38:
538:
237:
at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure). When used without qualification, the term latitude refers to geodetic latitude. For example,
336:
149:
between the zero meridian and the measured point. By convention for the Earth, Moon and Sun, it is expressed in degrees ranging from −180° to +180°. For other bodies a range of 0° to 360° is used. For this purpose, it is necessary to identify a
671:
533:{\displaystyle {\begin{aligned}X&={\big (}N+h{\big )}\cos {\phi }\cos {\lambda }\\Y&={\big (}N+h{\big )}\cos {\phi }\sin {\lambda }\\Z&=\left({\frac {b^{2}}{a^{2}}}N+h\right)\sin {\phi }\end{aligned}}}
911:
749:
341:
801:
964:
1020:. NOAA technical publications. U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services. p. 107
1096:
168:
Geodetic latitude measures how close to the poles or equator a point is along a meridian, and is represented as an angle from −90° to +90°, where 0° is the equator. The
579:
267:
is defined as the distance to the reference ellipsoid along a radial line to the geocenter. When used without qualification, as in aviation, the term
201:), also known as geodetic height (or geodetic altitude), is the distance between the point of interest and the ellipsoid surface, evaluated along the
967:
302:, in which case the geocentric and geodetic latitudes are equal and the latitude-dependent geocentric radius simplifies to a global mean
807:
17:
1104:
1166:
1161:
182:, which is the angle between the equatorial plane and a line from the center of the ellipsoid. For non-Earth bodies the terms
1049:
161:. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater
710:
565:
1126:
1080:
261:
Similarly, geodetic altitude is defined as the height above the ellipsoid surface, normal to the ellipsoid; whereas
326:
319:
115:
756:
919:
64:
1007:
239:
67:
31:
994:
307:
165:. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid.
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989:
218:
202:
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176:
to the reference ellipsoid. Depending on the flattening, it may be slightly different from the
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153:
8:
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76:
272:
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140:
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689:
666:{\displaystyle N={\frac {a^{2}}{\sqrt {a^{2}\cos ^{2}\phi +b^{2}\sin ^{2}\phi }}},}
287:
280:
229:
have different definitions. Geodetic latitude is defined as the angle between the
556:
552:
299:
295:
206:
984:
234:
173:
158:
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1133:
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refers to geodetic altitude (possibly with further refinements, such as in
1014:
National
Geodetic Survey (U.S.).; National Geodetic Survey (U.S.) (1986).
246:. There is no standard notation for geocentric latitude; examples include
37:
242:
is geodetic latitude. The standard notation for geodetic latitude is
132:
90:
1070:
268:
198:
136:
1038:
Awange, J.L.; Grafarend, E.W.; Paláncz, B.; Zaletnyik, P. (2010).
906:{\displaystyle \phi =\arctan \left((Z/p)/(1-e^{2}N/(N+h))\right).}
230:
71:
1037:
162:
1071:
Hofmann-Wellenhof, B.; Lichtenegger, H.; Collins, J. (1994).
172:
is the angle between the equatorial plane and a line that is
146:
209:
such that points inside the ellipsoid have negative height.
212:
922:
810:
759:
713:
582:
339:
744:{\displaystyle \lambda =\operatorname {atan2} (Y,X)}
958:
905:
795:
743:
688:from the rectangular coordinates usually requires
665:
532:
290:is not significant for a given application (e.g.,
219:Latitude § Geodetic and geocentric latitudes
1148:
1097:"A guide to coordinate systems in Great Britain"
324:Given geodetic coordinates, one can compute the
431:
415:
372:
356:
796:{\displaystyle h={\frac {p}{\cos \phi }}-N,}
275:). Geocentric altitude is typically used in
1044:. Springer Berlin Heidelberg. p. 156.
1064:
36:
30:For broader coverage of this topic, see
1124:
959:{\displaystyle p={\sqrt {X^{2}+Y^{2}}}}
14:
1149:
1118:
1041:Algebraic Geodesy and Geoinformatics
1103:. Appendices B1, B2. Archived from
1089:
213:Geodetic vs. geocentric coordinates
197:Ellipsoidal height (or ellipsoidal
24:
566:prime vertical radius of curvature
145:Longitude measures the rotational
25:
1178:
966:. More sophisticated methods are
157:, which for Earth is usually the
327:geocentric Cartesian coordinates
320:Geographic coordinate conversion
116:ellipsoidal-harmonic coordinates
1075:. Section 10.2.1. p. 282.
