{"id":4736,"date":"2019-12-18T14:08:19","date_gmt":"2019-12-18T14:08:19","guid":{"rendered":"http:\/\/adenilsongiovanini.com.br\/blog\/?p=4736"},"modified":"2022-08-10T11:57:54","modified_gmt":"2022-08-10T11:57:54","slug":"elipsoide-o-que-e-e-para-que-serve","status":"publish","type":"post","link":"https:\/\/adenilsongiovanini.com.br\/blog\/elipsoide-o-que-e-e-para-que-serve\/","title":{"rendered":"Elipsoide: o que \u00e9 e para que serve?"},"content":{"rendered":"<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Antes de entendermos exatamente o que \u00e9 o <strong>elipsoide<\/strong>, \u00e9 importante que voc\u00ea saiba que existe o elipsoide e o elipsoide de revolu\u00e7\u00e3o, sendo que na <span style=\"color: #0000ff; line-height: 1.3;\"><a style=\"color: #0000ff;\" href=\"https:\/\/mundoeducacao.bol.uol.com.br\/geografia\/geodesia.htm\" target=\"_blank\" rel=\"noopener noreferrer\">geod\u00e9sia<\/a><\/span> utiliza-se o elipsoide de revolu\u00e7\u00e3o para definir-se a forma da terra.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por causa disso, precisaremos primeiramente entender o que \u00e9 o elipsoide. Em seguida mergulharemos de cabe\u00e7a no elipsoide de revolu\u00e7\u00e3o, entendendo:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O que o mesmo \u00e9;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Quais seus par\u00e2metros e f\u00f3rmulas;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Quais os elipsoides mais utilizados;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O que \u00e9 um datum;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">etc.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4738\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ellipsoide_3d.jpg\" alt=\"Ellipsoide_3d\" width=\"300\" height=\"240\" \/><\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na matem\u00e1tica, um <b>elipsoide<\/b> \u00e9 uma superf\u00edcie cuja equa\u00e7\u00e3o em um sistema de <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/mundoeducacao.bol.uol.com.br\/matematica\/plano-cartesiano.htm\" target=\"_blank\" rel=\"noopener noreferrer\">coordenadas cartesianas<\/a><\/span> <i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i>x<\/i>&#8211;<i>y<\/i>&#8211;<i>z<\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i><i><\/i> \u00e9:<\/span><\/p>\n<dl>\n<dd><span class=\"mwe-math-element\" style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/303573ace88047e7932c90d55d2c691d44ce2d39\" alt=\"{\\displaystyle {x^{2} \\over a^{2}}+{y^{2} \\over b^{2}}+{z^{2} \\over c^{2}}=1}\" \/><\/span><\/dd>\n<\/dl>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">onde <i>a<\/i>, <i>b<\/i> e <i>c<\/i> s\u00e3o n\u00fameros reais positivos que determinam as dimens\u00f5es e a forma de um elipsoide triaxial.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-4741 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoide-triaxial-780x386.png\" alt=\"elipsoide triaxial\" width=\"780\" height=\"386\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoide-triaxial-780x386.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoide-triaxial-300x149.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoide-triaxial-768x380.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoide-triaxial.png 872w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Com isso:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Se dois dos n\u00fameros s\u00e3o iguais, o elipsoide \u00e9 um esferoide;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Se os tr\u00eas forem iguais, trata-se de uma esfera.<\/span><\/li>\n<\/ul>\n<p>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Supondo a \u2265 b \u2265 c, ent\u00e3o:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">a \u2260 b \u2260 c : o elipsoide \u00e9 <b>escaleno<\/b><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4742\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ellipsoide-escaleno.png\" alt=\"Ellipsoide escaleno\" width=\"497\" height=\"402\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ellipsoide-escaleno.png 497w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ellipsoide-escaleno-300x243.