Reflexões e contribuições para o ensino de gravitação clássica no nível médio

The subject of Classic Gravitation is part of the actual curriculum for High School in Brazil, and it is taught in the first year of that education level. This master thesis presents a research regarding the subject Classic Gravitation in High School. This research was based in two complementary guidelines of research and action. The first guideline was the analysis of 21 didactic books of physics which are the more frequently used in High School, in the city of Natal/RN. The second guideline, worked after being verified the most common deficiencies presents in the didactic books, was the elaboration, followed by a practical application, of a course suggesting how to approach that subject in the classroom. The Parâmetros Curriculares Nacionais para o Ensino Médio (National Curricular Parameters for High School PCNEM) defend that Classic Gravitation is very important in the student s formation and that its study helps the comprehension of many nature s phenomena. Because of this vision of that subject by the PCNEM, the 21 analyzed books were separated in two groups: the first one, containing 10 books, was edited before the spreading of PCNEM, and the second, with 11 books, after that spreading. Whatever the group to which the didactic books belonged, the great majority of them let that subject in a second plan; two of them even suggesting, in the teacher s orientations, that the subject Gravitation can be suppressed in case of insufficient time . These analyses points that the PCNEM had produced no changes in the conception of the authors that wrote books regarding that subject. To analyze the didactic books, we elaborated a script which was used as an analysis tool, in which we put in evidence the relative importance of the historic and philosophic contextualization of the subject, the quotidian experience of the students and the interdisciplinary approach, among other aspects. It became evident that the didactic books give very little emphasis to historic aspects of the knowledge construction, to the relations with the day-by-day questions and to the interdisciplinary character of the subject Gravitation. It calls attention the non concordance among the authors opinions regarding the necessary previous knowledge or prerequisites the students should fulfill in order to begin to study Gravitation. The course we elaborated was given to a group of teachers as well as to students. In those courses we treated theoretical and practical aspects and emphasized historical questions and the ones which are related to people s daily life. The course for teachers was realized as an extra-mural activity of the UFRN and was given by the author of this thesis at the Escola Estadual Francisco Ivo Cavalcanti (a state public school in Natal/RN). There were 23 teachers present, from several public schools and several fields of knowledge. The thesis supervisor and the master degree s colleagues of the author acted as collaborators , reporting the participants opinions and speeches. The course to the students, on the other hand, had the participation of 300 regular students who belonged to 6 different 1st year classes of the High School Escola Marista de Natal (RN), in which the author acts as a physics teacher. The student s course was realized as part of the regular curriculum activities, in which three classes stood under the responsibility of the author and other three classes in charge of another Marista s teacher, who participated as a collaborator . The teacher s course as well as the students one were given in two stages, with five hours each. The first stage was divided in two moments, the first one focused on the survey of the spontaneous conceptions about gravitation, in which we worked basically with experiments of free throwing and pendulum, and the second one focused in theoretical presentations and quarrels about universe s models. In the second stage of the course we improved the study of Kepler s laws and the Newton s Universal Gravitation law, and we used as motivating tools some practices involving the construction of the solar system in scale. As instruments for evaluating both courses we used questionnaires and reported the speeches with participants opinions, beyond usual written evaluations in the course for the students. The teachers who participated in the course showed very good wills in realizing interdisciplinary practices; nevertheless, according their own speeches, they frequently came across the difficulty of how to do . From the experience we had in both courses, we conclude that the approach we propose hear to the teaching of the subject Classic Gravitation , supported on the tripod theory, practice and historical and philosophical aspects, is viable and effective. One hopes that this research may contribute in the formation of a opinion, among the teachers, concerning how to approach the subject of Classic Gravitation, and may offer suggestions in order those who want to apply that approach may develop classroom practices aiming to improve the teaching of that subject, which has a singular importance in the formation of High School students

Interação estrela planeta: sobre o magnetismo de planetas gigantes gasosos

In this thesis we analyze the effects that the presence of a near gas giant planet can cause in its host star. It has been argued that the star planet interaction can cause changes in the coronal and chromospheric stellar activity. With this in mind, we analyze a sample of 53 extrasolar planets orbiting F, G and K main sequence stars, among them three super-Earths. In this analysis, we look for evidence of changes in the chromospheric activity due to the proximity of the giant planet. We show that, so far, there is not enough evidence to support such a hypothesis. Making use of the same sample and also taking in account available data for the Solar System, we revisit the so-called magnetic Bode s law. This law proposes the existence of a direct relationship between magnetism and rotation. By using estimations for the stellar and planetary magnetic momentM and the angular momentumL, we construct a Blackett s diagram (logL 􀀀logM). In this diagram is evident that the magnetic Bode s law is valid for both the Solar System and the new planetary systems

