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Mathématiques Et Espace
Atelier disciplinaire AD 5 Mathématiques et Espace Anne-Cécile DHERS, Education Nationale (mathématiques) Peggy THILLET, Education Nationale (mathématiques) Yann BARSAMIAN, Education Nationale (mathématiques) Olivier BONNETON, Sciences - U (mathématiques) Cahier d'activités Activité 1 : L'HORIZON TERRESTRE ET SPATIAL Activité 2 : DENOMBREMENT D'ETOILES DANS LE CIEL ET L'UNIVERS Activité 3 : D'HIPPARCOS A BENFORD Activité 4 : OBSERVATION STATISTIQUE DES CRATERES LUNAIRES Activité 5 : DIAMETRE DES CRATERES D'IMPACT Activité 6 : LOI DE TITIUS-BODE Activité 7 : MODELISER UNE CONSTELLATION EN 3D Crédits photo : NASA / CNES L'HORIZON TERRESTRE ET SPATIAL (3 ème / 2 nde ) __________________________________________________ OBJECTIF : Détermination de la ligne d'horizon à une altitude donnée. COMPETENCES : ● Utilisation du théorème de Pythagore ● Utilisation de Google Earth pour évaluer des distances à vol d'oiseau ● Recherche personnelle de données REALISATION : Il s'agit ici de mettre en application le théorème de Pythagore mais avec une vision terrestre dans un premier temps suite à un questionnement de l'élève puis dans un second temps de réutiliser la même démarche dans le cadre spatial de la visibilité d'un satellite. Fiche élève ____________________________________________________________________________ 1. Victor Hugo a écrit dans Les Châtiments : "Les horizons aux horizons succèdent […] : on avance toujours, on n’arrive jamais ". Face à la mer, vous voyez l'horizon à perte de vue. Mais "est-ce loin, l'horizon ?". D'après toi, jusqu'à quelle distance peux-tu voir si le temps est clair ? Réponse 1 : " Sans instrument, je peux voir jusqu'à .................. km " Réponse 2 : " Avec une paire de jumelles, je peux voir jusqu'à ............... km " 2. Nous allons maintenant calculer à l'aide du théorème de Pythagore la ligne d'horizon pour une hauteur H donnée. -
The Denver Observer December 2017
The Denver DECEMBER 2017 OBSERVER Messier 76, the Little Dumbbell Nebula, one of the deep-sky objects featured in this month’s “Skies.” Image © Joe Gafford. DECEMBER SKIES by Zachary Singer The Solar System of view in your ’scope will include the Moon’s Sky Calendar 3 Full Moon December will be a decent month for eastern section and the star, with plenty of 10 Last-Quarter Moon planetary events; though some planets are room. 17 New Moon slipping from view, others will take their I recommend you observe early—it 26 First-Quarter Moon place. We also have an occultation of Alde- should be a beautiful view, with the star a baran; as seen from Denver, the Moon will bright spark near the Moon’s edge, and over pass in front of the star at approximately the following minutes (they’ll go fast, just like In the Observer 4:06 PM, on the 30th. At that point, with the recent solar eclipse did), you can see the Moon move in its orbit around us, using the sunset still more than half an hour away, the President’s Message . .2 star won’t be visible to the naked eye, but it star for a benchmark. (Before 4:00 PM, look Society Directory. 2 should be in a telescope if you know where for Aldebaran outside the square, but along to look: Imagine a square drawn just large the diagonal from the Moon’s center to that Schedule of Events . 2 enough to touch the edges of the Moon, and lower-left edge.) About Denver Astronomical Society . -
Asteroid Shape and Spin Statistics from Convex Models J
Asteroid shape and spin statistics from convex models J. Torppa, V.-P. Hentunen, P. Pääkkönen, P. Kehusmaa, K. Muinonen To cite this version: J. Torppa, V.-P. Hentunen, P. Pääkkönen, P. Kehusmaa, K. Muinonen. Asteroid shape and spin statistics from convex models. Icarus, Elsevier, 2008, 198 (1), pp.91. 10.1016/j.icarus.2008.07.014. hal-00499092 HAL Id: hal-00499092 https://hal.archives-ouvertes.fr/hal-00499092 Submitted on 9 Jul 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Accepted Manuscript Asteroid shape and spin statistics from convex models J. Torppa, V.-P. Hentunen, P. Pääkkönen, P. Kehusmaa, K. Muinonen PII: S0019-1035(08)00283-2 DOI: 10.1016/j.icarus.2008.07.014 Reference: YICAR 8734 To appear in: Icarus Received date: 18 September 2007 Revised date: 3 July 2008 Accepted date: 7 July 2008 Please cite this article as: J. Torppa, V.-P. Hentunen, P. Pääkkönen, P. Kehusmaa, K. Muinonen, Asteroid shape and spin statistics from convex models, Icarus (2008), doi: 10.1016/j.icarus.2008.07.014 This is a PDF file of an unedited manuscript that has been accepted for publication. -
Binocular Universe: You're My Hero! December 2010
