Proposta de materiais didáticos para o ensino de estrelas a partir das concepções prévias de estudantes e professores

Este trabalho tem por objetivo apresentar um levantamento sobre os conhecimentos prévios dos estudantes e professores da escola básica a respeito dos conteúdos ensinados sobre as estrelas, tomando como base a literatura. A partir destas informações, este trabalho propõe a construção de três materiais didáticos com o propósito de facilitar a abordagem deste conteúdo pelo professor em sala de aula, assim como oportunizar um conhecimento científico atualizado, de forma alternativa e lúdica aos estudantes, a partir da aprendizagem significativa. Como materiais didáticos, temos como propostas a construção das constelações em 3D, o diagrama HR para localização e classificação das estrelas e um jogo de tabuleiro RPG estelar. Como texto de apoio aos professores, este trabalho traz uma breve revisão conceitual sobre as principais características das estrelas, assim como sugestões de temas interdisciplinares

Results on stellar occultations by (307261) 2002 MS4

Transneptunian Objects (TNOs) are the remnants of our planetary system and can retain information about the early stages of the Solar System formation. Stellar occultation is a groundbased method used to study these distant bodies which have been presenting exciting results mainly about their physical properties. The big TNO called 2002 MS4 was discovered by Trujillo, C. A., & Brown, M. E., in 2002 using observations made at the Palomar Observatory (EUA). It is classified as a hot classical TNO, with orbital parameters a = 42 AU, e = 0.139, and i = 17.7º. Using thermal measurements with PACS (Herschel) and MIPS (Spitzer Space Telescope) instruments, Vilenius et al. 2012 obtained a radius of 467 +/- 23.5 km and an albedo of 0.051.Predictions of stellar occultations by this body in 2019 were obtained using the Gaia DR2 catalogue and NIMA ephemeris (Desmars et al. 2015) and made available in the Lucky Star web page (https://lesia.obspm.fr/lucky-star/). Four events were observed in South America and Canada. The first stellar occultation was detected on 09 July 2019, resulting in two positives and four negatives chords, including a close one which proven to be helpful to constrain the body’s size. This detection also allowed us to obtain a precise astrometric position that was used to update its ephemeris and improve the predictions of the following events. Two of them were detected on 26 July 2019, separated by eight hours. The first event was observed from South America and resulted in three positive detections, while the second, observed from Canada, resulted in a single chord. Another double chord event was observed on 19 August 2019 also from Canada.Facultad de Ciencias Astronómicas y Geofísica

Constraints on the structure and seasonal variations of Triton's atmosphere from the 5 October 2017 stellar occultation and previous observations

