sistemas de cordenada utilizados en colombia

7/24/2019 Sistemas de Cordenada Utilizados en Colombia

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SISTEMAS DE CORDENADA UTILIZADOS EN COLOMBIA

CHRISTIAN ALDEMAR MONCAYO CORDOBA

ESCUELA DE INGENIEROS MILITARES

CENTRO DE EDUCACION MILITAR

BOGOT D.C

2015


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SISTEMAS DE CORDENADA UTILIZADOS EN COLOMBIA

CHRISTIAN ALDEMAR MONCAYO CORDOBA

TRABAJO

INGENIERO JAVIER VALENCIA SIERRA

ESCUELA DE INGENIEROS MILITARES

CENTRO DE EDUCACION MILITAR

BOGOT D.C

2015


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1.2.

3.4.5. CONTENIDO6. INTRODUCCION

9

. 1. !U" SON LAS COORDENADAS

10

#. 1.1 CLASES DE COORDENADAS 10

9. 1.2 TI$OS DE SISTEMA DE CORDENADAS

10

10. 1.2.1 SISTEMA DE COORDENADAS $OLARES

10

11. 1.2.2 SISTEMAS DE COORDENADAS CIL%NDRICAS 11

12. 1.2.3 SISTEMA DE COORDENADAS ES&"RICAS

12

13. 1.2.4 SISTEMA DE COORDENADAS GEOGR&ICAS

12

14. 1.2.4.1 S'()*+, -* //-*,-,( '*,( **,*( 13

15. 1.2.4.2 S'()*+, -* //-*,-,( '*,( /)//,*(

13

16.2. SISTEMAS DE COORDENADAS UTILIZADOS EN COLOMBIA

131.2.1 COORDENADAS GEOGR&ICAS

14

6


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1#. 2.1.1 $ARALELOS Y LATITUD

1519. 2.1.1.1 $,,*/(

1520. 2.1.1.2 L,)')- 1521. 2.1.2 MERIDIANOS Y LONGITUD 1622. 2.1.2.1 M*'-',/( 1623. 2.1.2.2 M*'-',/( )**()*(

1624. 2.1.2.3 L/')-

1625.2.3 SISTEMA INTERNACIONAL DE RE&ERENCIA TERRESTRE ITRS7

INTERNATIONAL TERRESTRIAL RE&ERENCE SYSTEM

126.2.4 COORDENADAS UTM 1#2.2.4.1 L,( //-*,-,( UTM / /*(8/-* , 8)/ ('/ , ,-,-/

222#.2.5 SISTEMAS DE RE&ERENCIA 2429. 2.6 MARCO INTERNACIONAL DE RE&ERENCIA TERRESTRE :ITR&;

INTERNATIONAL TERRESTRIAL RE&ERENCE &RAME,

146. L/( ('()*+,( -* //-*,-,( 8*+')* /)/( -* -,)/( */='/( 8,,

)''F, ,*( /+*( 8,, , ')*,'@. E(),( (/ ('()*+, -*

9


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***', )''F,-/ 8,, *8*(*), ,( >','/*( -* ,( ,,)*()',(

*/=',( '+=**( />(*,'/*( /+/ /,'F,'/*( -* S'()*+, -*

$/(''/,+'*)/ G/>, :G$S*)/ -*)/ -* 8,/ / +,8, -*)*+',-/.

153. 1.1 CLASES DE COORDENADAS

154. S'()*+, -* //-*,-,(; * *(8,'/ -*)*+',-/ * ('()*+, -*

//-*,-,( *'()*)* (* -*'* 8/ 8, / )*( **( /)//,*( -* ',

*(,,. S' (* ),), -* ('()*+, -* -/( **( (* ,>, -* ('()*+,

>'-'+*('/, 8/ / /),'/ (' /)'** )*( **( (* *(),, ,>,-/ -*

('()*+, )'-'+*('/,.