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">c = 0 : o elipsoide \u00e9 <b>plano<\/b> (duas elipses em simetria)<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4743\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/ellipsoid.jpg\" alt=\"elipsoide - conceito\" width=\"599\" height=\"448\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/ellipsoid.jpg 599w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/ellipsoid-300x224.jpg 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">b = c : esferoide em forma de charuto<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-4744\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esferoide-charuto.jpg\" alt=\"esferoide charuto\" width=\"758\" height=\"424\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esferoide-charuto.jpg 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esferoide-charuto-300x168.jpg 300w\" sizes=\"(max-width: 758px) 100vw, 758px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">a = b : esferoide em forma de comprimido<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-4746 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438-780x780.jpg\" alt=\"\u00fanico comprimido redondo\" width=\"780\" height=\"780\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438-780x780.jpg 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438-300x300.jpg 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438-150x150.jpg 150w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438-768x768.jpg 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/\u00fanico-comprimido-redondo-21189438.jpg 800w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">a = b = c : esfera<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4747\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera.png\" alt=\"esfera\" width=\"960\" height=\"960\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera.png 960w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera-300x300.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera-780x780.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera-150x150.png 150w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/esfera-768x768.png 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide de Revolu\u00e7\u00e3o<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3666\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png\" alt=\"elipsoide de revolu\u00e7\u00e3o\" width=\"503\" height=\"426\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png 503w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide-300x254.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Para entender o porque da necessidade de cria\u00e7\u00e3o do <strong>elipsoide de revolu\u00e7\u00e3o<\/strong>, voc\u00ea precisa entender a evolu\u00e7\u00e3o da forma da terra.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">No inicio, as pessoas consideravam a forma terra plana. Com o tempo, passamos a considerar a mesma uma esfera.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por\u00e9m, existia o mar e as montanhas. Desta maneira, a terra n\u00e3o era uma esfera, sendo que os cart\u00f3grafos com o tempo atribu\u00edram a terra o formato de <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ofitexto.com.br\/comunitexto\/voce-sabe-o-que-e-geoide\/\" target=\"_blank\" rel=\"noopener noreferrer\">geoide<\/a><\/span>.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Lembre-se que o <strong>geoide<\/strong> possui como conceito:<\/span><\/p>\n<p><em><strong><span style=\"color: #000000; font-family: arial, helvetica, sans-serif; font-size: 20px;\">O n\u00edvel m\u00e9dio dos mares, suposto em equil\u00edbrio, prolongado para dentro dos continente e sobre a influ\u00eancia da massa da terra e da for\u00e7a da gravidade.<\/span><\/strong><\/em><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Resumindo, \u00e9 esta figurinha:<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/geoide.jpg\" alt=\"geoide\" width=\"540\" height=\"373\" class=\"alignnone wp-image-4768 size-full\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/geoide.jpg 540w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/geoide-300x207.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"> Por\u00e9m, \u00e9 importante que voc\u00ea saiba que esta figura \u00e9 um modelo exagerado que possui como intuito ajudar as pessoas a entenderem melhor o que \u00e9 um geoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Esta forma geoidal \u00e9 a forma que mais se aproxima a forma real do planeta. S\u00f3 existia um problema, o posicionamento sobre a mesma necessitava da utiliza\u00e7\u00e3o de formulas matem\u00e1ticas complexas.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Com isso os geodesistas perceberam que precisavam criar uma forma mais simples. Uma forma matem\u00e1tica que fosse mais f\u00e1cil de ser utilizada pelos profissionais.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Foi ent\u00e3o que foi criado o elipsoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3666\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png\" alt=\"elipsoide\" width=\"503\" height=\"426\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png 503w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide-300x254.