Context. A stellar occultation by Neptune's main satellite, Triton, was observed on 5 October 2017 from Europe, North Africa, and the USA. We derived 90 light curves from this event, 42 of which yielded a central flash detection. Aims. We aimed at constraining Triton's atmospheric structure and the seasonal variations of its atmospheric pressure since the Voyager 2 epoch (1989). We also derived the shape of the lower atmosphere from central flash analysis. Methods. We used Abel inversions and direct ray-tracing code to provide the density, pressure, and temperature profiles in the altitude range similar to 8 km to similar to 190 km, corresponding to pressure levels from 9 mu bar down to a few nanobars. Results. (i) A pressure of 1.18 +/- 0.03 mu bar is found at a reference radius of 1400 km (47 km altitude). (ii) A new analysis of the Voyager 2 radio science occultation shows that this is consistent with an extrapolation of pressure down to the surface pressure obtained in 1989. (iii) A survey of occultations obtained between 1989 and 2017 suggests that an enhancement in surface pressure as reported during the 1990s might be real, but debatable, due to very few high S/N light curves and data accessible for reanalysis. The volatile transport model analysed supports a moderate increase in surface pressure, with a maximum value around 2005-2015 no higher than 23 mu bar. The pressures observed in 1995-1997 and 2017 appear mutually inconsistent with the volatile transport model presented here. (iv) The central flash structure does not show evidence of an atmospheric distortion. We find an upper limit of 0.0011 for the apparent oblateness of the atmosphere near the 8 km altitude.J.M.O. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) and the European Social Fund (ESF) through the PhD grant SFRH/BD/131700/2017. The work leading to these results has received funding from the European Research Council under the European Community's H2020 2014-2021 ERC grant Agreement nffi 669416 "Lucky Star". We thank S. Para who supported some travels to observe the 5 October 2017 occultation. T.B. was supported for this research by an appointment to the National Aeronautics and Space Administration (NASA) Post-Doctoral Program at the Ames Research Center administered by Universities Space Research Association (USRA) through a contract with NASA. We acknowledge useful exchanges with Mark Gurwell on the ALMA CO observations. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. J.L.O., P.S.-S., N.M. and R.D. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709), they also acknowledge the financial support by the Spanish grant AYA-2017-84637-R and the Proyecto de Excelencia de la Junta de Andalucia J.A. 2012-FQM1776. The research leading to these results has received funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement no. 687378, as part of the project "Small Bodies Near and Far" (SBNAF). P.S.-S. acknowledges financial support by the Spanish grant AYA-RTI2018-098657-J-I00 "LEO-SBNAF". The work was partially based on observations made at the Laboratorio Nacional de Astrofisica (LNA), Itajuba-MG, Brazil. The following authors acknowledge the respective CNPq grants: F.B.-R. 309578/2017-5; R.V.-M. 304544/2017-5, 401903/2016-8; J.I.B.C. 308150/2016-3 and 305917/2019-6; M.A. 427700/20183, 310683/2017-3, 473002/2013-2. This study was financed in part by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior -Brasil (CAPES) -Finance Code 001 and the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). G.B.R. acknowledges CAPES-FAPERJ/PAPDRJ grant E26/203.173/2016 and CAPES-PRINT/UNESP grant 88887.571156/2020-00, M.A. FAPERJ grant E26/111.488/2013 and A.R.G.Jr. FAPESP grant 2018/11239-8. B.E.M. thanks CNPq 150612/2020-6 and CAPES/Cofecub-394/2016-05 grants. Part of the photometric data used in this study were collected in the frame of the photometric observations with the robotic and remotely controlled telescope at the University of Athens Observatory (UOAO; Gazeas 2016). The 2.3 m Aristarchos telescope is operated on Helmos Observatory by the Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing of the National Observatory of Athens. Observations with the 2.3 m Aristarchos telescope were carried out under OPTICON programme. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 730890. This material reflects only the authors views and the Commission is not liable for any use that may be made of the information contained therein. The 1. 2m Kryoneri telescope is operated by the Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing of the National Observatory of Athens. The Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA) is managed by the Fondazione Clement Fillietroz-ONLUS, which is supported by the Regional Government of the Aosta Valley, the Town Municipality of Nus and the "Unite des Communes valdotaines Mont-Emilius". The 0.81 m Main Telescope at the OAVdA was upgraded thanks to a Shoemaker NEO Grant 2013 from The Planetary Society. D.C. and J.M.C. acknowledge funds from a 2017 'Research and Education' grant from Fondazione CRT-Cassa di Risparmio di Torino. P.M. acknowledges support from the Portuguese Fundacao para a Ciencia e a Tecnologia ref. PTDC/FISAST/29942/2017 through national funds and by FEDER through COMPETE 2020 (ref. POCI010145 FEDER007672). F.J. acknowledges Jean Luc Plouvier for his help. S.J.F. and C.A. would like to thank the UCL student support observers: Helen Dai, Elise Darragh-Ford, Ross Dobson, Max Hipperson, Edward Kerr-Dineen, Isaac Langley, Emese Meder, Roman Gerasimov, Javier Sanjuan, and Manasvee Saraf. We are grateful to the CAHA, OSN and La Hita Observatory staffs. This research is partially based on observations collected at Centro Astronomico HispanoAleman (CAHA) at Calar Alto, operated jointly by Junta de Andalucia and Consejo Superior de Investigaciones Cientificas (IAA-CSIC). This research was also partially based on observation carried out at the Observatorio de Sierra Nevada (OSN) operated by Instituto de Astrofisica de Andalucia (CSIC). This article is also based on observations made with the Liverpool Telescope operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council. Partially based on observations made with the Tx40 and Excalibur telescopes at the Observatorio Astrofisico de Javalambre in Teruel, a Spanish Infraestructura Cientifico-Tecnica Singular (ICTS) owned, managed and operated by the Centro de Estudios de Fisica del Cosmos de Aragon (CEFCA). Tx40 and Excalibur are funded with the Fondos de Inversiones de Teruel (FITE). A.R.R. would like to thank Gustavo Roman for the mechanical adaptation of the camera to the telescope to allow for the observation to be recorded. R.H., J.F.R., S.P.H. and A.S.L. have been supported by the Spanish projects AYA2015-65041P and PID2019-109467GB-100 (MINECO/FEDER, UE) and Grupos Gobierno Vasco IT1366-19. Our great thanks to Omar Hila and their collaborators in Atlas Golf Marrakech Observatory for providing access to the T60cm telescope. TRAPPIST is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant PDR T.0120.21. TRAPPIST-North is a project funded by the University of Liege, and performed in collaboration with Cadi Ayyad University of Marrakesh. E.J. is a FNRS Senior Research Associate