109:). The triad is also known as
892:
889:
877:
850:
842:
828:
738:
726:
700:are mutually involved through
126:
13:
1:
1167:Geographic coordinate systems
1162:Orthogonal coordinate systems
1132:. Section 5.4. Archived from
1000:
313:
111:Earth ellipsoidal coordinates
68:orthogonal coordinate system
32:Geographic coordinate system
27:Geographic coordinate system
7:
995:Planetary coordinate system
973:
551:are the equatorial radius (
308:spherical coordinate system
10:
1183:
1127:"The Mercator Projections"
980:Local geodetic coordinates
317:
292:interplanetary spaceflight
216:
130:
29:
18:Geodetic coordinate system
1073:GPS – theory and practice
990:Geodesics on an ellipsoid
330:of the point as follows:
286:If the impact of Earth's
203:ellipsoidal normal vector
113:(not to be confused with
676:In contrast, extracting
555:) and the polar radius (
569:, function of latitude
298:may be simplified as a
191:planetocentric latitude
185:planetographic latitude
120:ellipsoidal coordinates
960:
907:
797:
745:
667:
534:
240:geographic coordinates
223:Geodetic latitude and
57:
961:
908:
798:
746:
668:
535:
238:the latitude used in
205:; it is defined as a
131:Further information:
41:Geodetic coordinates
40:
920:
808:
757:
711:
580:
337:
61:Geodetic coordinates
1125:Osborne, P (2008).
273:orthometric heights
264:geocentric altitude
226:geocentric latitude
179:geocentric latitude
77:reference ellipsoid
956:
903:
793:
741:
663:
530:
528:
194:are used instead.
100:ellipsoidal height
58:
1051:978-3-642-12124-1
1017:Geodetic Glossary
954:
782:
658:
657:
559:), respectively.
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277:orbital mechanics
170:geodetic latitude
141:Vertical position
82:geodetic latitude
16:(Redirected from
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288:equatorial bulge
281:orbital altitude
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1101:Ordnance Survey
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557:semi-minor axis
553:semi-major axis
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300:spherical Earth
296:Earth ellipsoid
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207:signed distance
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107:geodetic height
105:(also known as
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95:
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80:. They include
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35:
28:
23:
22:
15:
12:
11:
5:
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1139:on 2012-01-18.
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985:Geodetic datum
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318:Main article:
315:
312:
304:Earth's radius
235:surface normal
233:plane and the
214:
211:
159:Prime Meridian
128:
125:
84:(north/south)
63:are a type of
26:
9:
6:
4:
3:
2:
1179:
1168:
1165:
1163:
1160:
1158:
1155:
1154:
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1128:
1121:
1107:on 2012-02-11
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1082:3-211-82839-7
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66:
62:
54:
50:
46:
39:
33:
19:
1134:the original
1120:
1109:. Retrieved
1105:the original
1100:
1091:
1072:
1066:
1055:. Retrieved
1040:
1033:
1022:. Retrieved
1016:
1009:
915:
675:
564:
542:
325:
323:
285:
262:
260:
224:
222:
196:
189:
183:
177:
169:
167:
151:
144:
114:
110:
106:
99:
94:(east/west)
89:
81:
75:
60:
59:
52:
48:
44:
306:(see also:
127:Definitions
74:based on a
65:curvilinear
1151:Categories
1111:2012-01-11
1057:2021-10-24
1024:2021-10-24
1001:References
314:Conversion
231:equatorial
217:See also:
968:available
857:−
821:
812:ϕ
785:−
779:ϕ
776:
724:
715:λ
690:iteration
655:ϕ
652:
626:ϕ
623:
523:ϕ
519:
455:λ
451:
444:ϕ
440:
396:λ
392:
385:ϕ
381:
133:Longitude
91:longitude
974:See also
269:altitude
199:altitude
154:meridian
137:Latitude
70:used in
1157:Geodesy
563:is the
294:), the
72:geodesy
1079:
1048:
916:where
818:arctan
543:where
174:normal
163:Airy-0
139:, and
98:, and
1137:(PDF)
1130:(PDF)
721:atan2
279:(see
152:zero
147:angle
1077:ISBN
1046:ISBN
696:and
684:and
547:and
188:and
773:cos
692:as
643:sin
614:cos
516:sin
448:sin
437:cos
389:cos
378:cos
310:).
283:).
123:).
118:or
1153::
1099:.
970:.
704::
680:,
573::
258:.
256:φ′
254:,
250:,
135:,
88:,
43:P(
1114:.
1085:.
1060:.
1027:.
950:2
946:Y
942:+
937:2
933:X
927:=
924:p
901:.
897:)
893:)
890:)
887:h
884:+
881:N
878:(
874:/
870:N
865:2
861:e
854:1
851:(
847:/
843:)
840:p
836:/
832:Z
829:(
825:(
815:=
791:,
788:N
769:p
764:=
761:h
751:.
739:)
736:X
733:,
730:Y
727:(
718:=
702:N
698:h
694:ϕ
686:h
682:λ
678:ϕ
661:,
647:2
637:2
633:b
629:+
618:2
608:2
604:a
597:2
593:a
587:=
584:N
571:ϕ
561:N
549:b
545:a
512:)
508:h
505:+
502:N
495:2
491:a
485:2
481:b
474:(
470:=
463:Z
432:)
427:h
424:+
421:N
416:(
411:=
404:Y
373:)
368:h
365:+
362:N
357:(
352:=
345:X
252:ψ
248:θ
244:φ
103:h
96:λ
86:ϕ
55:)
53:h
51:,
49:λ
47:,
45:ɸ
34:.
20:)
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