<Text-field style="Heading 1" layout="Heading 1">Termos</Text-field>

O Plano Cartesiano:

Dist\303\242ncia Entre Pontos

Vida extraterrestre foi o assunto de ci\303\252ncia de fic\303\247\303\243o e, justamente no ano passado cientistas na California, ap\303\263s v\303\241rias simula\303\247\303\265es extensas de computador, conclu\303\255ram que uma das nossas estrelas vizinhas mais pr\303\263ximas, Alpha Centauri, provavelmente possui planetas como a Terra em \303\263rbita dela.

Alfa Centauri \303\251 afastada 4.37 anos luz , o que significa que para se chegar l\303\241 \303\240 velocidade da luz levaremos 4.37. Tal dist\303\242ncia \303\251 cerca de 25.8 trilh\303\265es de milhas, ou de forma aproximada a dist\303\242ncia total viajada se cada pessoa na Terra desse uma volta completa no planeta uma vez.

Nesta apresenta\303\247\303\243o, iremos introduzir os conceitos de a dist\303\242ncia entre dois pontos e o ponto m\303\251dio de um segmento de reta.

Assumiremos que voc\303\252 esteja familiarizado com estes termos adicionais e conceitos, que est\303\243o sendo discutidos em outras apresenta\303\247\303\265es desta cole\303\247\303\243o: coordenadas, coordenada x, coordenada y, e o Teorema de Pit\303\241goras.

<Text-field style="Heading 1" layout="Heading 1">Conceitos Principais</Text-field>

<Text-field style="Heading 2" layout="Heading 2">A Dist\303\242ncia Entre Dois Pontos</Text-field>

Usando o teorema de Pit\303\241goras, podemos calcular o comprimento da hipotenusa de um tri\303\242ngulo ret\303\242ngulo se soubermos o comprimentos dos outros dois lados. Para encontrar a dist\303\242ncia entre dois pontos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSVtc3ViR0YkNiUtSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ji1JI21uR0YkNiVRIjFGJ0Y6L0Y+USdub3JtYWxGJ0Y3RjpGPS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEiLEYnRjpGRi8lJmZlbmNlR0Y8LyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjwvJSpzeW1tZXRyaWNHRjwvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGPC8lJ2FjY2VudEdGPC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYxNiUtRjQ2JlEieUYnRjdGOkY9RkBGSEY6RkZGOkZGRjpGRg== e 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, primeiros localizamos os pontos no plano Cartesiano.

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

Depois, podemos construir um tri\303\242ngulo ret\303\242ngulo desenhando a reta horizontal atrav\303\251s de 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 e uma vertical atrav\303\251s de 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.

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

Pelo Teorema de Pit\303\241goras sabemos que 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.

Agora, precisamos determinar os comprimentos a e b.

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

Ent\303\243o elevando ao quadrado os dois lados para chegar pr\303\263ximo da forma 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.

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

Ent\303\243o

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

A F\303\263rmula da Dist\303\242ncia

A dist\303\242ncia d entre dois pontos 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 e 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 \303\251 dada por:

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

<Text-field style="Heading 2" layout="Heading 2">O Ponto M\303\251dio de um Segmento de Reta</Text-field>

Sup\303\265e-se que voc\303\252 e seu amigo concordem em se encontrar \303\240 metade do caminho de suas casas. Voc\303\252 olha em um mapa para localizar seus dois endere\303\247os. Como voc\303\252 encontrar\303\241 seu ponto de encontro? Voc\303\252 coloca seu dedo no ponto m\303\251dio da reta entre os pontos que representam suas casas.

O ponto m\303\251dio de um segmento de reta \303\251 obtido pela aproxima\303\247\303\243o das coordenadas x e pela aproxima\303\247\303\243o das coordenadas y dos pontos finais de um segmento. Se denotarmos os pontos finais do segmento por 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 e 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, e o ponto m\303\251dio do segmento por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJ5RidGNEY3RjpGN0ZBRjdGQUY3RkE= ent\303\243o teremos:

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

<Text-field style="Heading 1" layout="Heading 1">Demonstra\303\247\303\243o</Text-field>

<Text-field style="Heading 2" layout="Heading 2">A Dist\303\242ncia Entre Dois Pontos</Text-field>

Clique ou arraste dois pontos no gr\303\241fico, e a dist\303\242ncia entre eles ser\303\241 computada, junto com as duas componentes da dist\303\242ncia.

Cheque Somente coordenadas inteiras se voc\303\252 quiser permitir que somente pontos de treli\303\247a sejam selecionados (por exemplo, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiUtRiM2Jy1JI21uR0YkNiVRIjJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y4RjsvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYlUSI0RidGOEY7RjhGO0Y4RjtGOEY7 n\303\243oLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSQxLjdGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y0RjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSQ0LjRGJ0Y0RjdGNEY3RjRGNy1GOzYuUSJ+RidGNEY3Rj4vRkFGNkZDRkVGR0ZJRktGTS9GUUZPRjRGNw==).