Binocular Universe: You're My Hero! December 2010 Phil Harrington on't you just love a happy ending? I know I do. Picture this. Princess Andromeda, a helpless damsel in distress, chained to a rock as a ferocious D sea monster loomed nearby. Just when all appeared lost, our hero -- Perseus! -- plunges out of the sky, kills the monster, and sweeps up our maiden in his arms. Together, they fly off into the sunset on his winged horse to live happily ever after. Such is the stuff of myths and legends. That story, the legend of Perseus and Andromeda, was recounted in last month's column when we visited some binocular targets within the constellation Cassiopeia. In mythology, Queen Cassiopeia was Andromeda's mother, and the cause for her peril in the first place. Left: Autumn star map from Star Watch by Phil Harrington Above: Finder chart for this month's Binocular Universe. Chart adapted from Touring the Universe through Binoculars Atlas (TUBA), www.philharrington.net/tuba.htm This month, we return to the scene of the rescue, to our hero, Perseus. He stands in our sky to the east of Cassiopeia and Andromeda, should the Queen's bragging get her daughter into hot water again. The constellation's brightest star, Mirfak (Alpha [α] Persei), lies about two-thirds of the way along a line that stretches from Pegasus to the bright star Capella in Auriga. Shining at magnitude +1.8, Mirfak is classified as a class F5 white supergiant. It radiates some 5,000 times the energy of our Sun and has a diameter 62 times larger. -
The Minor Planet Bulletin
THE MINOR PLANET BULLETIN OF THE MINOR PLANETS SECTION OF THE BULLETIN ASSOCIATION OF LUNAR AND PLANETARY OBSERVERS VOLUME 36, NUMBER 3, A.D. 2009 JULY-SEPTEMBER 77. PHOTOMETRIC MEASUREMENTS OF 343 OSTARA Our data can be obtained from http://www.uwec.edu/physics/ AND OTHER ASTEROIDS AT HOBBS OBSERVATORY asteroid/. Lyle Ford, George Stecher, Kayla Lorenzen, and Cole Cook Acknowledgements Department of Physics and Astronomy University of Wisconsin-Eau Claire We thank the Theodore Dunham Fund for Astrophysics, the Eau Claire, WI 54702-4004 National Science Foundation (award number 0519006), the [email protected] University of Wisconsin-Eau Claire Office of Research and Sponsored Programs, and the University of Wisconsin-Eau Claire (Received: 2009 Feb 11) Blugold Fellow and McNair programs for financial support. References We observed 343 Ostara on 2008 October 4 and obtained R and V standard magnitudes. The period was Binzel, R.P. (1987). “A Photoelectric Survey of 130 Asteroids”, found to be significantly greater than the previously Icarus 72, 135-208. reported value of 6.42 hours. Measurements of 2660 Wasserman and (17010) 1999 CQ72 made on 2008 Stecher, G.J., Ford, L.A., and Elbert, J.D. (1999). “Equipping a March 25 are also reported. 0.6 Meter Alt-Azimuth Telescope for Photometry”, IAPPP Comm, 76, 68-74. We made R band and V band photometric measurements of 343 Warner, B.D. (2006). A Practical Guide to Lightcurve Photometry Ostara on 2008 October 4 using the 0.6 m “Air Force” Telescope and Analysis. Springer, New York, NY. located at Hobbs Observatory (MPC code 750) near Fall Creek, Wisconsin. -
Asteroid Family Ages. 2015. Icarus 257, 275-289
Icarus 257 (2015) 275–289 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Asteroid family ages ⇑ Federica Spoto a,c, , Andrea Milani a, Zoran Knezˇevic´ b a Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy b Astronomical Observatory, Volgina 7, 11060 Belgrade 38, Serbia c SpaceDyS srl, Via Mario Giuntini 63, 56023 Navacchio di Cascina, Italy article info abstract Article history: A new family classification, based on a catalog of proper elements with 384,000 numbered asteroids Received 6 December 2014 and on new methods is available. For the 45 dynamical families with >250 members identified in this Revised 27 April 2015 classification, we present an attempt to obtain statistically significant ages: we succeeded in computing Accepted 30 April 2015 ages for 37 collisional families. Available online 14 May 2015 We used a rigorous method, including a least squares fit of the two sides of a V-shape plot in the proper semimajor axis, inverse diameter plane to determine the corresponding slopes, an advanced error model Keywords: for the uncertainties of asteroid diameters, an iterative outlier rejection scheme and quality control. The Asteroids best available Yarkovsky measurement was used to estimate a calibration of the Yarkovsky effect for each Asteroids, dynamics Impact processes family. The results are presented separately for the families originated in fragmentation or cratering events, for the young, compact families and for the truncated, one-sided families. For all the computed ages the corresponding uncertainties are provided, and the results are discussed and compared with the literature. The ages of several families have been estimated for the first time, in other cases the accu- racy has been improved. -
Jet-Induced Star Formation in 3C 285 and Minkowski's Object⋆
