coordinate system to actual locations on the Earth. The ECEF that is used for the
84:
990:
1147:
1014:
756:
605:
581:
538:
184:
169:
1008:
1210:
768:
686:
588:
Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed at
428:
179:
1013:. AIAA Education Series. American Institute of Aeronautics & Astronautics. p. 72.
559:
is a type of altitude defined as the difference between the two aforementioned quantities:
1183:
1167:
1154:
1067:
927:
691:
507:
732:, which use the observer's location as the reference point for bearings in altitude and
667:
637:
609:
495:
392:
159:
133:
1268:
744:
620:, which currently includes its own ellipsoid definition. Other local datums such as
1222:
740:
717:
652:
117:
1189:
1041:
666:, passing through the origin and extending from 180° longitude (negative) to the
513:
The distance from a given point of interest to the center of Earth is called the
74:
28:
479:
1042:"OGC Abstract Specification Topic 2: Referencing by coordinates Corrigendum"
764:
608:(in this case, a conventional three-dimensional right-handed system), and a
499:
153:
79:
37:
902:
891:
880:
869:
858:
847:
760:
332:
149:
138:
33:
1179:
733:
663:
212:
69:
46:
474:
that represents locations in the vicinity of the Earth (including its
617:
322:
282:
220:
1217:
475:
107:
27:
409:
302:
1176:
orientation of the coordinate system and additional information
748:
1170:
Clearer notes on converting ECEF coordinates to WGS-84 datum
636:
at the center of the chosen ellipsoid. In WGS 84, this is
628:
The ECEF coordinate system has the following parameters:
1161:
1182:
includes a utility CartConvert which converts between
1194:
1157:
Notes on converting ECEF coordinates to WGS-84 datum
933:
32:
The ECEF coordinates (x, y, z) shown in relation to
498:. Its most common use is in tracking the orbits of
1096:Snay, Richard A.; Soler, Tomás (December 1999).
712:Geocentric coordinates can be used for locating
1098:"Modern Terrestrial Reference Systems (Part 1)"
655:, and can actually be measured against an ECEF.
1075:United Nations Office for Outer Space Affairs
457:Earth-centered, Earth-fixed coordinate system
436:
8:
16:3-D coordinate system centered on the Earth
443:
429:
410:Spatial Reference System Identifier (SRID)
405:International Terrestrial Reference System
42:
1066:National Geospatial Intelligence Agency.
775:add actual distance as the Z axis to the
19:For broader coverage of this topic, see
1201:
955:
825:Polar view, Earth-centered, Earth fixed
45:
1068:"World Geodetic System 1984 datasheet"
909:(IRNSS are geosynchronous satellites)
7:
747:coordinates, with the center of the
268:
694:." Using Bowring's formula in 1976
670:(positive); in WGS 84, this is the
579:; it is not to be confused for the
536:, which is a generalization of the
415:Universal Transverse Mercator (UTM)
377:European Terrestrial Ref. Sys. 1989
982:Clynch, James R. (February 2006).
797:An example of Earth-centered frame
551:, not restricted to points on the
482:, and surrounding outer space) as
287:Ordnance Survey Great Britain 1936
253:Discrete Global Grid and Geocoding
144:Horizontal position representation
14:
1252:
1240:
1228:
1216:
1204:
818:
803:
755:can be aligned with the Earth's
590:geographic coordinate conversion
203:Global Nav. Sat. Systems (GNSSs)
53:
1280:Astronomical coordinate systems
728:. They are differentiated from
708:Astronomical coordinate systems
604:, ECEF consists of an abstract
367:N. American Vertical Datum 1988
397:Internet link to a point 2010
327:Geodetic Reference System 1980
245:Quasi-Zenith Sat. Sys. (QZSS)
1:
387:Chinese obfuscated datum 2002
773:celestial coordinate systems
649:international reference pole
465:geocentric coordinate system
337:Geographic point coord. 1983
1166:September 27, 2007, at the
944:Planetary coordinate system
785:galactic coordinate systems
297:Systema Koordinat 1942 goda
1296:
1046:Open Geospatial Consortium
726:Cartesian X, Y, and Z axes
705:
357:World Geodetic System 1984
18:
1275:Global Positioning System
1148:ECEF datum transformation
614:Global Positioning System
347:North American Datum 1983
317:South American Datum 1969
616:(GPS) is the geocentric
602:spatial reference system
472:spatial reference system
208:Global Pos. System (GPS)
175:Spatial reference system
21:Spatial reference system
1174:geodetic datum overview
1153:March 22, 2007, at the
1007:Chobotov, V.A. (2002).
965:GPS Satellite Surveying
922:Earth-centered inertial
812:Earth-centered inertial
730:topocentric coordinates
672:IERS Reference Meridian
662:is in the plane of the
963:Leick, Alfred (2004).
