Loading...
Publication
Determinação da Longitude por alturas próximas da meridiana
| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 1.23 MB | Adobe PDF |
Advisor(s)
Abstract(s)
Nesta dissertação de mestrado estuda-se o método proposto por Charles de Littrow em 1842, destinado ao cálculo aproximado da longitude por observações solares próximas da passagem meridiana. Ao contrário dos métodos tradicionais que calculam separadamente a latitude ao meio-dia solar e a longitude em momentos distintos, o processo de Littrow permite reduzir o intervalo entre ambas as observações, aproximando-se de uma solução simultânea para a posição astronómica.
Para além da análise do método, foi realizado um embarque, durante o qual se efetuaram observações com recurso ao sextante e a um cronómetro. As alturas solares foram observadas em pares, antes e depois da passagem meridiana do Sol, de forma a testar o método nas condições sugeridas por Littrow e por autores posteriores.
Os dados recolhidos foram tratados em folhas de cálculo, aplicando-se a fórmula de Littrow para a obtenção da longitude, a qual foi posteriormente comparada com a posição GPS registada no instante da passagem meridiana. Os resultados revelaram erros variáveis, em parte explicáveis por erros de leitura, pelas condições de mar e pela reduzida dimensão da amostra. No entanto, quando se substituíram as alturas observadas por alturas verdadeiras calculadas com base em trigonometria esférica, verificou-se uma melhoria significativa na precisão dos resultados. Esta constatação reforça a sensibilidade do método aos erros de observação e a importância do rigor nos dados utilizados.
O método de Littrow, embora aproximado, demonstra utilidade como ferramenta auxiliar na navegação astronómica, especialmente em circunstâncias onde os sistemas eletrónicos possam estar inoperacionais.
In this master’s thesis, the Littrow method proposed by Charles de Littrow in 1842 is studied, intended for the approximate calculation of longitude by means of solar observations close to the meridian passage. Unlike traditional methods that calculate latitude at local noon and longitude at different times, the Littrow process allows reducing the interval between both observations, approaching a quasi-simultaneous solution for astronomical positioning. In addition to the theoretical analysis of the method, a sea trial was carried out, during which observation data were collected using a sextant and a chronometer synchronized with the ship’s GPS system. Solar altitudes were observed in pairs, one before and one after the Sun’s meridian passage, so as to test the method under the conditions suggested by Littrow and by later authors. The collected data were processed using spreadsheets, applying the Littrow formula to obtain longitude, which was later compared with the GPS position recorded at the moment of meridian passage. The results revealed variable errors, partly explicable by reading errors, sea conditions, and the small sample size. However, when the observed altitudes were replaced with true solar altitudes computed through spherical trigonometry, a significant improvement in precision was observed. This finding reinforces the sensitivity of the method to observational errors and the importance of data quality. The Littrow method, though approximate, proves its usefulness as an auxiliary tool in astronomical navigation, especially in circumstances where electronicbased systems may be inoperative.
In this master’s thesis, the Littrow method proposed by Charles de Littrow in 1842 is studied, intended for the approximate calculation of longitude by means of solar observations close to the meridian passage. Unlike traditional methods that calculate latitude at local noon and longitude at different times, the Littrow process allows reducing the interval between both observations, approaching a quasi-simultaneous solution for astronomical positioning. In addition to the theoretical analysis of the method, a sea trial was carried out, during which observation data were collected using a sextant and a chronometer synchronized with the ship’s GPS system. Solar altitudes were observed in pairs, one before and one after the Sun’s meridian passage, so as to test the method under the conditions suggested by Littrow and by later authors. The collected data were processed using spreadsheets, applying the Littrow formula to obtain longitude, which was later compared with the GPS position recorded at the moment of meridian passage. The results revealed variable errors, partly explicable by reading errors, sea conditions, and the small sample size. However, when the observed altitudes were replaced with true solar altitudes computed through spherical trigonometry, a significant improvement in precision was observed. This finding reinforces the sensitivity of the method to observational errors and the importance of data quality. The Littrow method, though approximate, proves its usefulness as an auxiliary tool in astronomical navigation, especially in circumstances where electronicbased systems may be inoperative.
Description
Keywords
Longitude Navegação Astronómica Alturas Extra Meridianas Littrow Ângulo Horário Astronomical Navigation Extrameridian Altitudes Hour Angle