27:
527:
226:
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,
325:
138:
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
660:
522:{\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}}}
900:
738:
330:
790:
953:
1009:. NOAA technical publications. U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services. p. 107
1085:
157:
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
568:
256:
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
190:), also known as geodetic height (or geodetic altitude), is the distance between the point of interest and the ellipsoid surface, evaluated along the
956:
291:, in which case the geocentric and geodetic latitudes are equal and the latitude-dependent geocentric radius simplifies to a global mean
796:
1093:
1155:
1150:
171:, which is the angle between the equatorial plane and a line from the center of the ellipsoid. For non-Earth bodies the terms
1038:
150:. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater
699:
554:
1115:
1069:
250:
Similarly, geodetic altitude is defined as the height above the ellipsoid surface, normal to the ellipsoid; whereas
315:
308:
104:
745:
908:
53:
996:
228:
56:
20:
983:
296:
154:. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid.
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978:
207:
191:
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1002:
165:
to the reference ellipsoid. Depending on the flattening, it may be slightly different from the
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1004:
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8:
252:
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167:
65:
261:
1065:
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129:
1145:
678:
655:{\displaystyle N={\frac {a^{2}}{\sqrt {a^{2}\cos ^{2}\phi +b^{2}\sin ^{2}\phi }}},}
276:
269:
218:
have different definitions. Geodetic latitude is defined as the angle between the
545:
541:
288:
284:
195:
973:
223:
162:
147:
1139:
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refers to geodetic altitude (possibly with further refinements, such as in
1003:
National
Geodetic Survey (U.S.).; National Geodetic Survey (U.S.) (1986).
235:. There is no standard notation for geocentric latitude; examples include
26:
231:
is geodetic latitude. The standard notation for geodetic latitude is
121:
79:
1059:
257:
187:
125:
1027:
Awange, J.L.; Grafarend, E.W.; Paláncz, B.; Zaletnyik, P. (2010).
895:{\displaystyle \phi =\arctan \left((Z/p)/(1-e^{2}N/(N+h))\right).}
219:
60:
1026:
151:
1060:
Hofmann-Wellenhof, B.; Lichtenegger, H.; Collins, J. (1994).
161:
is the angle between the equatorial plane and a line that is
135:
198:
such that points inside the ellipsoid have negative height.
201:
911:
799:
748:
702:
571:
328:
733:{\displaystyle \lambda =\operatorname {atan2} (Y,X)}
947:
894:
784:
732:
677:from the rectangular coordinates usually requires
654:
521:
279:is not significant for a given application (e.g.,
208:Latitude § Geodetic and geocentric latitudes
1137:
1086:"A guide to coordinate systems in Great Britain"
313:Given geodetic coordinates, one can compute the
420:
404:
361:
345:
785:{\displaystyle h={\frac {p}{\cos \phi }}-N,}
264:). Geocentric altitude is typically used in
1033:. Springer Berlin Heidelberg. p. 156.
1053:
25:
19:For broader coverage of this topic, see
1113:
948:{\displaystyle p={\sqrt {X^{2}+Y^{2}}}}
1138:
1107:
1030:Algebraic Geodesy and Geoinformatics
1092:. Appendices B1, B2. Archived from
1078:
202:Geodetic vs. geocentric coordinates
186:Ellipsoidal height (or ellipsoidal
13:
555:prime vertical radius of curvature
134:Longitude measures the rotational
14:
1167:
955:. More sophisticated methods are
146:, which for Earth is usually the
316:geocentric Cartesian coordinates
309:Geographic coordinate conversion
105:ellipsoidal-harmonic coordinates
1064:. Section 10.2.1. p. 282.
98:). The triad is also known as
881:
878:
866:
839:
831:
817:
727:
715:
689:are mutually involved through
115:
1:
1156:Geographic coordinate systems
1151:Orthogonal coordinate systems
1121:. Section 5.4. Archived from
989:
302:
100:Earth ellipsoidal coordinates
57:orthogonal coordinate system
21:Geographic coordinate system
16:Geographic coordinate system
7:
984:Planetary coordinate system
962:
540:are the equatorial radius (
297:spherical coordinate system
10:
1172:
1116:"The Mercator Projections"
969:Local geodetic coordinates
306:
281:interplanetary spaceflight
205:
119:
18:
1062:GPS – theory and practice
979:Geodesics on an ellipsoid
319:of the point as follows:
275:If the impact of Earth's
192:ellipsoidal normal vector
102:(not to be confused with
665:In contrast, extracting
544:) and the polar radius (
558:, function of latitude
287:may be simplified as a
180:planetocentric latitude
174:planetographic latitude
109:ellipsoidal coordinates
949:
896:
786:
734:
656:
523:
229:geographic coordinates
212:Geodetic latitude and
46:
950:
897:
787:
735:
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524:
227:the latitude used in
194:; it is defined as a
120:Further information:
30:Geodetic coordinates
29:
909:
797:
746:
700:
569:
326:
50:Geodetic coordinates
1114:Osborne, P (2008).