155. C,-, 8)/ -* , //-*,-, /)'** ,/ *(8*'',-/ 8/ ,

8/*'@ /)//, -* *)/ -* 8/(''@ */),-/ * * 8)/

,)*'/+*)* /+>,-/ * , (* **), (/>* ** -*)*+',-/.

E()/( **( (* **), -*''-/( 8/ *)/ -'*)/ 8/ * /'* -* ,(

//-*,-,(.

156. 1.2 TIPOS DE SISTEMA DE CORDENADAS

15. 1.2.1 SISTEMA DE COORDENADAS POLARES: *()* )'8/ -* //-*,-,(

*), (/,+*)* / -/( **( 8/ / * (* ),), -* ('()*+, -*

10


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//-*,-,( >'-'+*('/, * * +'(+/ ,-, 8)/ 8/(''@ />*)/

>',-/ * * 8,/ *()= -*)*+',-/ 8/ =/ , -'(),',

*(8*', * *()* ('()*+, , >','@ -* 8)/ * * *(8,'/ *()=

-*)*+',-, 8/ =/ , -'(),', :+,')-' ,+,-,(

//-*,-,( ,)/=',( (* *'** , (>)'8/ -* //-*,-,( *(',(

,( ,*( (/ )''F,-,( 8,, -*)*+', , 8/(''@ -* '*)/ 8)/ -*)/ -*

8,/ *('/.

11. $*-* */),(* ,',( ,(*( -* *(),(. E ('()*+, +=( /+ =('/

//'-/ *( * -* , ,)')- , /')-. $*-* */),(* ,( (''*)*(

/+,(; DD -*'+, -*** :(* *'** , /( ,-/( 8/,*(',-/ * *(8,'/( *'-*/( ,* / **(,',+*)* -*>* (*/ (' /

('. $*-* */),(* ('()*+,( -* //-*,-,( /)//,*( ,-/ (*

),), -* *(8,'/ *'-*/ / , *()), -* ,'*-,- -* R'*+,

//-*,-,( /)//+,*(.

13. 1.2..2 Si)(', ( $##+(*,,) $&+7i/8*(,) #+#g#*,/(); /)'**

)*(/ +)'/ : )*(/ *(8*','F,-/ * -*)*+', /*8)/( +)'/(

/+/ -'(),', =/ /+*< * *8*(,-/ -* -*)*+',-, +,*,

)'** , /+, -',/,. $*-* */),(* ,(/ -* //-*,-,( *(',(

'-',( * +8* / *(),( ,,)*()',(.

14.

145. 2. SISTEMAS DE COORDENADAS UTILIADOS EN COLOMBIA16.1. D*(-* , *,'@ * 1902 -* , /'', -* L/')-*( &/)*,(

8*(/, -* IGAC , -* ,( 8''8,*( ,)''-,-*( , ('-/ , **,'@

-* '/+,'@ */-(', /',>* * (', -* +,/ -* ***', 8,, ,

13


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8/-'@ -* , ,)/,, /'', , -*)*+','@ -* -,)/( */='/( *

* 8,(. N/ />(),)* / /( ,,*( '*)'/( )*/@'/( ,,F,-/( *

* ,+8/ -* , G*/-*(', -,)* , (*-, +'),- -* ('/

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*'(* , /*'*', -* **+8,F, * ('()*+, */-('/ -* ***',

D,)+ BOGOT ,-/8),-/ * 1941 8/ ('()*+, +/-*/ /+8,)'>* ,

'* ')*,'/, * (/8/)* ,( )*//,( ,),*(.1#. S* *)'*-* * * * ,/ 2005 * I()'))/ G*/='/ A() C/-,FF'

IGAC , *)'-,- >*,+*), *,,-, -* /( ('()*+,( -* ***',

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,)'/ D,)+ B//)= * M,/ G*/)'/ N,'/, -* ***', MAGNA

/ ,-, -* /-/( ')*,'/,*( -* B,/ I)*,+*',/ -* D*(,//.