A&A 574, A34 (2015) Astronomy DOI: 10.1051/0004-6361/201424932 & c ESO 2015 Astrophysics Jet-induced star formation in 3C 285 and Minkowski’s Object? Q. Salomé, P. Salomé, and F. Combes LERMA, Observatoire de Paris, CNRS UMR 8112, 61 avenue de l’Observatoire, 75014 Paris, France e-mail: [email protected] Received 5 September 2014 / Accepted 6 November 2014 ABSTRACT How efficiently star formation proceeds in galaxies is still an open question. Recent studies suggest that active galactic nucleus (AGN) can regulate the gas accretion and thus slow down star formation (negative feedback). However, evidence of AGN positive feedback has also been observed in a few radio galaxies (e.g. Centaurus A, Minkowski’s Object, 3C 285, and the higher redshift 4C 41.17). Here we present CO observations of 3C 285 and Minkowski’s Object, which are examples of jet-induced star formation. A spot (named 3C 285/09.6 in the present paper) aligned with the 3C 285 radio jet at a projected distance of ∼70 kpc from the galaxy centre shows star formation that is detected in optical emission. Minkowski’s Object is located along the jet of NGC 541 and also shows star formation. Knowing the distribution of molecular gas along the jets is a way to study the physical processes at play in the AGN interaction with the intergalactic medium. We observed CO lines in 3C 285, NGC 541, 3C 285/09.6, and Minkowski’s Object with the IRAM 30 m telescope. In the central galaxies, the spectra present a double-horn profile, typical of a rotation pattern, from which we are able to estimate the molecular gas density profile of the galaxy. -
Composition of the L5 Mars Trojans: Neighbors, Not Siblings
Composition of the L5 Mars Trojans: Neighbors, not Siblings Andrew S. Rivkin a,1, David E. Trilling b, Cristina A. Thomas c,1, Francesca DeMeo c, Timothy B. Spahr d, and Richard P. Binzel c,1 aJohns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd. Laurel, MD 20723 bSteward Observatory, The University of Arizona, Tucson, AZ 85721 cDepartment of Earth, Atmospheric, and Planetary Sciences, M.I.T. Cambridge, MA 02139 dHarvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge MA 02138 arXiv:0709.1925v1 [astro-ph] 12 Sep 2007 Number of pages: 14 Number of tables: 1 Number of figures: 6 Email address: [email protected] (Andrew S. Rivkin). 1 Visiting Astronomer at the Infrared Telescope Facility, which is operated by the University of Hawaii under Cooperative Agreement no. NCC 5-538 with the National Aeronautics and Space Administration, Science Mission Directorate, Planetary As- tronomy Program. Preprint submitted to Icarus 29 May 2018 Proposed Running Head: Characterization of Mars Trojans Please send Editorial Correspondence to: Andrew S. Rivkin Applied Physics Laboratory MP3-E169 Laurel, MD 20723-6099, USA. Email: [email protected] Phone: (778) 443-8211 2 ABSTRACT Mars is the only terrestrial planet known to have Trojan (co-orbiting) aster- oids, with a confirmed population of at least 4 objects. The origin of these objects is not known; while several have orbits that are stable on solar-system timescales, work by Rivkin et al. (2003) showed they have compositions that suggest separate origins from one another. We have obtained infrared (0.8-2.5 micron) spectroscopy of the two largest L5 Mars Trojans, and confirm and extend the results of Rivkin et al. -
A Basic Requirement for Studying the Heavens Is Determining Where In
Abasic requirement for studying the heavens is determining where in the sky things are. To specify sky positions, astronomers have developed several coordinate systems. Each uses a coordinate grid projected on to the celestial sphere, in analogy to the geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle (the fundamental plane of the geographic system is the Earth's equator) . Each coordinate system is named for its choice of fundamental plane. The equatorial coordinate system is probably the most widely used celestial coordinate system. It is also the one most closely related to the geographic coordinate system, because they use the same fun damental plane and the same poles. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, projecting the geographic poles on to the celest ial sphere defines the north and south celestial poles. However, there is an important difference between the equatorial and geographic coordinate systems: the geographic system is fixed to the Earth; it rotates as the Earth does . The equatorial system is fixed to the stars, so it appears to rotate across the sky with the stars, but of course it's really the Earth rotating under the fixed sky. The latitudinal (latitude-like) angle of the equatorial system is called declination (Dec for short) . It measures the angle of an object above or below the celestial equator. The longitud inal angle is called the right ascension (RA for short). -