494:measurements from its
40:
1105:Professional Surveyor
939:Orbital state vectors
706:Further information:
463:), also known as the
103:Geographical distance
31:
714:astronomical objects
504:satellite navigation
277:Sea Level Datum 1929
129:Geodetic coordinates
984:"Earth Coordinates"
789:spherical astronomy
751:as the origin. The
557:geocentric altitude
553:reference ellipsoid
515:geocentric distance
307:European Datum 1950
265:Standards (history)
165:Reference ellipsoid
113:Figure of the Earth
996:on April 18, 2015.
753:plane of reference
743:, astronomers use
685:An example is the
185:Vertical positions
41:
1020:978-1-60086-097-3
1010:Orbital Mechanics
757:celestial equator
606:coordinate system
582:geodetic altitude
539:geocentric radius
453:
452:
401:
400:
180:Spatial relations
170:Satellite geodesy
125:
1287:
1257:
1256:
1255:
1245:
1244:
1243:
1233:
1232:
1231:
1221:
1220:
1209:
1208:
1207:
1200:
1135:
1134:
1132:
1130:
1125:on June 13, 2011
1121:. Archived from
1115:
1109:
1108:
1102:
1093:
1087:
1086:
1084:
1082:
1077:. United Nations
1072:
1063:
1057:
1056:
1054:
1052:
1038:
1032:
1031:
1029:
1027:
1004:
998:
997:
995:
989:. Archived from
988:
979:
973:
972:
960:
905:
900:
894:
889:
883:
878:
872:
867:
861:
856:
850:
845:
839:
837:
822:
807:
769:galactic equator
722:three dimensions
578:
565:
550:
535:
445:
438:
431:
269:
248:
240:
232:
224:
216:
156:
115:
57:
43:
1295:
1294:
1290:
1289:
1288:
1286:
1285:
1284:
1265:
1264:
1263:
1253:
1251:
1241:
1239:
1229:
1227:
1215:
1205:
1203:
1195:
1168:Wayback Machine
1155:Wayback Machine
1144:
1139:
1138:
1128:
1126:
1117:
1116:
1112:
1100:
1095:
1094:
1090:
1080:
1078:
1070:
1065:
1064:
1060:
1050:
1048:
1040:
1039:
1035:
1025:
1023:
1021:
1006:
1005:
1001:
993:
986:
981:
980:
976:
962:
961:
957:
952:
928:Geodetic system
918:
913:
912:
911:
910:
908:
898:
897:
887:
886:
876:
875:
865:
864:
854:
853:
843:
842:
835:
834:
828:
827:
826:
823:
815:
814:
808:
799:
798:
710:
704:
692:Geodetic system
598:
577:
563:
560:
549:
543:
518:
449:
420:
419:
266:
258:
257:
246:
238:
230:
222:
214:
198:
190:
189:
148:
98:
90:
89:
65:
24:
17:
12:
11:
5:
1293:
1291:
1283:
1282:
1277:
1267:
1266:
1262:
1261:
1249:
1237:
1225:
1213:
1193:
1192:
1187:
1177:
1171:
1158:
1143:
1142:External links
1140:
1137:
1136:
1119:"Polar motion"
1110:
1088:
1058:
1033:
1019:
999:
974:
954:
953:
951:
948:
947:
946:
941:
936:
930:
925:
917:
914:
907:
906:
895:
884:
873:
862:
851:
840:
831:
830:
829:
824:
817:
816:
809:
802:
801:
800:
796:
795:
794:
793:
703:
700:
683:
682:
675:
668:prime meridian
656:
641:
638:center of mass
610:geodetic datum
597:
594:
575:
547:
496:center of mass
451:
450:
448:
447:
440:
433:
425:
422:
421:
418:
417:
412:
407:
399:
398:
395:
389:
388:
385:
379:
378:
375:
369:
368:
365:
359:
358:
355:
349:
348:
345:
339:
338:
335:
329:
328:
325:
319:
318:
315:
309:
308:
305:
299:
298:
295:
289:
288:
285:
279:
278:
275:
267:
264:
263:
260:
259:
256:
255:
250:
242:
234:
226:
218:
210:
205:
199:
196:
195:
192:
191:
188:
187:
182:
177:
172:
167:
162:
160:Map projection
157:
146:
141:
136:
134:Geodetic datum
131:
126:
110:
105:
99:
96:
95:
92:
91:
88:
87:
82:
77:
72:
66:
63:
62:
59:
58:
50:
49:
15:
13:
10:
9:
6:
4:
3:
2:
1292:
1281:
1278:
1276:
1273:
1272:
1270:
1260:
1250:
1248:
1238:
1236:
1226:
1224:
1219:
1214:
1212:
1202:
1198:
1191:
1188:
1185:
1181:
1180:GeographicLib
1178:
1175:
1172:
1169:
1165:
1162:
1159:
1156:
1152:
1149:
1146:
1145:
1141:
1124:
1120:
1114:
1111:
1106:
1099:
1092:
1089:
1076:
1069:
1062:
1059:
1047:
1043:
1037:
1034:
1022:
1016:
1012:
1011:
1003:
1000:
992:
985:
978:
975:
970:
966:
959:
956:
949:
945:
942:
940:
937:
934:
931:
929:
926:
923:
920:
919:
915:
904:
896:
893:
885:
882:
874:
871:
863:
860:
852:
849:
841:
833:
832:
821:
813:
806:
792:
790:
786:
782:
778:
774:
770:
766:
762:
758:
754:
750:
746:
742:
737:
735:
731:
727:
723:
719:
715:
709:
701:
699:
697:
696:Survey Review
693:
688:
680:
676:
673:
669:
665:
661:
657:
654:
650:
646:
642:
640:of the Earth.