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/geodesia-e-cartografia-conceitos-e-aplicacoes\/\" style=\"color: #0000ff;\">geod\u00e9sia<\/a><\/span>, o elipsoide de revolu\u00e7\u00e3o \u00e9 o modelo geom\u00e9trico utilizado para a realiza\u00e7\u00e3o dos c\u00e1lculos geod\u00e9sicos.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O mesmo pode ser definido como a forma geom\u00e9trica gerada pela rota\u00e7\u00e3o de uma semi-el\u00edpse em torno de um de seus eixos (<span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/inicial.html\" target=\"_blank\" rel=\"noopener noreferrer\">LAGEO &#8211; UFRGS<\/a><\/span>).<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um elipsoide de revolu\u00e7\u00e3o fica perfeitamente definido por meio de dois par\u00e2metro. S\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Semi-eixo menor (tamb\u00e9m conhecido como achatamento);<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Semi-eixo maior.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide &#8211; Achatamento<\/span><\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O achatamento de um elipsoide \u00e9 a rela\u00e7\u00e3o:<\/span><\/p>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"alignleft\" src=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/2.JPG\" border=\"2\" title=\"\" alt=\"\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Excentricidade<\/span><\/strong><\/span><\/h3>\n<p style=\"text-align: left;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A excentricidade de um elipsoide nada mais \u00e9 do que a propor\u00e7\u00e3o entre a diferen\u00e7a de comprimento dos semi-eixos de uma elipse e o semi-eixo maior.<\/span><\/p>\n<p align=\"center\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"alignleft\" src=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/3.JPG\" border=\"2\" title=\"\" alt=\"\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Grande Normal (N)<\/span><\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4740\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/grande_normal.jpg\" alt=\"grande_normal\" width=\"705\" height=\"490\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/grande_normal.jpg 705w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/grande_normal-300x209.jpg 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Denomina-se de grande normal o segmento de reta que une o ponto H&#8217; ao ponto H na figura acima. <\/span><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">Para calcular a grande normal, faz-se uso da equa\u00e7\u00e3o da elipse.<\/span><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" src=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/16.JPG\" width=\"137\" height=\"51\" border=\"2\" title=\"\" alt=\"\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Al\u00e9m da excentricidade e da grande normal, existem mais alguns par\u00e2metros que s\u00e3o calculados na geod\u00e9sia. S\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Pequena normal (N&#8217;);<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Raio de curvatura da se\u00e7\u00e3o meridiana;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Raio de curvatura da se\u00e7\u00e3o paralela;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Raio de curvatura do paralelo;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Comprimento de um arco de paralelo e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Comprimento de um arco de meridiano.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Os diferentes c\u00e1lculos realizados na geod\u00e9sia e que geraram as f\u00f3rmulas mostradas neste artigo podem serem visualizados no <a style=\"color: #000000;\" href=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/inicial.html\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: #0000ff;\">site da UFRGS<\/span>.<\/a><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide &#8211; Da necessidade de diferentes referenciais geod\u00e9sicos<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter wp-image-4751 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoides-780x453.png\" alt=\"elipsoide\" width=\"780\" height=\"453\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoides-780x453.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoides-300x174.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoides-768x446.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/elipsoides.png 850w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ao possu\u00edrem somente 2 fatores, os elipsoides acabam se adequando melhor a determinada por\u00e7\u00e3o da superf\u00edcie terrestre.