M3_1_4a:-enddrag();M3_1_4a:-click();M3_1_4a:-drag();Ni8tJSdDVVJWRVNHNiY3JDckJCEjUyEiIiQiIyEpISIiNyQkISNTISIiJCEjPyEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUlRk9OVEc2JCUmVElNRVNHIiM3LSUmU1RZTEVHNiMlJUxJTkVHLSUnUE9JTlRTRzYoNyQkISNTISIiJCIjISkhIiI3JCQhI1MhIiIkISM/ISIiLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJSdTWU1CT0xHNiQlJkNST1NTRyIjOi0lJUZPTlRHNiQlJlRJTUVTRyIjNy0lJlNUWUxFRzYjJSZQT0lOVEctJSdDVVJWRVNHNic3JzckJCEjUyEiIiQiIyEpISIiNyQkISNTISIiJCIjISkhIiI3JCUqdW5kZWZpbmVkRyUqdW5kZWZpbmVkRzckJCEjUyEiIiQhIz8hIiI3JCQhI1MhIiIkIiMhKSEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIkLSUlRk9OVEc2JCUmVElNRVNHIiM3LSUmU1RZTEVHNiMlJUxJTkVHLSUlVklFV0c2JDskISQrIiEiIiQiJCsiISIiOyQhJCsiISIiJCIkKyIhIiItJiUmX0FYSVNHNiMiIiI2Jy0lK19HUklETElORVNHNiQlKERFRkFVTFRHLSUpX1ZJU0lCTEVHNiMiIiMtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIi0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJiUmX0FYSVNHNiMiIiM2Jy0lK19HUklETElORVNHNiQlKERFRkFVTFRHLSUpX1ZJU0lCTEVHNiMiIictJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIi0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJStBWEVTTEFCRUxTRzYlUSJ4NiJRInk2Ii0lJUZPTlRHNiUlJlRJTUVTRyUoREVGQVVMVEciIzctJSZUSVRMRUc2JS0lKV9UWVBFU0VURzYjLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY2LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2I1FHRXhlbXBsb35kZX5EaXN0JiMyMjY7bmNpYX5lbnRyZX5Qb250b3M2Ii8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbjYiLyUlc2l6ZUdRIzEyNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHQ2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiItJSVGT05URzYkJSZUSU1FU0ciIzctJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUlRk9OVEc2JCUmVElNRVNHIiM3LSUqQVhFU1NUWUxFRzYjJSdOT1JNQUxHLSUpX1ZJU0lCTEVHNiMiIigtJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQhPSEiIi0lKUJPVU5EU19ZRzYjJCIkKyQhIiItJS1CT1VORFNfV0lEVEhHNiMkIiVdTyEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiU1TiEiIi0lKUNISUxEUkVORzYiLSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIkZyIhIiItJSlCT1VORFNfWUc2IyQiJCFIISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlNVAhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlZ04hIiItJSlDSElMRFJFTkc2Ig==Ig==

<Text-field style="Heading 2" layout="Heading 2">O Ponto M\303\251dio de um Segmento de Reta</Text-field>

Clique ou arraste dois pontos no gr\303\241fico, e seus pontos m\303\251dios ser\303\243o mostrados, junto com as duas componentes da reta, e seus pontos m\303\251dios.

Cheque Use somente coordenadas inteiras se voc\303\252 quiser permitir que somente pontos de trli\303\247a sejam selecionados (por exemplo, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiUtRiM2Jy1JI21uR0YkNiVRIjJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y4RjsvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYlUSI0RidGOEY7RjhGO0Y4RjtGOEY7 n\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSQxLjdGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIixGJ0Y0RjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSQ0LjRGJ0Y0RjdGNEY3RjRGNy1GOzYuUSJ+RidGNEY3Rj4vRkFGNkZDRkVGR0ZJRktGTS9GUUZPRjRGNw==).

M3_1_4b:-enddrag();M3_1_4b:-click();M3_1_4b:-drag();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Ig==

<Text-field style="Heading 1" layout="Heading 1">Exemplos</Text-field>

<Text-field style="Heading 2" layout="Heading 2">O Ponto M\303\251dio \303\251 Realmente no Meio?</Text-field>

Usando a f\303\263rmula de dist\303\242ncia apresentada acima, podemos facilmente checar que o ponto m\303\251dio de uma reta est\303\241 realmente a meio caminho de cada final. Dados dois pontos, 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 e 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, o ponto m\303\251dio do segmento de reta juntando-os \303\251 o ponto 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. O comprimento do segmento de reta \303\251 somente a dist\303\242ncia entre seus pontosfinais, que s\303\243o

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

Deixe LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEibUYnRjJGNUY4RjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= ser a dist\303\242ncia do ponto m\303\251dio ao ponto 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. Ent\303\243o

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRictSSVtc3ViR0YkNiUtRiw2JlEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRiw2JlEibUYnRkdGSkZNRkdGSkZNLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGSi9GTlEnbm9ybWFsRic=

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

JSFH

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

JSFH

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

JSFH

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

JSFH

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

JSFH

Ent\303\243o o ponto m\303\251dio \303\251 no meio.