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-/+*)/( * (()*), , '+8/),', -* +', , *()* */ ('()*+, ,(

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+*/.1#0. D* / ,)*'/ ,8/,-/( * /*8)/( -* */-*(', ,)/,, )/8/,,

('()*+,( -* 8/(''/,+'*)/ (* 8*(*)@ 8/*)/ -* '*()','@ ,)*

, E(*, -* M*-'/ A+>'*)* -* , U'*('-,- -* A)'/', / **''/

8=)'/ * -'/ *), -* *),( -* 8/(''@ +/ +=( 8*'(,( ,/-*( , ('()*+, )'*, 8,, =*, '('), -* )*')/'/ //+>',/

/ ,)/,, , , *(,, -* +,/ *(/'@ * , ,), /'', -* 8,(.1#1.12. 2.1 COORDENADAS GEOGRFICAS

14


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1#5.1#6.1#. L,( //-*,-,( */=',( (/ /)/ -* *,( '+,',',( *

8*+')* >', / *,)')- , * , (8*''* -* , T'*,. E()*

/)/ -* *,( /*(8/-* , /( +*'-',/( 8,,*/(.1.19.19;.191.192.193.19.195.196.194.19.199. Fig. h!:""%%%.!+#()#+(*/i*(,.$/"g(#g+,i,g+,/"$##+(*,,)g(#g.h'

2;;.201. C,'* 8)/ -* *()/ 8,*), 8*-* >',(* , //*(* *

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8,,*/( , , L*, -* *,-/ * +,)'** ('*+8* , +'(+, -'(),',

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*)* ,'* 8,,*/ * *,-/.

L, ,)')- *(),>** ,( -'(),',( *)* /( 8,,*/(.

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/( 8//(. S* , -*)*+',-/ /+/ M*'-',/ -* /'* , ,* * 8,(, 8/

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G**' -''-* , , T'*, * -/( H*+'(*'/(; H*+'(*'/ O*()*

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/*(8/-* , H*+'(*'/ O'-*), 1#0 +*'-',/( ,', * *()*

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/,'/(* , (8*''* )**()*.

249.250. S* >,(, 8*( * , 8/*'@ -* -'/ *'8(/'-* ('*-/ , 8/*'@

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/'*; /( 8)/( -* *'8(/'-* (* 8/*), (/>* ''-/ ),*)* ,

+*'-',/ *(),>*'-/ :* ,+,*+/( +*'-',/ *),2;UTM.!

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8,,*/( #0 S #4 N +'*),( * * *()/ -* ,( F/,( -* , T'*, 7,(

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2#5. 7 ,/ -* 500 X+ ESTE 0 X+ /)* ,-/ /('-*,+/( **+'(*'/ /)*

2#6. 7 ,/ -* 500 X+ ESTE 10.000 X+ /)* ,-/ /('-*,+/( *

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C,)/ +,/ (*, , *(/'@ *( -*' * ,-/ -* /( ,-,-/( :1 +*)/

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305.306.30.30#.

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$&,+,#311.312.

313.

314.315.316.

314. 31#.319. L,( //-*,-,( */=',( (* )''F, * , 8,)* -* /( ('()*+,( SIG

/+/ (* 8*-* ,,'F, (* (, 8/* (/ /*8)/( * , '* +-',

(* +,*, 8*-* (*' 8,, /)** * (// ('()*+, , />*), -*

)/-, , )'*, /)/,-, / 8,=+*)/( ('+',*(.320.321. C/+/ **+8/ 8/-*+/( * ,( //-*,-,( +/(),-,( * ('()*+,( /+/

* G//* E,) G//* M,8( A'( A'* (/),* CAD 8,,

+/-*,+'*)/ -* -,)/( *)* /)/(.

322.323.324.

325.326.32.

32#.

329.330.

331.332.333.

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1;2.53445;1?5@

353.

