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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. -
Spring Fever Strikes
The MARCH 2002 DENVER OBSERVER Newsletter of the Denver Astronomical Society One Mile Nearer the Stars How Many in One Night?? Gearing up for the Messier Marathon? Those folks who are new to astronomy may not yet be able to relate to the sheer joy of braving the early-spring temperatures (brrrrr) for a full night (and morning—I’m talking dusk to dawn, here) of observing some of the most beautiful objects in the heavens. Why now? Because for only a few weeks during the year is it possible to see all of the Messier objects in one night. Astronomers will dig in their heels and tripods, get out the star charts (See Page 7), and knock off one object after the next. Some people actually catalog 70 of the available 110 targets and submit their achievements to the Astronomical League for the coveted Messier Certificate. Others just like to look at the beautiful celestial wonders like the one in the photo to the left. Either way, get out to the The Pleaides (M45) DSS on the weekend of the 15th and enjoy Image © Joe Gafford, 2002 the views!—PK Spring Fever Strikes President’s Corner .......... 2 MARCH SKIES 2002 f you’ve been reading your astronomy magazines, you know that by month’s Schedule of Events ......... 2 Iend, four naked-eye planets will grace the night skies. Jupiter is the main show-stopper but Saturn, Mars, and finally Venus will sparkle for all, moon or no moon. Remember that a Officers ......................... 2 little high-cloud haze can be good for telescopic planet observations. -
02 Southern Cross
Asterism Southern Cross The Southern Cross is located in the constellation Crux, the smallest of the 88 constellations. It is one of the most distinctive. With the four stars Mimosa BeCrux, Ga Crux, A Crux and Delta Crucis, forming the arms of the cross. The Southern Cross was also used as a remarkably accurate timepiece by all the people of the southern hemisphere, referred to as the ‘Southern Celestial Clock’ by the portuguese naturalist Cristoval D’Acosta. It is perpendicular as it passes the meridian, and the exact time can thus be calculated visually from its angle. The german explorer Baron Alexander von Humboldt, sailing across the southern oceans in 1799, wrote: “It is a timepiece, which advances very regularly nearly 4 minutes a day, and no other group of stars affords to the naked eye an observation of time so easily made”. Asterism - An asterism is a distinctive pattern of stars or a distinctive group of stars in the sky. Constellation - A grouping of stars that make an imaginary picture in the sky. There are 88 constellations. The stars and objects nearby The Main-Themes in asterism Southern Cross Southern Cross Ga Crux A Crux Mimosa, Be Crux Delta Crucis The Motives in asterism Southern Cross Crucis A Bayer / Flamsteed indication AM Arp+Madore - A Catalogue of Southern peculiar Galaxies and Associations [B10] Boss, 1910 - Preliminary General Catalogue of 6188 Stars C Cluster CCDM Catalogue des composantes d’étoiles doubles et multiples CD Cordoba Durchmusterung Declination Cel Celescope Catalog of ultraviolet Magnitudes CPC -
MESSIER 13 RA(2000) : 16H 41M 42S DEC(2000): +36° 27'
MESSIER 13 RA(2000) : 16h 41m 42s DEC(2000): +36° 27’ 41” BASIC INFORMATION OBJECT TYPE: Globular Cluster CONSTELLATION: Hercules BEST VIEW: Late July DISCOVERY: Edmond Halley, 1714 DISTANCE: 25,100 ly DIAMETER: 145 ly APPARENT MAGNITUDE: +5.8 APPARENT DIMENSIONS: 20’ Starry Night FOV: 1.00 Lyra FOV: 60.00 Libra MESSIER 6 (Butterfly Cluster) RA(2000) : 17Ophiuchus h 40m 20s DEC(2000): -32° 15’ 12” M6 Sagitta Serpens Cauda Vulpecula Scutum Scorpius Aquila M6 FOV: 5.00 Telrad Delphinus Norma Sagittarius Corona Australis Ara Equuleus M6 Triangulum Australe BASIC INFORMATION OBJECT TYPE: Open Cluster Telescopium CONSTELLATION: Scorpius Capricornus BEST VIEW: August DISCOVERY: Giovanni Batista Hodierna, c. 1654 DISTANCE: 