<Text-field style="Heading 2" layout="Heading 2">Medindo Dist\303\242ncias Reais</Text-field>

Quando algo \303\251 perto o suficiente ou facilmente acess\303\255vel, medir sua dist\303\242ncia sempre \303\251 f\303\241cil. Uma fita m\303\251trica pode ser usada, ou se o objeto e o observador poderem ser colocados em algum sistema cartesiano ent\303\243o um m\303\251todo similar ao m\303\251todo Pitag\303\263rico descrito acima pode ser empregado. Na realidade, v\303\241rias coisas n\303\243o s\303\243o t\303\243o acess\303\255veis. Por exemplo, antigamente seria necess\303\241rio \303\240s vezes saber qual a dist\303\242ncia do navio \303\240 costa. O m\303\251todo que foi desenvolvido \303\251 conhecido como princ\303\255pio de parallax. Come\303\247ando por marcar dois pontos bem separados na costa, A e B. Denotando a posi\303\247\303\243o dos barcos como C, os \303\242ngulos \342\210\240BAC e \342\210\240ABC e a dist\303\242ncia de A para B s\303\243o o suficiente para determinar a dist\303\242ncia at\303\251 a costa.

Uma modifica\303\247\303\243o desse m\303\251todo pode ser usada para determinar a dist\303\242ncia da Terra ao Sol. Esse m\303\251todo \303\251 baseado na observa\303\247\303\243o da \303\263rbita de V\303\252nus atrav\303\251s da face do sol atrav\303\251s de duas loca\303\247\303\265es bem separadas em latitude. \303\223rbitas de V\303\252nus s\303\243o eventos bastante raros, ocorrendo duas vezes, 8 anos de diferen\303\247a, aproximadamente a cada 121,5 e 105,5 anos cada. Nesse s\303\251culo, eles ocorrem em 8 de Junho de 2004, e 6 de Junho de 2012. A observa\303\247\303\243o da \303\263rbita de V\303\252nus em 1769 foi a raz\303\243o para a primeira viagem do capit\303\243o ingl\303\252s James Cook para o sul do Pac\303\255fico. Infelizmente, o equipamento observacional do dia n\303\243o era suficientemente preciso para a coleta de dados acurados, e n\303\243o foi at\303\251 a \303\263rbita de V\303\252nus no final de 1800 que astr\303\264nomos foram capazes de obter uma dist\303\242ncia Terra-Sol estimada que era pr\303\263ximo do valor conhecido hoje.

Para objetos ainda mais longe, tais como estrelas mais pr\303\263ximas, a Terra n\303\243o possui di\303\242metro grande o suficiente para usar como reta de base para uma medida paralaxe, mas a \303\263rbita da Terra possui. Fazendo medi\303\247\303\265es dos \303\242ngulos Sol-Terra-estrela em intervalos de seis meses e usando a dist\303\242ncia de retas como base entre as duas observa\303\247\303\265es do dobro da dist\303\242ncia do Sol \303\240 Terra (metade de um ciclo orbital completo), dist\303\242ncias \303\240 estrelas como Alfa Centauri podem ser determinadas com precis\303\243o.

Para objetos mais afastados que as estrelas mais pr\303\263ximas, o princ\303\255pio do paralaxe n\303\243o ser\303\241 mais vi\303\241vel. Tais objetos incluem estrelas e nebulosas da nossa gal\303\241xia mais distantes, outras gal\303\241xias, quasares distantes, e a fronteira do universo conhecido. Para os mais pr\303\263ximos desses - objetos na nossa gal\303\241xia ou em outras gal\303\241xias mais pr\303\263ximas - o brilho de estrelas pode ser usado para calcular dist\303\242ncias. Se o verdadeiro brilho de uma estrela \303\251 conhecido (o que acontece com certas estrelas) ent\303\243o a diferen\303\247a entre ele e o brilho aparente pode ser usado para calcular o qu\303\243o distante ela est\303\241 (j\303\241 que o brilho diminui com o aumento da dist\303\242ncia).

Para objetos que est\303\243o muito distantes para essa t\303\251cnica existe outro fen\303\264meno, conhecido como desvio para o vermelho, que pode ser usado. O desvio para o vermelho refere \303\240 observa\303\247\303\243o de que a luz emitida por objetos muito distantes \303\251 deslocada para o fim vermelho do espectro eletromagn\303\251tico (onda longa). Isto se deve ao fato de que objetos distantes se distanciam de n\303\263s, da mesma forma que as ondas sonoras de uma ambul\303\242ncia mudam se ela vem na sua dire\303\247\303\243o ou se ela se afasta, as ondas luminosas s\303\243o esticadas por esse movimento. por causa do quanto maior a dist\303\242ncia de um objeto, mais r\303\241pido ele se distancia de n\303\263s, a luz de objetos mais pr\303\263ximos exibem maiores deslocamentos para o fim vermelho do espectro. Por conta disso, a dist\303\242ncia ao mais distante objeto observ\303\241vel (atualmente quasares) pode ser medida.

JSFH