35. 2.5 SISTEMAS DE REFERENCIA355.356. U ('()*+, -* ***', *( * /)/ -* /*'/*( /*8)/(

)*@'/( ,-*,-,+*)* +/-*,-/( * 8*+')* -*'' * ,'*

+/+*)/ , /'*),'@ >','@ *(,, -* )*( **( //-*,-/( ] Y

Z^. D,-/ * ('()*+, -* ***', *( +/-*/ :, /*8'@ ,

'-*,< ()* *( *,'F,-/ :+,)*','F,-/< +*-',)* 8)/( *,*( ,(

//-*,-,( (/ -*)*+',-,( (/>* * ('()*+, -* ***', -,-/ -'/

/)/ -* 8)/( (* -*/+', +,/ -* ***', :R**** &,+*


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S'()*+, C//-*,-/ G*/)'/ +'*),( * (' -'/ /'* *()=

-*(8,F,-/ -* */*)/ (* //* /+/ S'()*+, G*/-('/ L/,.35. C/*'/,+*)* ,( 8/(''/*( ] Y Z^ (* *8*(, * )+'/( -*

//-*,-,( '*,( ,)')- : < /')- :`, (' *( /, (* )*-= D,)+ G*/-('/ L/,.35#. E()/( )'+/( (* //* ),+>' /+/ D,)+ H/'F/),*( , * ((

//-*,-,( : `< (* -*'* '-*8*-'*)*+*)* -* , ,), :H


22/32

362.363.36.Fig.13 h!:""i',g(.)/i()h,+($*.$#'"&*i,ii$,+#g+,i,!+#0($$i#*()-;9111216613-

!h!,!!;1"95"&-*-i--,--i-i-$,+#g+,i,-!+#0($$i#*()-33-42.!g$=125;5;9

365.2.6 MARCO INTERNACIONAL DE REFERENCIA TERRESTRE ITRF:

INTERNATIONAL TERRESTRIAL REFERENCE FRAME366.

364.36.Fig. 1 h!:""i+.(*)g.ig*.+"

369.

30. E ('()*+, */)'/ )''F,-/ * G*/-*(', *( * S'()*+, C/*'/,-* R***', T**()* :ITRS; I)*,)'/, T**()', R**** S()*+


23/32

*)/ -* +,(,( )**()* :'*-/ /,/( ,)+@(*,, / *(8*)/ , , /)*F, )**()*.

31.32. L, *,'F,'@ :+,)*','F,'@< -* ITRS *( * +,/ ITR& :I)*,)'/,

T**()', R**** &,+*(*,-,( +*-',)* )',( */-(',( *(8,',*( -* +

,), 8*'('@. L,( */'-,-*( (/ ''-,( , * * +/'+'*)/ -* ,(

8,,( )*)@',( (( -*/+,'/*( ),+>' ,)*, ,( //-*,-,( -*

(( *(),'/*( 8*/ *()/( +/'+'*)/( / ,*), ,( @>'),( -* /( (,)')*(.

E()/ (* ),-* * * 8,, , />(*,'@ '(),)=*, (/>* , (8*''*

-* , T'*, * +,/ -* ***', )**()* ITR& -'** -* ('()*+, -*

***', (,)*'), />',-/ * ,( //-*,-,( ITR& (*, ),(,-,-,( *

* )'*+8/ -* ,*-/ / ( ,','@ 8/ /( **)/( -* , -'=+', )**()*.33. D,-, , -*8*-*', -* ,( //-*,-,( */-(',( / *(8*)/ ,

)'*+8/ * ITR& *( /+8*+*),-/ '-',-/ , 8/, 8,, , , ,(

8/(''/*( -* (( *(),'/*( (/ '*)*(.34.35. $/ **+8/ , -*/+','@ ITR&94 '-', * ,( //-*,-,( -* *(),

*- *()= -*''-,( 8,, * 1 -* **/ -* 1993. S ),(,-/ , *,(

-'**)*( '+8', , ,8','@ -* */'-,-*(. E +,/ -* ***', +=(

26


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*'*)*+*)* ,,-/ *( * ITR&2000 * , /''-* / , *,

-*'''@ -* GS#4 :G1150< :/- G*/-*)' S()*+ 19#4 (*+,, G$S

N/. 1150< ')/-'-, , 8,)' -* 1 -* **/ -* 2000.