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"> Isso fez com que ao longo do tempo os geodesistas e <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/educalingo.com\/pt\/dic-pt\/cartografo\" target=\"_blank\" rel=\"noopener noreferrer\">cart\u00f3grafos<\/a><\/span> precisassem adotar diferentes elipsoides para diferentes por\u00e7\u00f5es do globo terrestre.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Veja na imagem abaixo os elipsoides mais utilizados ao longo do tempo.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"size-large wp-image-4748 aligncenter\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Elipsoidesusadosaolongodotempo-1024x768.jpg\" alt=\"Elipsoides usados ao longo do tempo\" width=\"1024\" height=\"768\" \/><\/span><\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A diferen\u00e7a entre elipsoide e datum<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-large wp-image-4752\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum-e-elips\u00f3ide-1024x768.jpg\" alt=\"datum e elipsoide\" width=\"1024\" height=\"768\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A palavra <strong>datum<\/strong> teve sua origem no latim e significa detalhe.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na realidade, um <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/datum-planimetrico-e-datum-altimetrico\/\" style=\"color: #0000ff;\">datum<\/a><\/span> nada mais \u00e9 do que um modelo matem\u00e1tico te\u00f3rico que representa a superf\u00edcie da terra. Desta maneira, um datum possui 3 par\u00e2metros, s\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um ponto de amarra\u00e7\u00e3o;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um norte (orienta\u00e7\u00e3o);<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um elipsoide.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O surgimento do datum foi necess\u00e1rio justamente pela necessidade de se amarrar as <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/curso-topografia\/\" style=\"color: #0000ff;\">diferentes superf\u00edcies existentes<\/a><\/span>:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Geoide;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Superf\u00edcie f\u00edsica.<\/span><\/li>\n<\/ul>\n<p>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\">A <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"http:\/\/www.carto.eng.uerj.br\/cdecart\/download\/NBR14166.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">NBR 14.166<\/a><\/span>, em sua contracapa traz uma imagem que ajudar\u00e1 voc\u00ea a entender melhor estas superf\u00edcies.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-3664 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/nbr-14.166-datum-elipsoide-780x509.png\" alt=\"nbr 14.166 datum e elipsoide\" width=\"780\" height=\"509\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/nbr-14.166-datum-elipsoide-780x509.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/nbr-14.166-datum-elipsoide-300x196.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/nbr-14.166-datum-elipsoide-768x501.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/nbr-14.166-datum-elipsoide.png 1167w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"> Perceba que conforme falei, existe a superf\u00edcie f\u00edsica, o geoide e o elipsoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Al\u00e9m disso, existe a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ufrgs.br\/lageo\/calculos\/conceitos.html\" target=\"_blank\" rel=\"noopener noreferrer\">altitude geom\u00e9trica<\/a><\/span>, que \u00e9 em rela\u00e7\u00e3o ao elipsoide e a <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/datum-vertical-o-que-e-e-qual-o-do-brasil\/\" style=\"color: #0000ff;\">altitude<\/a><\/span> ortom\u00e9trica que \u00e9 em rela\u00e7\u00e3o ao geoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Diante da exist\u00eancia destas superf\u00edcies, o problema enfrentado pelos Geodesistas era como amarar as mesmas.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por exemplo, a altitude obtida com <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"http:\/\/adenilsongiovanini.com.br\/blog\/receptor-gnss-quando-utilizar\/\" target=\"_blank\" rel=\"noopener noreferrer\">receptores GNSS<\/a><\/span> \u00e9 em rela\u00e7\u00e3o ao elipsoide, ou seja, altitude geom\u00e9trica. Por\u00e9m, a mesma n\u00e3o pode ser utilizada em obras de engenharia.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Isso porque em <strong>obras de engenharia deve-se utilizar a altitude ortom\u00e9trica<\/strong> que \u00e9 em rela\u00e7\u00e3o ao geoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Enfim, os geodesistas precisavam de alguma maneira amarrar as diferentes superf\u00edcies e altitudes existentes.