262:orthometric heights
253:geocentric altitude
215:geocentric latitude
168:geocentric latitude
66:reference ellipsoid
945:
892:
782:
730:
652:
519:
517:
183:are used instead.
89:ellipsoidal height
47:
1040:978-3-642-12124-1
1006:Geodetic Glossary
943:
771:
647:
646:
548:), respectively.
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266:orbital mechanics
159:geodetic latitude
130:Vertical position
71:geodetic latitude
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277:equatorial bulge
270:orbital altitude
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1090:Ordnance Survey
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546:semi-minor axis
542:semi-major axis
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289:spherical Earth
285:Earth ellipsoid
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196:signed distance
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118:
96:geodetic height
94:(also known as
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74:
69:. They include
31:
24:
17:
12:
11:
5:
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1128:on 2012-01-18.
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974:Geodetic datum
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307:Main article:
304:
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293:Earth's radius
224:surface normal
222:plane and the
203:
200:
148:Prime Meridian
117:
114:
73:(north/south)
52:are a type of
15:
9:
6:
4:
3:
2:
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1096:on 2012-02-11
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1071:3-211-82839-7
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1123:the original
1109:
1098:. Retrieved
1094:the original
1089:
1080:
1061:
1055:
1044:. Retrieved
1029:
1022:
1011:. Retrieved
1005:
998:
904:
664:
553:
531:
314:
312:
274:
251:
249:
213:
211:
185:
178:
172:
166:
158:
156:
140:
133:
103:
99:
95:
88:
83:(east/west)
78:
70:
64:
49:
48:
41:
37:
33:
295:(see also:
116:Definitions
63:based on a
54:curvilinear
1140:Categories
1100:2012-01-11
1046:2021-10-24
1013:2021-10-24
990:References
303:Conversion
220:equatorial
206:See also:
957:available
846:−
810:
801:ϕ
774:−
768:ϕ
765:
713:
704:λ
679:iteration
644:ϕ
641:
615:ϕ
612:
512:ϕ
508:
444:λ
440:
433:ϕ
429:
385:λ
381:
374:ϕ
370:
122:Longitude
80:longitude
963:See also
258:altitude
188:altitude
143:meridian
126:Latitude
59:used in
1146:Geodesy
552:is the
283:), the
61:geodesy
1068:
1037:
905:where
807:arctan
532:where
163:normal
152:Airy-0
128:, and
87:, and
1126:(PDF)
1119:(PDF)
710:atan2
268:(see
141:zero
136:angle
1066:ISBN
1035:ISBN
685:and
673:and
536:and
177:and
762:cos
681:as
632:sin
603:cos
505:sin
437:sin
426:cos
378:cos
367:cos
299:).
272:).
112:).
107:or
1142::
1088:.
959:.
693::
669:,
562::
247:.
245:φ′
243:,
239:,
124:,
77:,
32:P(
1103:.
1074:.
1049:.
1016:.
939:2
935:Y
931:+
926:2
922:X
916:=
913:p
890:.
886:)
882:)
879:)
876:h
873:+
870:N
867:(
863:/
859:N
854:2
850:e
843:1
840:(
836:/
832:)
829:p
825:/
821:Z
818:(
814:(
804:=
780:,
777:N
758:p
753:=
750:h
740:.
728:)
725:X
722:,
719:Y
716:(
707:=
691:N
687:h
683:ϕ
675:h
671:λ
667:ϕ
650:,
636:2
626:2
622:b
618:+
607:2
597:2
593:a
586:2
582:a
576:=
573:N
560:ϕ
550:N
538:b
534:a
501:)
497:h
494:+
491:N
484:2
480:a
474:2
470:b
463:(
459:=
452:Z
421:)
416:h
413:+
410:N
405:(
400:=
393:Y
362:)
357:h
354:+
351:N
346:(
341:=
334:X
241:ψ
237:θ
233:φ
92:h
85:λ
75:ϕ
44:)
42:h
40:,
38:λ
36:,
34:ɸ
23:.
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