36. 2.4 SISTEMA DE REFERENCIA GEOCNTRICO PARA LASAMRICAS- SIRGAS

3. E ITR& , ('-/ *)*-'-/ :-*('',-/< * * /)'*)* ,+*',/

+*-',)* SIRGAS :S'()*+, -* R***', G*/)'/ 8,, ,( A+',('+'*)/ /+/*/ (/>* * /)'*)* 8/ / ),)/ ,(

/-''/*( **(,',( 8,, * ,( *-*( ,'/,*( *() ',-,( ,

ITR&.3#.39. E -,)+ */-('/ /*(8/-'*)* *()= -*''-/ , 8,)' -* /( 8,=+*)/(

-* *'8(/'-* GRS#0 :G*/-*)' R**** S()*+ 19#0',-/( * A+', C*),

E(),-/( U'-/( C,,-=. E *(),-/ -* *(), *, ,+8,, *( , *-

/+/*,+*)* -'()'>'-, (/>* * /)'*)* //+,-, 8/ 1#3

*(),'/*( ,( //-*,-,( *()= ,,-,( * * ITR&200# 8/,

2000.4.3#1.382.383.384.385.386.387.

27

Fig. 15 SIRGAS Sistema deReferencia Geocntrico ara !as

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388.38,.390.391.

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395.

396.39. E +,)*'+'*)/ -* SIRGAS '* ,-*+=( -* , 8*(*,'@ (', -*

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(,)'(,* /( **'+'*)/( * 8*'('@ -* /( (,'/( -* '/+,'@*/***',-, * /( -'**)*( 8,(*(. E C//+>', * IGAC /,'(+/

,'/, *,,-/ -* -*)*+', *(),>** +,)** 8/8/'/, /(

('()*+,( /'',*( -* ***', */-('/ ,'+)'/ +,)'/

:D**)/( N/. 2113b1992 20#b2004< '''@ , 8,)' -* ,( *(),'/*( SIRGAS

28


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, -*)*+','@ -* , R*- B=(', G$S -*/+',-, MAGNA :M,/

G*/)'/ N,'/, -* R***',< * 8/ *(), **'-, , SIRGAS (*

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,(/',-/ /*(8/-* / * *'8(/'-* GRS#0 :G*/-*)' R**** S()*+19#0',-, (/>* , F/, -* /**', -* )*(

8,,( , -'=+', )*)@', :8,,( '-,( F/,( -*-*/+,'@


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'/,+'*)/ /)'/ ,-+''(),-,( -*(-* ( S*-* C*), 8/*(,-,(

* /)/ / * C*)/ -* A='('( R*'/, -* IGS * * DG&I -* +/-/

* (( 8/(''/*( ),+>' (*, /'*),-,( 8*+,*)*+*)* / * ITR&

'*)*.22.23. 2.9 MODELO GEOIDAL PARA COLOMBIA GEOCOL2;;424.425. L, )''F,'@ -* S'()*+, MAGNA7SIRGAS *()= -'*),+*)* *,'/,-,

/ , -*'''@ -* , (8*''* -* ***', *)', * 8*+'), />)**

,),( =(',( :**'-,( , '* +*-'/ -* +,< , 8,)' -* '/+,'@ G$S.

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-'**)*( 8*/ ('+',*( :*/'-* / ,('7*/'-*< (* /( ,='('( ('/(

+,)*+=)'/( * (* -*(,/* * * 8*(*)* -/+*)/ (* ,* ***',

'-'()'), , /( -/( )+'/( 8,, / *)*-* * )*)/ / *8','/*(

8/8',( -* , G*/-*(', &(',. E */'-* :,('7*/'-*< * C//+>', (* ,

-*)*+',-/ +*-',)* , )', *+/*b*()/*. "(), 8*+')* *,'/, ,(

,,)*()',( *'/,*( :/')-*( -* /-, ,,< -* ,+8/ -* ,*-,-

*8*(,-,( * M/-*/ G*/8/)*', G/>, :MGG, , ('-/ ,,-, / * M/-*/

TEG74 :T*,( E,) G,') 4 T,8* *) ,. 2001< , /, / ,/+,,(

,'+)',( +*-',( :2d 2d


28/32

426.

