On the transit of Venus 2012: Method of computation for prediction of contact timings

Transit of Venus over the solar disc is an extremely rare event. The phenomenon occurred last time on June 8, 2004 when the entire event was visible from all parts of India. Another Transit of Venus is going to occur on June 6, 2012, though the entire event will not be visible from India. The Positional Astronomy Centre publishes data on Transit of Mercury and Venus in its annual publication ‘The Indian Astronomical Ephemeris’. In this paper an attempt has been made to provide documentation on the methodology for computation of contact timings of the event. Using the methodology, the geocentric contact timings and local contact timings for important places of India for the event of Transit of Venus of June 6, 2012 have been predicted. The result thus obtained for different geocentric phases of the event has been compared with the predicted timings published by The Nautical Almanac Office, United States Naval Observatory and NASA.

A matemática aplicada à astronomia para o ensino básico: concepções de discentes e relato de experiência de uma oficina

Resumo: Neste artigo relatamos uma experiência de realização de uma oficina para um grupo de 30 estudantes do Ensino Fundamental e Médio que participaram de um projeto de extensão da Universidade Estadual de Maringá (Paraná) denominado TIME – Teoria e Investigação em Matemática Elementar. Na oficina relacionamos matemática e astronomia com uma proposta de construção do instrumento Quadrante. Ademais, com a finalidade de entender as concepções dos discentes sobre geometria nãoeuclidiana e conhecimentos sobre astronomia, elaboramos um questionário respondido previamente. A investigação efetuada se baseou nos pressupostos da pesquisa qualitativa do tipo descritiva. As nossas observações mostram que o trabalho com a astronomia possibilitou aos estudantes desenvolverem noções sobre geometria não euclidiana e euclidiana para o entendimento do funcionamento do instrumento. Além disso, testificamos a fragilidade relacionada ao pouco conhecimento dos estudantes da Educação Básica no que diz respeito aos conceitos básicos de Astronomia.Palavras-chave: Geometria não Euclidiana; Astronomia de Posição; Instrumento Astronômico. Mathematics applied to astronomy in the framework of basic education: conceptions of discents and experience report of a workshopAbstract: In this article we report an experience of conducting a workshop aimed at a group of 30 elementary and high school students who participated in an extension project at the State University of Maringá (Paraná) called TIME – Teoria e Investigação em Matemática Elementar (Theory and Research in Elementary Mathematics). In the workshop we related mathematics and astronomy to a proposal to build the Quadrant instrument. Furthermore,in order to understand students’ conceptions about non-Euclidean geometry and knowledge about astronomy, we prepared a questionnaire previously answered. The investigation carried out is based on the assumptions of qualitative research of the descriptive type. Our observations show that working with astronomy enabled students to develop notions about non-Euclidean and Euclidean geometry to understand how the instrument works. In addition, we testify the fragility related to the lack of knowledge of Basic Education students regarding the basic concepts of Astronomy.Keywords: Non-Euclidean Geometry; Positional Astronomy; Astronomical Instrument.

Astrometric Calibration of the Clementine Meridian Line (1702) of S. Maria degli Angeli on the Zodiacal Signs, in the IGEA Observational Campaign (2018/21)

The meridian line is a basic instrument for positional astronomy, it was used to study the motion of Sun, Moon, planets and the position of stars by measuring position and time of their passage through the meridian plane. The accuracy of such positions was dependent on precise theories of the atmospheric refraction (Cassini, 1655 and Laplace, 1825) and by the use of reference marks present originally on the meridian line, and now cancelled by the centuries. From October 27, 2018 the new pinhole of the meridian line in the Basilica of S. Maria degli Angeli in Rome (1702) is a circle 25 mm wide and 6.11 mm thick and its position is fixed, in order to perform a series of observations of astrometric quality, the IGEA campaign. The comparison of the observed positions of the meridian passages of the Sun, Southern and Northern limbs, with the ephemerides of Calsky.org and Stellarium 0.20.2 for the Sun are examined for the dates of the ingresses into the zodiacal signs, when the ecliptic longitude is exactly 0°/180° (Aries and Libra, spring and fall equinox), 30°/150° (Taurus, Virgo), 60°/120° (Gemini, Leo), 90° (Cancer), 330°/210° (Pisces, Scorpio), 300°/240° (Aquarius/Sagittarius), 270° (Capricorn). The former geometrical calibration of the marks present on the line, with a total station, is compared with another calibration done with a metal and laser meter. The first star on the floor of the Basilica representing the position of the Sun on August 20, 1702 when the pope Clement XI visited the meridian line, financed by him, has been calibrated with the solar image. The present pinhole is 4.4±0.1 mm South with respect to the original one of 1702.

Geometria esférica: um estudo da interposição entre Matemática e Astronomia

ResumoEste artigo trata do recorte da pesquisa em andamento, que tem por finalidade investigar os conhecimentos que são necessários para os estudos do conceito de Geometria Esférica e a sua interposição entre as disciplinas de Matemática e Astronomia, nos anos finais da Educação Básica. Sendo assim, busca-se responder a seguinte questão: Qual é a base do conhecimento para o ensino de Astronomia Posicional no 3º ano do Ensino Médio? Para responder a essa indagação, recorre-se a um estudo bibliográfico em produções textuais que contemplam a Astronomia Posicional no seu contexto histórico de origem. O referencial teórico pretendido para organização do objeto matemático baseia-se na Teoria Antropológica do Didático de Yves Chevallard (1992). Sob esta ótica, os objetos têm inter-relações hierárquicas que permitem identificar as suas respetivas estruturas ecológicas na gênese de conceitos matemáticos apoiados na ideia de nicho, habitat, cadeia alimentar e ecossistema. Palavras-Chave: Geometria Esférica; Astronomia Posicional; Organização Matemática; Organização Didática.AbstractThis article treaties with the research still ongoing that aims to investigate the knowledge needed to study the concept of Spherical Geometry and its interposition between Mathematics and Astronomy in the final years of Basic Education. Thus, we try to answer the following question: What is the knowledge base for the teaching of Positional Astronomy in the 3rd year of High School? To answer this question, a bibliographic study is used in textual productions that contemplate Positional Astronomy in its historical context of origin. The theoretical framework for the organization of the mathematical object is based on Yves Chevallard's (1992) Anthropological Theory of Didactics. From this point of view, objects have hierarchical interrelations that allow their respective ecological structures to be identified in the genesis of mathematical concepts based on the idea of niche, habitat, food chain and ecosystem.Keywords: Spherical Geometry; Positional Astronomy; Mathematical Organisation; Didactical Organization.

Active Learning in Physics, Astronomy and Engineering with NASA’s General Mission Analysis Tool

Astrodynamics is the study of the motion of artificial satellites and spacecraft, subject to both natural and artificially induced forces. It combines celestial mechanics, attitude dynamics and aspects of positional astronomy to describe spacecraft motion and enable the planning and analysis of missions. It is of significant interdisciplinary interest with relevance to physics, astronomy and spaceflight engineering, but can be challenging to deliver in an effective, engaging manner because of the often abstract nature of some concepts, the four-dimensional nature of the problems, and the computation required to explore realistic astrodynamics behaviour. The University of Leicester has adopted NASA’s General Mission Analysis Tool as a core resource to support active learning in this subject for students at Level 6 (BSc) and Level 7 (MSc). This paper describes our approach to the implementation of GMAT as an essential element of teaching and learning in the subject.