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Foi neste contexto que os mesmos criaram o datum. Conforme expliquei anteriormente, um datum possui 3 par\u00e2metros. S\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um elipsoide;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um ponto de amarra\u00e7\u00e3o que serve para amarar o elipsoide a superf\u00edcie f\u00edsica e ao geoide;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">E um norte que faz com que o datum fique orientado de maneira certa.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3939\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum.png\" alt=\"datum\" width=\"679\" height=\"385\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum.png 679w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum-300x170.png 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Perceba que \u00e9 por isso que quando se utiliza um <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/software-de-geoprocessamento-os-14-principais\/\" style=\"color: #0000ff;\">software de geoprocessamento<\/a><\/span>, o que se faz \u00e9 a transforma\u00e7\u00e3o, por exemplo, do <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/sad69\/\" style=\"color: #0000ff;\">datum SAD69<\/a><\/span> para o datum <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/curso-cartografia\/\" style=\"color: #0000ff;\">SIRGAS 2000<\/a><\/span>!<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">E n\u00e3o do elipsoide sad 69 para o elipsoide <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/sirgas-2000\/\" style=\"color: #0000ff;\">SIRGAS 2000<\/a><\/span>.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Perceba que o elipsoide \u00e9 apenas um dos par\u00e2metros que comp\u00f5em o datum.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>Detalhe at\u00edpico<\/strong>: O plural da palavra datum \u00e9 data e n\u00e3o &#8220;datuns&#8221;, como a regra geral nos induz a acreditar.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por exemplo:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">&#8220;Os data SAD 69 e SIRGAS 2000 s\u00e3o geoc\u00eantricos&#8221;.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>Elipsoide &#8211; Principais data existentes<\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4753\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/coordtrans-datum-shifts11.gif\" alt=\"Elipsoide - Principais data existentes\" width=\"366\" height=\"229\"><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ap\u00f3s a cria\u00e7\u00e3o do conceito datum, surgiu um problema secund\u00e1rio, o mesmo utiliza um elipsoide de base, que possui apenas 2 par\u00e2metros.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Com isso, ao se configurar os par\u00e2metros para que o datum se adeque mais a determinada por\u00e7\u00e3o da superf\u00edcie terrestre, em outros locais o mesmo ficava muito distante da superf\u00edcie.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ou seja, acontecia algo parecido com um cobertor de pobre.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Imagine esta cena:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Uma pessoa grande tentando se cobrir com um cobertor menor do que ela. Se a mesma cobrir os p\u00e9s descobre a cabe\u00e7a, se cobrir a cabe\u00e7a, descobre os p\u00e9s.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ou seja, com isso surgiram diferentes data, cada um se adequando mais a determinado continente ou Pa\u00eds.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A \u00fanica exce\u00e7\u00e3o \u00e9 o <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/datum-wgs84-o-que-e-parametros-e-versoes\/\" style=\"color: #0000ff;\">WGS84<\/a><\/span> que tenta se adequar o melhor poss\u00edvel a todo o planeta. Ou seja, mundialmente falando, existem v\u00e1rios DATA (plural de DATUM).<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Veja na imagem abaixo os data SAD69 Alegre e WGS84.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-3673 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/sad-69-e-sirgas-WGS-84-780x348.jpeg\" alt=\"elipsoide - sad 69 e sirgas WGS 84\" width=\"780\" height=\"348\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/sad-69-e-sirgas-WGS-84-780x348.jpeg 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/sad-69-e-sirgas-WGS-84-300x134.jpeg 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/sad-69-e-sirgas-WGS-84-768x343.jpeg 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/sad-69-e-sirgas-WGS-84.jpeg 824w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Perceba que o SAD 69 foi configurado sob medida para o Brasil, enquanto o WGS 84 tenta se adequar a todo o planeta.