24.Fig14 h!:""+(7i),).&i)+i,/.(&.$#"#)"i*(H.!h!"UDG(#"+"!+i*(+F+i(*/0"362"64;

2.29. 2.1; ANTIGUO DATUM GEODSICO ORIONTAL DE COLOMBIA:

DATUM BOGOT430. A)*( -* , -*'''@ -* S'()*+, MAGNA7SIRGAS , 8,),/+, -*

***', ,'/, *(),>, /()')'-, 8/ -,)+ */-('/ /'F/),

,-/8),-/ * 1941 / *'8(/'-* ,(/',-/ /*(8/-* / * I)*,'/,

-* 1924 / 8)/ -,)+ (* /,'F@ * * O>(*,)/'/ A()/@+'/ -*

B//)= -* , ( /+>*. A 8,)' -* *()* +,/ * IGAC I''@ ,* 60

,/( * *(),>*'+'*)/ -* , *- */-(', -* /)/ /'F/), :ARENA;A)', R*- N,'/,'-/( (/>* ,( +>*( +=( 8/+'*)*( -* )*')/'/ ,'/,

*/ ,(),-/( , 8,)' -* 33 *(),'/*( ,()/@+',(. E(), *- -'/ ,8// ,

/( )'*( -* (*-/ /-* ()/( , ( *F , /( -* )** /-* 8,, /

, (* *+8*,/ +)/-/( )/8/='/( -* 8*'('@ :)',,'@

>'(*'@ )',)*,'@ 8/'/,'@< * ( -*)*+','@. L, 8*'('@ -*

,( //-*,-,( /'F/),*( : `< ,( />)*'-,( -*8*-* -'*),+*)* -* ,

*)'-+>* -* ,( +*-''/*( ,,*( @8)',( , , ,, *)* 001K

01K. A('+'(+/ , ,), -* /( )'*( */-('/( (* -*)*+'@ , 8,)' -*

31


29/32

D,)+ B*,*), , ),( -* '*,'@ )'//+)', , 8*'('@ /

*( +*/ * 0#0 +.431.432. E D,)+ BOGOT +,)*','F, , ITRS / */ ('()*+=)'/ -*

,8/'+,-,+*)* 250 + , * ( /'* (* **), -*(8,F,-/ -*

*/*)/ 530 +. E()/ (''', * ,( 8/(''/*( -*''-,( (/>* * D,)+

BOGOT ,8,** -*(8,F,-,( * , ,)'-,- ('+', / *(8*)/ , ,(

8/(''/*( -*''-,( (/>* MAGNA7SIRGAS. E */ *,)'/ -* , *-

ARENA ,, -* ,*-/ / , *'@ -* 8,( / * / 8*+')* /)/

,8/8',-/ 8,, *,),+'*)/( G$S 8*'(/( , -'**', -* MAGNA7

SIRGAS * *( ('()*+, -* ***', )'-'+*('/, * D,)+ BOGOT

*( +,/ >'-'+*('/, * * * (* -'(8/* -* //-*,-,( '*,(: `< ,), (/>* * '* +*-'/ -* +, :H


30/32

455. FIG. 18

"tt#$$%%%2.igac.go'.co#88$igac)%e&$serFi!es$Fi!e$-AGA0)fina!$ar9rans."tm

456.