1600 ly MicroscopiumDIAMETER: 12 – 25 ly Pavo APPARENT MAGNITUDE: +4.2 APPARENT DIMENSIONS: 25’ – 54’ AGE: 50 – 100 million years Telrad Indus MESSIER 7 (Ptolemy’s Cluster) RA(2000) : 17h 53m 51s DEC(2000): -34° 47’ 36” BASIC INFORMATION OBJECT TYPE: Open Cluster CONSTELLATION: Scorpius BEST VIEW: August DISCOVERY: Claudius Ptolemy, 130 A.D. DISTANCE: 900 – 1000 ly DIAMETER: 20 – 25 ly APPARENT MAGNITUDE: +3.3 APPARENT DIMENSIONS: 80’ AGE: ~220 million years FOV:Starry 1.00Night FOV: 60.00 Hercules Libra MESSIER 8 (THE LAGOON NEBULA) RA(2000) : 18h 03m 37s DEC(2000): -24° 23’ 12” Lyra M8 Ophiuchus Serpens Cauda Cygnus Scorpius Sagitta M8 FOV: 5.00 Scutum Telrad Vulpecula Aquila Ara Corona Australis Sagittarius Delphinus M8 BASIC INFORMATION Telescopium OBJECT TYPE: Star Forming Region CONSTELLATION: Sagittarius Equuleus BEST -
Winter Constellations
Winter Constellations *Orion *Canis Major *Monoceros *Canis Minor *Gemini *Auriga *Taurus *Eradinus *Lepus *Monoceros *Cancer *Lynx *Ursa Major *Ursa Minor *Draco *Camelopardalis *Cassiopeia *Cepheus *Andromeda *Perseus *Lacerta *Pegasus *Triangulum *Aries *Pisces *Cetus *Leo (rising) *Hydra (rising) *Canes Venatici (rising) Orion--Myth: Orion, the great hunter. In one myth, Orion boasted he would kill all the wild animals on the earth. But, the earth goddess Gaia, who was the protector of all animals, produced a gigantic scorpion, whose body was so heavily encased that Orion was unable to pierce through the armour, and was himself stung to death. His companion Artemis was greatly saddened and arranged for Orion to be immortalised among the stars. Scorpius, the scorpion, was placed on the opposite side of the sky so that Orion would never be hurt by it again. To this day, Orion is never seen in the sky at the same time as Scorpius. DSO’s ● ***M42 “Orion Nebula” (Neb) with Trapezium A stellar nursery where new stars are being born, perhaps a thousand stars. These are immense clouds of interstellar gas and dust collapse inward to form stars, mainly of ionized hydrogen which gives off the red glow so dominant, and also ionized greenish oxygen gas. The youngest stars may be less than 300,000 years old, even as young as 10,000 years old (compared to the Sun, 4.6 billion years old). 1300 ly. 1 ● *M43--(Neb) “De Marin’s Nebula” The star-forming “comma-shaped” region connected to the Orion Nebula. ● *M78--(Neb) Hard to see. A star-forming region connected to the Orion Nebula. -
August 13 2016 7:00Pm at the Herrett Center for Arts & Science College of Southern Idaho
Snake River Skies The Newsletter of the Magic Valley Astronomical Society www.mvastro.org Membership Meeting President’s Message Saturday, August 13th 2016 7:00pm at the Herrett Center for Arts & Science College of Southern Idaho. Public Star Party Follows at the Colleagues, Centennial Observatory Club Officers It's that time of year: The City of Rocks Star Party. Set for Friday, Aug. 5th, and Saturday, Aug. 6th, the event is the gem of the MVAS year. As we've done every Robert Mayer, President year, we will hold solar viewing at the Smoky Mountain Campground, followed by a [email protected] potluck there at the campground. Again, MVAS will provide the main course and 208-312-1203 beverages. Paul McClain, Vice President After the potluck, the party moves over to the corral by the bunkhouse over at [email protected] Castle Rocks, with deep sky viewing beginning sometime after 9 p.m. This is a chance to dig into some of the darkest skies in the west. Gary Leavitt, Secretary [email protected] Some members have already reserved campsites, but for those who are thinking of 208-731-7476 dropping by at the last minute, we have room for you at the bunkhouse, and would love to have to come by. Jim Tubbs, Treasurer / ALCOR [email protected] The following Saturday will be the regular MVAS meeting. Please check E-mail or 208-404-2999 Facebook for updates on our guest speaker that day. David Olsen, Newsletter Editor Until then, clear views, [email protected] Robert Mayer Rick Widmer, Webmaster [email protected] Magic Valley Astronomical Society is a member of the Astronomical League M-51 imaged by Rick Widmer & Ken Thomason Herrett Telescope Shotwell Camera https://herrett.csi.edu/astronomy/observatory/City_of_Rocks_Star_Party_2016.asp Calendars for August Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 New Moon City Rocks City Rocks Lunation 1158 Castle Rocks Castle Rocks Star Party Star Party Almo, ID Almo, ID 7 8 9 10 11 12 13 MVAS General Mtg. -