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por\u00e9m, no Brasil tr\u00eas data foram oficialmente reconhecidos pelo <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ibge.gov.br\/geociencias\/modelos-digitais-de-superficie\/modelos-digitais-de-superficie\/10855-modelo-de-ondulacao-geoidal.html?=&amp;t=o-que-e\" target=\"_blank\" rel=\"noopener noreferrer\">IBGE<\/a><\/span> (Instituto Brasileiro de Geografia e Estat\u00edstica) e utilizados por algum per\u00edodo.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>C\u00f3rrego Alegre (Sistema Geod\u00e9sico C\u00f3rrego Alegre)<\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4755\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/c\u00f3rrego-alegre.jpg\" alt=\"c\u00f3rrego alegre\" width=\"400\" height=\"405\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/c\u00f3rrego-alegre.jpg 400w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/c\u00f3rrego-alegre-296x300.jpg 296w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O c\u00f3rrego alegre foi adotado na d\u00e9cada de 50, tendo como par\u00e2metros:<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000; font-family: arial, helvetica, sans-serif; font-size: 20px;\">Ponto de amarra\u00e7\u00e3o: O ponto C\u00f3rrego Alegre;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide (superf\u00edcie de refer\u00eancia): Elipsoide Internacional de Hayford de 1924<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Orienta\u00e7\u00e3o: Determinada astronomicamente.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><strong>SAD69<\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter wp-image-4754 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69-780x518.png\" alt=\"sad 69\" width=\"780\" height=\"518\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69-780x518.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69-300x199.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69-768x510.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69-360x240.png 360w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sad-69.png 850w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O IBGE atrav\u00e9s de PDF dispon\u00edvel em seu site, tr\u00e1s as seguintes informa\u00e7\u00f5es a respeito do SAD 69.<\/span><\/p>\n<blockquote style=\"border: 2px double #009900; background: #f0fff0 none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: #323232; padding-left: 15px; padding-top: 10px; padding-bottom: 10px;\">\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O SAD69 \u00e9 um sistema geod\u00e9sico regional de concep\u00e7\u00e3o cl\u00e1ssica. A sua utiliza\u00e7\u00e3o pelos pa\u00edses Sul-americanos foi recomendada em 1969 atrav\u00e9s da aprova\u00e7\u00e3o do relat\u00f3rio final do Grupo de Trabalho sobre o Datum Sul-americano, pelo Comit\u00ea de Geod\u00e9sia reunido na XI Reuni\u00e3o Panamericana de Consulta sobre <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/curso-cartografia-online\/\" style=\"color: #0000ff;\">Cartografia<\/a><\/span>, recomenda\u00e7\u00e3o n\u00e3o seguida pela totalidade dos pa\u00edses do continente. Apenas em 1979 ele foi oficialmente adotado como <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/sistema-de-referencia\/\" style=\"color: #0000ff;\">sistema de refer\u00eancia<\/a><\/span> para trabalhos geod\u00e9sicos e cartogr\u00e1ficos desenvolvidos em territ\u00f3rio brasileiro.<\/span><\/p>\n<\/blockquote>\n<p>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><strong>Fonte<\/strong>: ftp:\/\/geoftp.ibge.gov.br\/informacoes_sobre_posicionamento_geodesico\/sirgas\/sisref_2.pdf Par\u00e2metros do SAD 69:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Elipsoide: Elipsoide do sistema geod\u00e9sico de refer\u00eancia GRS-67, aceito e recomendado pela UGGI, em Lucerna, no ano de 1967.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ponto de amarra\u00e7\u00e3o: V\u00e9rtice chu\u00e1.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">orienta\u00e7\u00e3o: Azimute geod\u00e9sico da dire\u00e7\u00e3o inicial Chu\u00e1-Uberaba (\u03be=0.31 \u03b7=-3.52 N=0 m)<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Origem: topoc\u00eantrico<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>SIRGAS 2000<\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-4756\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sirgas-2000.png\" alt=\"sirgas 2000\" width=\"640\" height=\"498\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sirgas-2000.png 640w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/sirgas-2000-300x233.