639:
635:
631:
630:
629:
626:
623:
619:
615:
611:
607:
603:
595:
593:
591:
586:
584:
583:
574:
570:
566:
558:
555:surface. The
554:
546:
541:
540:
533:
529:
525:
521:
516:
511:
509:
505:
501:
497:
493:
489:
485:
481:
477:
473:
470:
466:
462:
458:
446:
441:
439:
434:
432:
427:
426:
424:
423:
416:
413:
411:
408:
406:
403:
402:
396:
394:
391:
390:
386:
384:
381:
380:
376:
374:
371:
370:
366:
364:
361:
360:
356:
354:
351:
350:
346:
344:
341:
340:
336:
334:
331:
330:
326:
324:
321:
320:
316:
314:
311:
310:
306:
304:
301:
300:
296:
294:
291:
290:
286:
284:
281:
280:
276:
274:
271:
270:
262:
261:
254:
251:
249:
243:
241:
235:
233:
227:
225:
221:BeiDou (BDS)
219:
217:
211:
209:
206:
204:
201:
200:
194:
193:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
155:
151:
147:
145:
142:
140:
137:
135:
132:
130:
127:
123:
122:circumference
119:
114:
111:
109:
106:
104:
101:
100:
94:
93:
86:
83:
81:
78:
76:
73:
71:
68:
67:
61:
60:
56:
52:
51:
48:
44:
39:
35:
30:
26:
22:
1259:Solar System
1127:. Retrieved
1123:the original
1113:
1104:
1091:
1081:December 16,
1079:. Retrieved
1074:
1061:
1051:December 25,
1049:. Retrieved
1045:
1036:
1024:. Retrieved
1009:
1002:
991:the original
977:
964:
958:
838: Earth
810:Polar view,
745:heliocentric
741:nearby stars
738:
718:Solar System
711:
702:In astronomy
695:
684:
678:
659:
653:polar motion
644:
633:
627:
600:As with any
599:
587:
580:
572:
568:
561:
556:
544:
537:
531:
527:
523:
519:
514:
512:
491:
487:
483:
478:, interior,
464:
460:
456:
454:
197:Technologies
152: /
64:Fundamentals
25:
1247:Outer space
1235:Spaceflight
1129:December 7,
1026:October 24,
771:. These 3D
75:Geodynamics
1269:Categories
950:References
777:equatorial
724:along the
500:satellites
480:atmosphere
1211:Astronomy
1190:EPSG:4978
765:Milky Way
763:, or the
596:Structure
469:cartesian
459:(acronym
154:Longitude
80:Geomatics
38:longitude
1184:geodetic
1164:Archived
1151:Archived
916:See also
903:IRNSS-1I
892:IRNSS-1G
881:IRNSS-1F
870:IRNSS-1E
859:IRNSS-1C
848:IRNSS-1B
787:used in
781:ecliptic
761:ecliptic
687:NGS data
510:motion.
333:ISO 6709
231:(Europe)
229:Galileo
215:(Russia)
213:GLONASS
150:Latitude
139:Geodesic
97:Concepts
34:latitude
1197:Portals
734:azimuth
716:in the
664:equator
508:crustal
502:and in
476:surface
467:, is a
393:Geo URI
363:NAVD 88
273:NGVD 29
247:(Japan)
239:(India)
223:(China)
85:History
70:Geodesy
47:Geodesy
1017:
935:(ITRS)
901:
899:
890:
888:
879:
877:
868:
866:
857:
855:
846:
844:
836:
783:, and
759:, the
679:Y axis
660:X axis
645:Z axis
634:origin
622:NAD 83
618:WGS 84
490:, and
383:GCJ-02
373:ETRS89
353:WGS 84
343:NAD 83
323:GRS 80
283:OSGB36
237:NAVIC
118:radius
1223:Stars
1101:(PDF)
1071:(PDF)
994:(PDF)
987:(PDF)
969:Wiley
924:(ECI)
313:SAD69
293:SK-42
108:Geoid
1131:2010
1083:2021
1053:2018
1028:2021
1015:ISBN
739:For
677:The
658:The
643:The
632:The
461:ECEF
455:The
303:ED50
120:and
36:and
767:'s
749:Sun
720:in
522:= (
1271::
1103:.
1073:.
1044:.
967:.
791:.
779:,
736:.
592:.
585:.
571:−
567:=
542:,
530:+
526:+
517:,
486:,
1199::
1133:.
1107:.
1085:.
1055:.
1030:.
971:.
674:.
576:0
573:R
569:R
564:′
562:h
548:0
545:R
534:)
532:Z
528:Y
524:X
520:R
492:Z
488:Y
484:X
444:e
437:t
430:v
124:)
116:(
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