45.45#.459.6;. 3. GLOSARIO461. e CA$ C*), A-*( G$S $/*)462. e CASA C*), ,- S/) A+*', G$S $/*)463. e CIO C/*)'/, I)*,)'/, O''464. e DG&I D*)(*( G*/-a)'(*( &/(('()'))465. e &AGS &*-*,)'/ / A()//+', ,- G*/8(', S*'*(466. e GEOCOL M/-*/ G*/'-, 8,, C//+>',46. e GNSS G/>, N,',)'/ S,)*')* S()*+(

46#. e G$S G/>, $/(')'/' S()*+469. e GRS#0 G*/-*)' R**** S()*+ 19#040. e IAG I)*,)'/, A((/',)'/ / G*/-*(41. e IAU I)*,)'/, A()//+', U'/42. e ICDE I,*()), C//+>',, -* D,)/( E(8,',*(43. e IERS I)*,)'/, E,) R/),)'/ ,- R**** S()*+( S*'*44. e IGAC I()'))/ G*/='/ A() C/-,FF'45. e IGS I)*,)'/, G$S S*'*46. e IGS7RNAAC7SIR R*'/, N*)/X A((/',)* A,('(

C*)* SIRGAS4. e IHO I)*,)'/, H-/,8' O,'F,)'/

4#. e ILS I)*,)'/, L,)')-* S*'*49. e ITR& I)*,)'/, T**()', R**** &,+*4#0. e ITRS I)*,)'/, T**()', R**** S()*+4#1. e IUGG I)*,)'/, U'/ / G*/-*( ,- G*/8('(4#2. e MAGNA M,/ G*/)'/ N,'/, -* R***',4#3. e OACI O,'F,'@ -* A','@ C'' I)*,'/,4#4. e SAGA S/) A+*', G*/-,+'( $/*)4#5. e SIRGAS S'()*+, -* R***', G*/)'/ 8,, ,( A+',(4#6. e SNA$$ S/) A+*', N,F, $,)* M/)'/ $/*)4#. e GS#4 /- G*/-*)' S()*+ 19#4. . CONCLUSIONES

4#9.490.

L,( //-*,-,( */=',( 8*-* *8*(*), , 8/(''@ -* />*)/( *

,'* , -* , )'*,.

33


31/32

491.

E( '-'(8*(,>* //* /( -'**)*( ('()*+,( -* //-*,-,( 8,, ,

/*), +*-''@ ,( F/,( /,',( ,'/( ,)/*( * 8*-, ,*),

/( *(),-/(.

492.

A-*+=( -* ,( //-*,-,( */=',( L,)')- L/')- (* 8*-*

*8*(, //-*,-,( * //-*,-,( UTM.

493.494.

E ('()*+, MAGNA.7 SIRGAS E( +,/ */)'/ 8*'(/ /

-*(,// (* , -,-/ >,/ /( '*,+*)/( -* , */-*(', ')*,'/, -*

*/ *()= -*''-/ -* ,*-/ / /( +/-*/( ('/( 7 +,)*+=)'/(

)',( +=( ,,F,-,( -* +-/. E()* /()')* +,/ ,'/,

8,, , -*'''@ -* /-*,-,( * C//+>',.

495.496.49.49#.499.500.501.5;2.5;3. 5. BIBLIOGRAFIA504.505.

INSTITUTO COLOMBIANO DE NORMAS T"CNICAS. N/+,(

//+>',,( 8,, , 8*(*),'@ -* T*('( T,>,/( -* G,-/( /)/(

),>,/( -* '*()','@ (*), ,),'F,'@. S,), * -* B//)= D.C.200#.NTC 14#6.

506. T'8/( -* //-*,-,( +,*,-/( * C//+>', I()'))/ G*/='/ A()

C/-,FF' 2004 E),-/ -* I)**) * 1070572015 -*(-*;

34


32/32

))8;bb2.',././b',f*>bU(*&'*(b&'*bMAGNAEBf',b

-/+*)/(b)'8/(g20-*g20//-*,-,(.8-

50.50#. U, 8=', *>.509. ))8;bb.*8(./+b-/+*)/(b)+b//-*,-,(f)+.)+510.

511. U, 8=', *>;512. ))8;bb.)'8/(./b)'8/(7-*7//-*,-,(bh'FF3(5Z/)2Y

513.

35
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