(704) Interamnia from Its Occultations and Lightcurves
International Journal of Astronomy and Astrophysics, 2014, 4, 91-118 Published Online March 2014 in SciRes. http://www.scirp.org/journal/ijaa http://dx.doi.org/10.4236/ijaa.2014.41010 A 3-D Shape Model of (704) Interamnia from Its Occultations and Lightcurves Isao Satō1*, Marc Buie2, Paul D. Maley3, Hiromi Hamanowa4, Akira Tsuchikawa5, David W. Dunham6 1Astronomical Society of Japan, Yamagata, Japan 2Southwest Research Institute, Boulder, USA 3International Occultation Timing Association, Houston, USA 4Hamanowa Astronomical Observatory, Fukushima, Japan 5Yanagida Astronomical Observatory, Ishikawa, Japan 6International Occultation Timing Association, Greenbelt, USA Email: *[email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Received 9 November 2013; revised 9 December 2013; accepted 17 December 2013 Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract A 3-D shape model of the sixth largest of the main belt asteroids, (704) Interamnia, is presented. The model is reproduced from its two stellar occultation observations and six lightcurves between 1969 and 2011. The first stellar occultation was the occultation of TYC 234500183 on 1996 De- cember 17 observed from 13 sites in the USA. An elliptical cross section of (344.6 ± 9.6 km) × (306.2 ± 9.1 km), for position angle P = 73.4 ± 12.5˚ was fitted. The lightcurve around the occulta- tion shows that the peak-to-peak amplitude was 0.04 mag. and the occultation phase was just be- fore the minimum. -
Virgo the Virgin
Virgo the Virgin Virgo is one of the constellations of the zodiac, the group tion Virgo itself. There is also the connection here with of 12 constellations that lies on the ecliptic plane defined “The Scales of Justice” and the sign Libra which lies next by the planets orbital orientation around the Sun. Virgo is to Virgo in the Zodiac. The study of astronomy had a one of the original 48 constellations charted by Ptolemy. practical “time keeping” aspect in the cultures of ancient It is the largest constellation of the Zodiac and the sec- history and as the stars of Virgo appeared before sunrise ond - largest constellation after Hydra. Virgo is bordered by late in the northern summer, many cultures linked this the constellations of Bootes, Coma Berenices, Leo, Crater, asterism with crops, harvest and fecundity. Corvus, Hydra, Libra and Serpens Caput. The constella- tion of Virgo is highly populated with galaxies and there Virgo is usually depicted with angel - like wings, with an are several galaxy clusters located within its boundaries, ear of wheat in her left hand, marked by the bright star each of which is home to hundreds or even thousands of Spica, which is Latin for “ear of grain”, and a tall blade of galaxies. The accepted abbreviation when enumerating grass, or a palm frond, in her right hand. Spica will be objects within the constellation is Vir, the genitive form is important for us in navigating Virgo in the modern night Virginis and meteor showers that appear to originate from sky. Spica was most likely the star that helped the Greek Virgo are called Virginids. -
The Minor Planet Bulletin 44 (2017) 142
THE MINOR PLANET BULLETIN OF THE MINOR PLANETS SECTION OF THE BULLETIN ASSOCIATION OF LUNAR AND PLANETARY OBSERVERS VOLUME 44, NUMBER 2, A.D. 2017 APRIL-JUNE 87. 319 LEONA AND 341 CALIFORNIA – Lightcurves from all sessions are then composited with no TWO VERY SLOWLY ROTATING ASTEROIDS adjustment of instrumental magnitudes. A search should be made for possible tumbling behavior. This is revealed whenever Frederick Pilcher successive rotational cycles show significant variation, and Organ Mesa Observatory (G50) quantified with simultaneous 2 period software. In addition, it is 4438 Organ Mesa Loop useful to obtain a small number of all-night sessions for each Las Cruces, NM 88011 USA object near opposition to look for possible small amplitude short [email protected] period variations. Lorenzo Franco Observations to obtain the data used in this paper were made at the Balzaretto Observatory (A81) Organ Mesa Observatory with a 0.35-meter Meade LX200 GPS Rome, ITALY Schmidt-Cassegrain (SCT) and SBIG STL-1001E CCD. Exposures were 60 seconds, unguided, with a clear filter. All Petr Pravec measurements were calibrated from CMC15 r’ values to Cousins Astronomical Institute R magnitudes for solar colored field stars. Photometric Academy of Sciences of the Czech Republic measurement is with MPO Canopus software. To reduce the Fricova 1, CZ-25165 number of points on the lightcurves and make them easier to read, Ondrejov, CZECH REPUBLIC data points on all lightcurves constructed with MPO Canopus software have been binned in sets of 3 with a maximum time (Received: 2016 Dec 20) difference of 5 minutes between points in each bin.