PUBLIC OBSERVING NIGHTS the William D. Mcdowell Observatory
THE WilliamPUBLIC D. OBSERVING mcDowell NIGHTS Observatory FREE PUBLIC OBSERVING NIGHTS WINTER Schedule 2019 December 2018 (7PM-10PM) 5th Mars, Uranus, Neptune, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Oribion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884) 12th Mars, Uranus, Neptune, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Oribion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884) 19th Moon, Mars, Uranus, Neptune, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Oribion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884) 26th Moon, Mars, Uranus, Neptune, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Oribion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884)? January 2019 (7PM-10PM) 2nd Moon, Mars, Uranus, Neptune, Sirius, Almach (double star), Pleiades (M45), Orion Nebula (M42), Open Cluster (M35) 9th Mars, Uranus, Neptune, Sirius, Almach (double star), Pleiades (M45), Orion Nebula (M42), Open Cluster (M35) 16 Mars, Uranus, Neptune, Sirius, Almach (double star), Pleiades (M45), Orion Nebula (M42), Open Cluster (M35) 23rd, Moon, Mars, Uranus, Neptune, Sirius, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Orion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884) 30th Moon, Mars, Uranus, Neptune, Sirius, Almach (double star), Pleiades (M45), Andromeda Galaxy (M31), Orion Nebula (M42), Beehive Cluster (M44), Double Cluster (NGC 869 & 884) February 2019 (7PM-10PM) 6th -
Binocular Challenge Here
AHSP Binocular Observing Award Compiled by Phil Harrington www.philharrington.net • To qualify for the BOA pin, you must see 15 of the following 20 binocular targets. Check off each as you spot them. Seen # Object Const. Type* RA Dec Mag Size Nickname 1. M13 Her GC 16 41.7 +36 28 5.9 16' Great Hercules Globular 2. M57 Lyr PN 18 53.6 +33 02 9.7 86"x62" Ring Nebula 3. Collinder 399 Vul AS 19 25.4 +20 11 3.6 60' Coathanger/Brocchi’s Cluster 3.1 4. Albireo Cyg Dbl 19 30.7 +27 57 35” Color Contrasting Double 5.1 5. M27 Vul PN 19 59.6 +22 43 8.1 8’x6’ Dumbbell Nebula 6. NGC 6992 Cyg SNR 20 56.4 +31 43 - 60'x8 Veil Nebula (east) 7. NGC 7000 Cyg BN 20 58.8 +44 20 - 120'x100' North America Nebula 8. M15 Peg GC 21 30.0 +12 10 7.5 12’ Great Pegasus Cluster 9. M39 Cyg OC 21 32.2 +48 26 4.6 32' 10. Barnard 168 Cyg DN 21 53.2 +47 12 - 100'x10' West of Cocoon Nebula 11. IC 5146 Cyg BN/OC 21 53.5 +47 16 - 12'x12' Cocoon Nebula 12. M110 And Gx 00 40.4 +41 41 10 17’x10’ 13. M32 And Gx 00 42.8 +40 52 10 8’x6’ 14. M31 And Gx 00 42.8 +41 16 4.5 178’ Andromeda Galaxy 15. NGC 457 Cas OC 01 19.1 +58 20 6.4 13’ Owl Cluster/ET Cluster 16. -
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). -
Evolution of Star Clusters in Time-Variable Tidal Fields
Evolution of Star Clusters in Time-Variable Tidal Fields A Thesis Submitted to the Faculty of Drexel University by Ernest N. Mamikonyan in partial fulfillment of the requirement for the degree of Doctor of Philosophy December 12, 2013 Contents 1 Introduction 1 1.1 TypesofStarClusters............................ 2 1.1.1 GlobularClusters .......................... 3 1.1.2 OpenClusters............................ 4 1.2 Mass Function: From Young to Globular . 5 2 Arbitrary Tidal Acceleration 8 2.1 ApproximatingTidalEffects. 9 2.1.1 Tidal Acceleration Tensor . 10 2.2 Stellar Dynamics with KIRA ........................ 11 2.2.1 CircularOrbitinPoint-MassPotential . 14 2.3 GalaxyMergerSimulations . 