Transneptunian and centaur objects positions from stellar occultations on the Gaia era

Most of the small bodies of the outer Solar System, with the exception of Pluto, were discovered after 1992. It is believed that due to their distance to the Sun, these objects can have information about the Solar System’s formation and dynamical evolution. Therefore, a detailed study of these bodies can contribute significantly to the Solar System’s evolution theory. However, the direct observation of light reflected from the surface of the body allow us determine astrometric position with large error bars. A diameter of 1000 km, at distance of 45 UA from Earth results on angular size of 30 milliseconds of arc on sky plane. So, these bodies appears in the images as dim points of light. Although it’s possible to determine their diameters from termal images, the uncertainties are around 20% of body’s size. An efficient observational alternative has been used on the study of this class of objects, the stellar occultation. The technique consists on the photometric observation of a star, while an object transits in front of it, on the tangent plane of sky. The study of temporal variation of the star brightness allows the accurate characterization the object. With uncertainties of the order of a few kilometers, the information obtained from a stellar occultation allows us to build the object instantaneous profile. The object’s diameter, shape and relative center can be calculated from this profile. We can also detect or discover structures, such as rings, around the main body. This work analyzes 25 stellar occultations by Centaurs and Transneptunian objects, detected between 2009 and 2017. The data set involves events analyzed for the first time here, and events that had results published in the literature. Using the tangent plane on the celestial sphere, and with an observer in Earth’s center, the object’s center was determined, relative to the occulted star. Star positions were taken from the Gaia catalogue, which have uncertainties of the order of a kilometer at the object’s distance, therefore, the calculated center error bars are very precise. This central position is compared with ephemeris in the closest approach instant. Usually, the measured and calculated positions are different allowing us to derive an offset. This offset is used to correct the body ephemeris. Therefore, we obtain the object’s celestial coordinates at the moment of closest approach. These astrometric positions are used to propagate the object’s ephemeris in time. Although careful astrometric measurements are used to calculate the ephemeris, stellar occultation provides high precision positions, allowing improvements on the calculated ephemerid. Better ephemeris allows better predictions for future events, and so the correct places over Earth where they can be observed, contributing to the characterization of this class of small Solar System objects.Grande parte dos pequenos corpos do Sistema Solar exterior, a exceção de Plutão, foram descobertos após 1992. Acredita-se que, pela distância ao Sol, possam conservar informações sobre a formação e evolução dinâmica do Sistema Solar. Portanto, o estudo detalhado destes distantes objetos pode contribuir significativamente com o aprimoramento dos modelos evolutivos de nosso sistema planetário. No entanto, a observação direta da luz refletida pela superfície destes objetos permite uma astrometria com grandes barras de erros associadas. Um diâmetro na ordem de 1000 km, a uma distância de 45 UA da Terra resulta em um tamanho angular de cerca de 30 milissegundos de arco no plano do céu. Assim estes corpos aparecem nas imagens com tamanho reduzido e pouco brilho. Embora seja possível determinar o diâmetro a partir de dados térmicos da superfície, as incertezas associadas superam 20% do seu tamanho. Uma eficiente alternativa observacional vem sendo empregada no estudo desta classe de objetos, a observação de ocultações estelares. A técnica consiste na aquisição de dados fotométricos de uma estrela enquanto um objeto transita em frente a ela, no plano do céu. O estudo da variação temporal do brilho estelar observado permite caracterizar o corpo ocultador com precisão. Com incertezas na ordem de poucos quilômetros, as informações obtidas de ocultações estelares permitem construir o perfil instantâneo do objeto. O diâmetro, forma e centro relativo do objeto podem ser calculados a partir deste perfil. Estruturas presentes em torno do corpo principal, como anéis, também podem ser descobertas, graças a precisão da técnica. Neste trabalho são cuidadosamente analisados 25 eventos de ocultações estelares por Centauros e Transnetunianos, detectadas entre 2009 e 2017. O conjunto de dados compreende ocultações analisadas aqui pela primeira vez, e resultados já publicados na literatura. Utilizando o plano tangente a esfera celeste, com o observador no centro da Terra, foram calculados os centros dos objeto em relação as estrelas ocultadas. As posições estelares fornecidas pelo catálogo Gaia possuem erros de alguns quilômetros a distância do objeto, portanto, a incerteza na determinação desta posição relativa e pequena. Esta posição e então comparada à coordenada fornecida pela efeméride para o instante de maior aproximação, que geralmente apresenta um deslocamento em relação a posição prevista. Dessa maneira, obtém-se um offset do corpo a ser corrigido no referido instante. Obtém-se, portanto, as coordenadas celeste do objeto ocultador no instante de maior aproximação. Estas posições astrométricas são utilizadas para propagar no tempo as efemérides dos objetos envolvidos. Embora as efemérides usem dados de cuidadosas observações astrométricas, dados oriundos de ocultações estelares trazem grande precisão, aprimorando efemérides calculadas. E com boas efemérides ´ e possível prever novas ocultações estelares, com boa precisão temporal e determinação acurada da região do planeta em que poderá ser observada, auxiliando assim a caracterização destes pequenos corpos do Sistema Solar