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O <strong>SIRGAS 2000<\/strong> (Sistema de Refer\u00eancia Geoc\u00eantrico para as Am\u00e9ricas) foi definido pelo IBGE como o <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/sistema-geodesico-brasileiro-o-que-e\/\" style=\"color: #0000ff;\">Sistema Geod\u00e9sico Brasileiro<\/a><\/span>.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O mesmo foi criado em outubro de 1993 e possui como principal objetivo estabelecer um sistema de refer\u00eancia geoc\u00eantrico para a Am\u00e9rica do Sul.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">As constantes do mesmo s\u00e3o id\u00eanticas \u00e0s do WGS 84, sendo que o mesmo possui origem geoc\u00eantrica.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na imagem abaixo voc\u00ea pode ver os par\u00e2metros de transforma\u00e7\u00e3o entre os diferentes data:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-3670 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Par\u00e2metros-de-transforma\u00e7\u00e3o-entre-os-diferentes-data-780x417.png\" alt=\"elipsoide - Par\u00e2metros de transforma\u00e7\u00e3o entre os diferentes data\" width=\"780\" height=\"417\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Par\u00e2metros-de-transforma\u00e7\u00e3o-entre-os-diferentes-data-780x417.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Par\u00e2metros-de-transforma\u00e7\u00e3o-entre-os-diferentes-data-300x161.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Par\u00e2metros-de-transforma\u00e7\u00e3o-entre-os-diferentes-data-768x411.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Par\u00e2metros-de-transforma\u00e7\u00e3o-entre-os-diferentes-data.png 1168w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px; font-family: arial, helvetica, sans-serif; color: #000000;\"><strong>Elipsoide &#8211; Materializa\u00e7\u00e3o do datum<\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-large wp-image-4757\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-768x1024.jpg\" alt=\"elipsoide - materializa\u00e7\u00e3o do datum\" width=\"768\" height=\"1024\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-768x1024.jpg 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-225x300.jpg 225w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-585x780.jpg 585w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-1152x1536.jpg 1152w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum-1536x2048.jpg 1536w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/materializa\u00e7\u00e3o-do-datum.jpg 1920w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A materializa\u00e7\u00e3o do datum se d\u00e1 atrav\u00e9s do estabelecimento de uma rede de esta\u00e7\u00f5es geod\u00e9sicas implantadas e pelo IBGE.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Estas esta\u00e7\u00f5es possuem com coordenadas tridimensionais estabelecidas atrav\u00e9s de t\u00e9cnicas de posicionamento espacial de alta precis\u00e3o.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">utilizando-se do <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/curso-rtk-conheca-o-mais-completo-do-brasil\/\" style=\"color: #0000ff;\">posicionamento pelo GNSS<\/a><\/span>, o IBGE implantou uma s\u00e9rie destas esta\u00e7\u00f5es estrategicamente distribu\u00eddas ao longo do territ\u00f3rio nacional.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Veja na imagem abaixo um exemplo de marco implantado pelo IBGE.<\/span><\/p>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter wp-image-3672\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/Marco-geod%C3%A9sico.jpg\" alt=\"Marco geod\u00e9sico\" width=\"758\" height=\"651\"><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Se voc\u00ea quer<strong> MERGULHAR FUNDO e aprender a prestar servi\u00e7os com grande velocidade e com seguran\u00e7a<\/strong>, <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/cursos-online\/\">acesse este link<\/a><\/span> e conhe\u00e7a os mesmos.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; line-height: 1.3;\">Entre eles, o <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/curso-de-autocad-para-topografia\/\" target=\"_blank\" rel=\"noopener noreferrer\">Curso de Confec\u00e7\u00e3o de Plantas Topogr\u00e1ficas<\/a><\/span>. <span style=\"color: #000000;\">Um <\/span><\/span><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; line-height: 1.3;\">curso pr\u00e1tico\u00a0<\/span><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; line-height: 1.3;\">com o qual voc\u00ea vai <strong>aprender a produzir as 15 diferentes plantas produzidas em um escrit\u00f3rio de topografia<\/strong>.