Um estudo sobre o momentum angular total de estrelas com planetas

Since Michel Mayor and his student Didier Queloz s pioneer announcement, in 1995, of the existence of a planet orbiting the star 51 Peg, up to present date, 695 extrasolar planets orbiting stars of spectral type F, G, K and M have been discovered. A study on the behavior of the total angular momentum of the planetary systems known up to present date becomes relevant when we know that about 98% of the angular momentum of the solar system is associated with the planets, although they represent only 0.15 percent of the mass of the whole system. In this dissertation we study the behavior of stellar angular momentum, orbital angular momentum and total angular momentum in a sample of 282 stars harboring planets, including 40 multiple systems. We observed that planetary systems containing more than one known planet have both higher orbital angular momentum and total angular momentum compared to those who have only one planet. This analysis shows that multiplanet systems tend to have higher momenta, suggesting that the planets in such systems that contribute to the greater portion momenta have been found. Thus, planetary systems with lower values for the momenta represent the best candidates to the discovery of new planets

FROZEN ORBITS AROUND EUROPA

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical evolution of Saturn's F ring dust particles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gravitational Capture of Asteroids by Gas Drag

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Irregular satellites of Jupiter: capture configurations of binary-asteroids

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Emmenthal distribution of highly inclined asteroids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Silagem de grãos úmidos de milho em substituição ao milho seco da ração de frangos de corte criados em dois sistemas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Enzima e simbiótico para frangos criados nos sistemas convencional e alternativo

O objetivo deste trabalho foi estudar os efeitos da inclusão de enzima e simbiótico nas rações de frangos de corte criados nos sistemas convencional e alternativo sobre o desempenho, rendimento de carcaça, cortes e gordura abdominal e também avaliar economicamente o uso destes aditivos em ambos os sistemas de criação. Foram utilizados 720 pintos machos Cobb, com um dia de idade, distribuídos em um delineamento em blocos casualizados no esquema fatorial 2x3, com dois sistemas de criação: convencional (com promotor de crescimento) e alternativo (sem promotor de crescimento) e três aditivos: sem outro aditivo (SA), com simbiótico (SI) e com enzima + simbiótico (SIE), com 4 repetições de 30 aves cada. Aos 42 dias de idade, o fator de produção (FP) foi menor (P<0,05) para aves SA (324), quando comparadas às tratadas com SI (334) e SIE (337). Aves criadas no sistema convencional apresentaram maior (P<0,05) FP (338), quando comparadas às do sistema de criação alternativo (325). No sistema alternativo, a conversão alimentar foi melhor (P<0,05) para aves SI (1,77), quando comparadas às SIE (1,82) e SA (1,85). O uso de SI e SIE favorece o desempenho dos frangos aos 42 dias de idade e não influencia o rendimento de carcaça, cortes e gordura abdominal, tanto no sistema convencional como no alternativo, sendo que estes aditivos aumentam os custos de produção em ambos os sistemas. O sistema alternativo de criação proporciona maior retorno econômico, apesar do menor fator de produção.

Gravitational deflection of massive particles in classical and semiclassical general relativity

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is Phi(C)[GRAPHICS]where v(0) is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is Phisc[GRAPHICS]This result shows that the propagation of the =2E spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of similar to2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

On the dynamics of some resonances of Phobos in the future

A probable capture of Phobos into an interesting resonance was presented in our previous work. With a simple model, considering Mars in a Keplerian and circular orbit, it was shown that once captured in the resonance, the inclination of the satellite reaches very high values. Here, the integrations are extended to much longer times and escape situations are analyzed. These escapes are due to the interaction of new additional resonances, which appear as the inclination starts to increase reaching some specific values. Compared to classical capture in mean motion resonances, we see some interesting differences in this problem. We also include the effect of Mars' eccentricity in the process of the capture. The role played by this eccentricity becomes important, particularly when Phobos encounters a double resonance at a approximate to 2.619R(M). Planetary perturbations acting on Mars and variation of its equator are also included. In general, some possible scenarios of the future of Phobos are presented.

Effect of Jupiter's mass growth on satellite capture

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter's mass. We considered the particle's initial conditions to be prograde, at pericenter, in the region 100R(4) <= a <= 400R(4) and 0 <= e <= 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85R(Hill) (Hills' radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45R(Hill) from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.