Recent results of stellar occultations by (60558) Echeclus

<p><span dir="ltr" role="presentation">Centaurs are small objects of the Solar System with orbits between Jupiter and Neptune (5.2 AU</span> <span dir="ltr" role="presentation"><</span> <span dir="ltr" role="presentation">q</span> <span dir="ltr" role="presentation"><</span> <span dir="ltr" role="presentation">30 AU) (Jewitt </span><span dir="ltr" role="presentation">2009), being an important population due to the presence of cometary activity (about 13% of Centaurs shows cometary </span><span dir="ltr" role="presentation">activity) (Bauer et al. 2008).</span> <span dir="ltr" role="presentation">However, after the discovery of ring systems orbiting Chariklo (Braga-Ribas et al. 2013) </span><span dir="ltr" role="presentation">and Haumea (Ortiz et al. 2017) and the proposition of a ring around Chiron (Ruprecht et al. 2015; Ortiz et al. 2015), we </span><span dir="ltr" role="presentation">wonder if these structures are common around the small bodies or if specific conditions are necessary for their formation </span><span dir="ltr" role="presentation">and maintenance (Sicardy et al. 2020). </span><span dir="ltr" role="presentation">Discovered in March 2000, the active Centaur 174P/Echeclus (60558) has an equivalent diameter estimated in </span><span dir="ltr" role="presentation">59</span> <span dir="ltr" role="presentation">±</span> <span dir="ltr" role="presentation">4 km (Bauer et al. 2013) and 64</span><span dir="ltr" role="presentation">.</span><span dir="ltr" role="presentation">6</span> <span dir="ltr" role="presentation">±</span> <span dir="ltr" role="presentation">1</span><span dir="ltr" role="presentation">.</span><span dir="ltr" role="presentation">6 km (Duffard et al. 2014), and showed cometary activity on different occasions: </span><span dir="ltr" role="presentation">December 2005 (Choi & Weissman 2006), May 2011 (Jaeger et al. 2011), August 2016 (Miles 2016), and December 2017 </span><span dir="ltr" role="presentation">Kareta et al. (2019). To determine the main body’s size and shape and investigate whether material ejections during the </span><span dir="ltr" role="presentation">outbursts could have fed possible rings or a shell of diffuse material around Echeclus, we predicted and observed stellar </span><span dir="ltr" role="presentation">occultations by this Centaur in 2019, 2020, and 2021. <br /></span></p> <p><span dir="ltr" role="presentation">Stellar occultations by Echeclus were predicted using the Gaia DR2 catalog and NIMA ephemeris (Desmars et al. 2015). </span><span dir="ltr" role="presentation">The prediction map of the 2019 October 29 event put the shadow’s path over South America, but all the telescopes that </span><span dir="ltr" role="presentation">participated in this campaign missed the occultation path, providing five negative chords. The 2020 January 22 event is </span><span dir="ltr" role="presentation">also predicted to pass over South America, resulting in two positive and four negative chords.</span> Finally, we predicted t<span dir="ltr" role="presentation">he last event</span><span dir="ltr" role="presentation"> over Japan in 2021 January 19, resulting in one positive and ten negative chords.