<\/span><\/span><\/p>\n<p><a href=\"https:\/\/adenilsongiovanini.com.br\/curso-de-autocad-para-topografia\/\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" class=\"aligncenter wp-image-31689\" src=\"https:\/\/adenilsongiovanini.com.br\/wp-content\/uploads\/2022\/07\/planta-de-topografia-1024x612.png\" alt=\"\" width=\"770\" height=\"460\" \/><\/a><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Clique <a href=\"https:\/\/adenilsongiovanini.com.br\/curso-de-autocad-para-topografia\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: #0000ff;\">neste link<\/span><\/a> e conhe\u00e7a melhor o mesmo.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Gratid\u00e3o por voc\u00ea ter lido o artigo. \ud83d\ude4f<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; font-size: 24px;\"><strong>Aprenda a Prestar Servi\u00e7os de Topografia Cadastral Atrav\u00e9s de um Livro Formado Por Mais de 547 <\/strong><\/span><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; font-size: 24px;\"><strong>Estudos de Caso e E<\/strong><\/span><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; font-size: 24px;\"><strong>xemplos Pr\u00e1ticos<\/strong><\/span><\/h2>\n<h2 style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter size-large wp-image-25393\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/08\/livro-de-topografia-780x386.png\" alt=\"\" width=\"780\" height=\"386\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/08\/livro-de-topografia-780x386.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/08\/livro-de-topografia-300x148.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/08\/livro-de-topografia-768x380.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/08\/livro-de-topografia.png 1536w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/h2>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">A <span style=\"text-decoration: underline;\"><em>1 clique de dist\u00e2ncia de voc\u00ea<\/em><\/span> encontra-se o <strong>MAIS COMPLETO LIVRO DE TOPOGRAFIA DO BRASIL<\/strong>.<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">O mesmo \u00e9 formado por mais de 547 Estudos de Caso, Conhecimentos Pr\u00e1ticos, Exemplos, Aplica\u00e7\u00f5es, Planilhas e Chacklists!<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Se voc\u00ea quer <em>(ou precisa)<\/em> aprender a prestar servi\u00e7os de Topografia, este livro servir\u00e1 como uma luva para voc\u00ea.<\/span><\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">D\u00ea uma espiadinha no sum\u00e1rio do mesmo:<\/span><\/span><\/p>\n<p><center><iframe width=\"95%\" height=\"990\" src=\"https:\/\/drive.google.com\/file\/d\/1Ceor37i07URpOWB8CUnuUWq8aOuR7VSf\/preview\" data-mce-fragment=\"1\"><\/iframe><\/center><\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">Para conhecer melhor a estrutura do livro, juntar-se a dezenas de profissionais e adquirir sua c\u00f3pia \u00e9 s\u00f3 clicar no bot\u00e3o abaixo:<\/span><\/span><\/p>\n<div class=\"su-button-center\">\n<div class=\"su-button-center\"><span style=\"color: #000000; font-size: 20px;\"><div class=\"su-button-center\"><a href=\"https:\/\/adenilsongiovanini.com.br\/biblia-do-agrimensor\/\" class=\"su-button su-button-style-3d\" style=\"color:#000000;background-color:#2BCC2F;border-color:#23a426;border-radius:9px\" target=\"_blank\" rel=\"nofollow\" id=\"1\"><span style=\"color:#000000;padding:0px 24px;font-size:18px;line-height:36px;border-color:#6bdc6e;border-radius:9px;text-shadow:0px 0px 0px #000000\"> \u279c Quero Conhecer Melhor o Livro, Pois Quero e Preciso Aprender Mais Sobre a Presta\u00e7\u00e3o de Servi\u00e7os de Topografia<\/span><\/a><\/div><\/span><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Antes de entendermos exatamente o que \u00e9 o elipsoide, \u00e9 importante que voc\u00ea saiba que existe o elipsoide e o elipsoide de revolu\u00e7\u00e3o, sendo que na geod\u00e9sia utiliza-se o elipsoide de revolu\u00e7\u00e3o para definir-se a forma da terra. Por causa disso, precisaremos primeiramente entender o que \u00e9 o elipsoide. Em [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4763,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4736","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-topografia-cadastral"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Elipsoide: o que \u00e9 e para que serve? - Adenilson Giovanini<\/title>\n<meta name=\"description\" content=\"Descubra o que \u00e9 um elipsoide, para o que o mesmo serve, quais seus par\u00e2metros, quais os diferentes referenciais geod\u00e9sicos existentes.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/elipsoide-o-que-e-e-para-que-serve\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Elipsoide: o que \u00e9 e para que serve? 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