16 2.3.1 TidalHistories............................ 19 2.4 N-BodySimulations ............................ 24 2.4.1 N-BodyUnits ............................ 26 2.4.2 Scaling ................................ 26 3 Mass Loss Model 30 i 3.1 Accelerated Two-Body Relaxation . 30 3.2 FluctuationsintheJacobiRadius. 34 3.3 Results .................................... 36 3.4 Discussion.................................. 37 3.4.1 Limitations ............................. 40 4 Globular Cluster Mass Functions 44 4.1 MassFunctionEvolution . 47 4.2 Results .................................... 48 4.2.1 SinkParticles ............................ 48 4.2.2 DiskParticles ............................ 50 4.2.3 HaloParticles ............................ 55 5 Conclusions and Future Work 57 Appendix A Implementation of Tidal Fields in KIRA 63 Appendix B Computing Tidal Acceleration from GADGET Output 66 ii List of Figures 1.1 Infrared image of the globular cluster Omega Centauri. It is the most massive cluster in the Galaxy and thought to be a remnant of a dwarf galaxy absorbed by the Milky Way. (NASA/JPL-Caltech/ NOAO/AURA/NSF)............................. 3 1.2 The Pleiades open cluster in the infrared. It is one of the most well- known and spectacular objects in the Galaxy. -
Star Clusters
Star Clusters Culpeper Astronomy Club (CAC) Meeting May 21, 2018 Overview • Introductions • Main Topic: Star Clusters - Open and Globular • Constellations: Bootes, Canes Venatici, Coma Berenices • Observing Session - TBD Observing Session – 29 April 18 • Kicked off at about 6:30 p.m • Ended at about 1:30 a.m • Set up several telescopes • Three refractor’s (RAS -7”, f/12) • 11” CPC 1100 SCT (Dennis) • 12” Meade SCT • Targets included: • Venus • Moon • Several double stars • Several deep sky objects • Jupiter • Checked out Saturn and Mars at after arriving home – 2:30 a.m. Loaner Telescopes Jupiter near Opposition • Taken on 13 May 2018 by Jerry Sykes (Opposition 8 May) • Taken with a 120mm refractor, 3x barlow and ASI224mc video camera • First time using his ASI224mc camera • Took several videos through breaks in the clouds • Shot 21,700 frames in a little over two minutes. • Used 29% of 21,700 frames • Captured using Sharpcap • Stacked in AS!3 • Processed in Registax6 Stellar Evolution - The Birth • Stars are born within the clouds of dust and gas scattered throughout most galaxies (Orion Nebula) • Swirling cloud gives rise to knots with sufficient mass that the gas and dust can begin to collapse under its own gravitational attraction • As cloud collapses, material at the center heats up and begins gathering dust and gas (Protostar) • Spinning clouds may break up into two or three blobs resulting in paired or groups of multiple stars • Not all of this material ends up as part of a star — the remaining dust can become planets, asteroids, -
The Brightest Stars Seite 1 Von 9
The Brightest Stars Seite 1 von 9 The Brightest Stars This is a list of the 300 brightest stars made using data from the Hipparcos catalogue. The stellar distances are only fairly accurate for stars well within 1000 light years. 1 2 3 4 5 6 7 8 9 10 11 12 13 No. Star Names Equatorial Galactic Spectral Vis Abs Prllx Err Dist Coordinates Coordinates Type Mag Mag ly RA Dec l° b° 1. Alpha Canis Majoris Sirius 06 45 -16.7 227.2 -8.9 A1V -1.44 1.45 379.21 1.58 9 2. Alpha Carinae Canopus 06 24 -52.7 261.2 -25.3 F0Ib -0.62 -5.53 10.43 0.53 310 3. Alpha Centauri Rigil Kentaurus 14 40 -60.8 315.8 -0.7 G2V+K1V -0.27 4.08 742.12 1.40 4 4. Alpha Boötis Arcturus 14 16 +19.2 15.2 +69.0 K2III -0.05 -0.31 88.85 0.74 37 5. Alpha Lyrae Vega 18 37 +38.8 67.5 +19.2 A0V 0.03 0.58 128.93 0.55 25 6. Alpha Aurigae Capella 05 17 +46.0 162.6 +4.6 G5III+G0III 0.08 -0.48 77.29 0.89 42 7. Beta Orionis Rigel 05 15 -8.2 209.3 -25.1 B8Ia 0.18 -6.69 4.22 0.81 770 8. Alpha Canis Minoris Procyon 07 39 +5.2 213.7 +13.0 F5IV-V 0.40 2.68 285.93 0.88 11 9. Alpha Eridani Achernar 01 38 -57.2 290.7 -58.8 B3V 0.45 -2.77 22.68 0.57 144 10.