</span></p> <p><span dir="ltr" role="presentation">With the positive detections of 2020, we fit an ellipse with an equivalent diameter of 59 ± 4 km to the edges of the chords. The resulting ellipse has a semi-major axis a’ = 36 km and oblateness ε′ = 0.325. From the rotational light curves (Rousselot et al., 2021), we note that 2020 stellar occultation occurs near the maximum absolute brightness. Thus, the surface seen during the occultation event was close to the maximum possible. So we were able to compare the ellipse fitted to the chords to the 3D model and pole orientations proposed by (Rousselot et al. 2021). By propagating the Echeclus rotation, we compare the 3D model to the 2021 stellar occultation, where we rule out some of the proposed pole solutions due to the close negative chord. We also fitted the 3D model to the chords, obtaining the triaxial dimensions of Echeclus as a × b × c = 36.5 × 28.0 × 24.5 km, resulting in an area-equivalent diameter of D<sub>equiv</sub> = 61.8 ± 0.6 km, which is in agreement with the area-equivalent diameters presented in the literature.<br /></span></p> <p><span dir="ltr" role="presentation">We used all three event data sets to look for sudden drops in flux (evidence of confined material) or shallow and extensive drops (evidence of coma). The best light curves in terms of spatial resolution and SNR were: La Silla/NTT in 2019, which covered about 7,000 km in the sky plane; SOAR in 2020, covering 14,000 km in the sky plane and Okazaki/Japan in 2021, which covered about 9,000 km in the sky plane. With these light curves, we determined lower limits for detection for apparent opacity at the 3σ level as 0.145, 0.189, and 0.258, respectively. In addition, limits for the equivalent width were also determined for these three data sets, with values of 0.19 km for La Silla/NTT, 0.36 km for SOAR, and 0.18 km for Okazaki.</span></p> <p><span dir="ltr" role="presentation"><br role="presentation" /><strong>Acknowledgments</strong>: C.L.P. is thankful for the support of the CAPES scholarship. The following authors acknowledge the respective CNPq grants: F.B-R 309578/2017-5; J.I.B.C. 308150/2016-3 and 305917/2019-6; F.L.R. CAPES scholarship. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). ARGJr acknowledges FAPESP grant 2018/11239-8.</span></p> <p><span dir="ltr" role="presentation"><strong>References</strong></span></p> <p><span dir="ltr" role="presentation">Bauer, J. M., Choi, Y.-J., Weissman, P. R., et al. 2008, PASP, 120, 393<br />Bauer, J. M., Grav, T., Blauvelt, E., et al. 2013, The Astrophysical Journal, 773, 22<br />Braga-Ribas, F., Sicardy, B., Ortiz, J. L., et al. 2013, ApJ, 773, 26<br />Choi, Y.-J. & Weissman, P. 2006, in AAS/Division for Planetary Sciences Meeting Abstracts, Vol. 38, 37.05<br />Desmars, J., Camargo, J. I. B., Braga-Ribas, F., et al. 2015, A&A, 584, A96<br />Duffard, R., Pinilla-Alonso, N., Santos-Sanz, P., et al. 2014, A&A, 564, A92<br />Jaeger, M., Prosperi, E., Vollmann, W., et al. 2011, IAU Circ., 9213, 2<br />Jewitt, D. 2009, AJ, 137, 4296<br />Kareta, T., Sharkey, B., Noonan, J., et al. 2019, AJ, 158, 255<br />Miles, R. 2016, CBET, 4313<br />Ortiz, J. L., Duffard, R., Pinilla-Alonso, N., et al. 2015, A&A, 576, A18<br />Ortiz, J. L., Santos-Sanz, P., Sicardy, B., et al. 2017, Nature, 550, 219<br />Rousselot, P., Kryszczyńska, A., Bartczak, P., et al. 2021, MNRAS, 507, 3444<br />Ruprecht, J. D., Bosh, A. S., Person, M. J., et al. 2015, Icarus, 252, 271<br />Sicardy, B., Renner, S., Leiva, R., et al. 2020, The Trans-Neptunian Solar System, 249</span></p&gt

Results on stellar occultations by (307261) 2002 MS4

Transneptunian Objects (TNOs) are the remnants of our planetary system and can retain information about the early stages of the Solar System formation. Stellar occultation is a ground-based method used to study these distant bodies which have been presenting exciting results mainly about their physical properties. The big TNO called 2002 MS4 was discovered by Trujillo, C. A., & Brown, M. E., in 2002 using observations made at the Palomar Observatory (EUA). It is classified as a hot classical TNO, with orbital parameters a = 42 AU, e = 0.139, and i = 17.7°. Using thermal measurements with PACS (Herschel) and MIPS (Spitzer Space Telescope) instruments, Vilenius et al. 2012 obtained a radius of 467 +/- 23.5 km and an albedo of 0.051.Predictions of stellar occultations by this body in 2019 were obtained using the Gaia DR2 catalogue and NIMA ephemeris (Desmars et al. 2015) and made available in the Lucky Star web page (https://lesia.obspm.fr/lucky-star/). Four events were observed in South America and Canada. The first stellar occultation was detected on 09 July 2019, resulting in two positives and four negatives chords, including a close one which proven to be helpful to constrain the body"s size. This detection also allowed us to obtain a precise astrometric position that was used to update its ephemeris and improve the predictions of the following events. Two of them were detected on 26 July 2019, separated by eight hours. The first event was observed from South America and resulted in three positive detections, while the second, observed from Canada, resulted in a single chord. Another double chord event was observed on 19 August 2019 also from Canada.Due to its size, it is expected that 2002 MS4 is in hydrostatic equilibrium. Thirouin, A. 2013 obtained a rotational light curve of 2002 MS4 and determined two possible periods (7.33 h and 10.44 h) with low amplitude variation (0.05 +/- 0.01 mag). Admitting that it has a Maclaurin shape, the projected limb in the sky plane for Earth-based observers should be the same in the 09 July and 26 July events. The multi-chord detection allows determining an interval of parameters for size and shape. Considering that the same figure should have been observed in the 09 July event, we could use the both chords and the negative observations to constrain its physical parameters. With that, we could determine that 2002 MS4 has an equivalent radius of 385 +/- 1 km (Figure 1). Our results indicate that this TNO is about 100 km smaller in diameter than the value obtained by Vilenius et al. 2012, implying an albedo of 0.076 (Hv = 4.0 +/- 0.6) . The astrometric positions derived from these data were also helpful to improve forthcoming stellar occultations, in special the one crossing Europe on 08 August this year. More data from stellar occultations and observations of rotational light curves will help to confirm these results and assumptions.Acknowledgements: F.L.R is thankful for the support of the CAPES scholarship. The following authors acknowledge the respective CNPq grants: F.B-R 309578/2017-5; R.V-M 304544/2017-5, 401903/2016-8; J.I.B.C. 308150/2016-3; M.A 427700/2018-3, 310683/2017-3, 473002/2013-2. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). G.B-R acknowledges CAPES-FAPERJ/PAPDRJ grant E26/203.173/2016, M.A FAPERJ grant E-26/111.488/2013 and A.R.G-Jr FAPESP grant 2018/11239-8. B.E.M thanks the CAPES/Cofecub-394/2016-05 grant. P.S-S. acknowledges financial support by the Spanish grant AYA-RTI2018-098657-J-I00 "LEO-SBNAF" (MCIU/AEI/FEDER, UE). We would like to acknowledge financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofı́sica de Andalucı́a (SEV-2017-0709) and the financial support by the Spanish grant AYA-2017-84637-R. Part of the results were based on observations taken at the 1.6 m telescope on Pico dos Dias Observatory of the National Laboratory of Astrophysics (LNA/Brazil). Part of this work was carried out within the "Lucky Star" umbrella that agglomerates the efforts of the Paris, Granada and Rio teams. It is funded by the European Research Council under the European Community"s H2020 (2014-2020/ERC Grant Agreement No. 669416). This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. ReferencesAssafin, M. et al. PRAIA - Platform for Reduction of Astronomical Images Automatically. In: Tanga, P.; Thuillot, W. (Ed.). Gaia follow-up network for the solar system objects : Gaia FUN-SSO workshop proceedings, held at IMCCE -Paris Observatory, France, November 29 - December 1, 2010 / edited by Paolo Tanga, William Thuillot.- ISBN 2-910015-63-7, p. 85-88. [S.l.: s.n.], 2011. p. 85-88.Desmars, J. et al. Orbit determination of trans-Neptunian objects and Centaurs for the prediction of stellar occultations. Astronomy & Astrophysics, v. 584, p. A96, dez. 2015.Thirouin, A. Study of Trans-Neptunian Objects using photometric techniques and numerical simulations. Dissertation. Editorial de la Universidad de Granada. Spain, 2013.Trujillo, C. A., Brown, M. E., Minor Planet Electronic Circulars - MPEC 2002-W27. Disponível em: \url{https://minorplanetcenter.net//iau/mpec/K02/K02W27.html}.Vilenius, E. "TNOs are cool": a survey of the trans-Neptunian region. VI. Herschel/PACS observations and thermal modelling of 19 classical Kuiper belt objects. Astronomy & Astrophysics. v. 541, A94, 2012