Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
AGA5802 Astrofísica Observacional Astronomical coordinates & planning observations II Bibliography: Any book (or chapter) on coordinates. Some basic astrometry in slides from Prof. Roberto Boczko + myself (Elementos de Astronomia): http://www.astro.iag.usp.br/~jorge/aga205_2011/ Prof. Jorge Meléndez 1 Spherical triangle A Is the region of the sphere limited by the intersection of 3 planes passing by the center of the sphere c b O C A, B, C = vertices a B a,b,c = sides Spherical triangle A c r b r O B r a C a , b , c : sides of the spherical triangle = measurements of the central angles Sin & cosine formula in a spherical triangle A Important relations for Spherical Trigonometry c B b a Co-seno cos a = cos b . cos c + sen b . sen c . cos A C Seno sen a sen b sen c ---- = ---- = ---sen A sen B sen C Seno & Co-seno sen a . cos B = cos b . sen c - sen b . cos c . cos A Sin & Cosine of (900- x) sin x Sine 90-x sin (900-x) = cos x x cos x CoSine cos (900-x) = sin x Angle between 2 cities PN cos a = cos b . cos c + sen b . sen c . cos A Greenwich 90o- j' q Co-seno cos q = cos (90- j) . cos (90- j' ) + sen (90- j) . sen (90- j' ) . cos ( l' - l ) j l j' N L l' cos q = sen j . sen j' + cos j . cos j' . cos ( l' - l ) Se |l`- l| >1800 q` = 3600 - q PS Angle between 2 stars PN cos a = cos b . cos c + sen b . sen c . cos A Co-seno Dados: 90o- d' a ,d a' , d' q a' g Se |a`- a| >1800 q` = 3600 - q a d' N d L cos q = cos (90- d) . cos (90- d' ) + sen (90- d) . sen (90- d' ) . cos ( a' - a ) cos q = sen d . sen d' + cos d . cos d' . cos ( a' - a ) PS What is the condition for the rise or set of an astronomical object? Z Passagem meridiana PS E h=0 or z = 90o Rise N S W Set Y Z Passagem meridiana PS E N AN Rise AO AN Azimuth at rise & set in the North & South hemispheres S Z Passagem meridiana PN W Set Rise Y AN: Azimuth at Rise AN N AO AN AO : Azimuth at Set ASet = 360o - ARise E Set W S Z Passagem meridiana SP Rise E HN N HO S Simmetry of the rise & set in relation to the local meridian W Meridian crossing Z NP Set E Rise HN Y HO N HOcaso = - HNascer Set W S Azimuth & Hour of rise & set of an astronomical object Z 360-A PN Spherical triangle at set H Z j PN H 90o - d 90o 90o N d W Y Azimuth at rise and set cos a = cos b . cos c + sen b . sen c . cos A Z H a = 90 – d b = z = 90 (zenital distance) c = 90 – j A = 360 – A PN Q cos (90-d) = cos z. cos(90-j) + sen (90-j) . sen z . cos (360-A) cos (90-d) = sen (90-j) . cos (360-A) sen d = cos j . cos A cos A = sen d / cos j 0 A 180o No Nascer: A = A No Ocaso: A = 360o - A Hour angle at rise and set Z H PN cos a = cos b . cos c + sen b . sen c . cos A Q cos z = cos (90-j) . cos (90-d) + sen (90-j) . sen (90-d) . cos H 0 = sen j . sen d + cos j . cos d . cos H cos H = - sen j . sen d / cos j . cos d cos H = - tan j . tan d 0 H 1800 At set: Ho = H At rise: Hn = - H Zenital distance of an extended object at rise & set z = 900 + s Zenith s(SOL) ~ s(LUA) ~ 16’ z Horizon Observer s Terra s: angular semi-diameter Dispersion, refraction and twilights Twinkling: brightness fluctuations Seeing: blurring + twinkling Star Zenith: short path less twinkle Horizon: long path more twinkle Atmosphere Binary system (without correction) With adaptive optics Adaptive optics Center of the Milky Way Light dispersion in the atmosphere Dispersion D n: refraction index N: density of molecules Rayleigh formula for dispersion In Earth’s atmosphere D = k / l4 0 Color of radiation l Refraction Light Medium 1 Medium 2 Change in direction due to the change from one medium to other Refraction index n c : light speed in vacuum (n = 1) c vacuum n nc/v v Medium n 1 Snell Descartes Snell-Descartes Law Medium 2 n2 = c/v2 Normal Medium 1 n1 = c/v1 Normal n1 . sen i = n2 . sen r i i r n2 > n1 : change in angle due to refraction =i-r r n2 < n1 Atmospheric refraction Normal to the surface at incidence point One spherical layer Incident ray Atmosphere Earth Real Tangent to the surface at incident point Refraction in layers Real position Atmosphere Earth Atmospheric refraction Apparent position Zenith The object seems always higher than at its real position Real position Atmosphere Horizon O Earth Color dependence of the observed position ‘Upper atmosphere limit’ Earth atmosphere Ground Position of the star on the CCD depends on color Angle of refractional change (arc minutes) Angle of refractional change as a function of star’s altitude D 36´ 900 80 70 60 50 40 30 20 10 0 Zen. Dist. 30 h Horizonte 24 18 hD 12 6 0 Zenith Horizon 0 Ground 10 20 30 40 50 60 70 80 900 Altitude (h) Zenith Rise and set including refraction Zenith Apparent Real Horizon Observer 34’ Earth r: angular change due to refraction z = 900 + r Twilight solar light before sunrise or after sunset Dispersion & Twilight Twilight is the result of the dispersion of solar light at high layers of the atmosphere Zenith Light dispersion in the high atmosphere Horizon < 18o Earth Ilumination during twilights Illumination on horizontal plate [lux] 1000 Civil twilight 100 Nautical twilight Day 10 Night Astronomical twilight Full moon at zenith 1 0,1 Contribution of stellar light is more than solar light 0,01 Horizon 0,001 0,0001 Plate -080 -000 50´ -060 -120 -180 Altitude of Sun’s center Z Zenital distance z at start and end of each twilight Z Sun Horizon West 90o 50’ Civil 96o Nautical East 6o 6o 6o 6o 6o 6o 102o Evening 96o Nautical 102o Astronomical Astronomical 108o 90o 50’ Civil Night 108o Morning Sunrise, Meridian Crossing and Sunset A.R. & Dec de Mintaka? Declination How to obtain the coordinates? How bright is my target? Magnitude? R.A. 37 Planning observations Coordinates : Simbad http://simbad.u-strasbg.fr/simbad/sim-fid Simbad Epoch 2000 magnitudes R.A. (α) dec (δ) OPD format -0.081 -0.024 OPD: proper motion in “/ano: Divide SIMBAD’s value by 1000 Observing tools https://www.eso.org/sci/observing/tools/calendar.html 41 https://www.eso.org/sci/observing/to ols/calendar/skycalc.html 42 43 Astronomical Sky Calendar http://www.briancasey.org/artifacts/astro/skycalendar.cgi 44 45 Object visibility http://catserver.ing.iac.es/staralt/ Airmass Altitude Airmass = sec z = 1/cos z z : zenital distance Limits of 1.6m at OPD zenital distance <= 60 (could be larger, but be careful) 48 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Useful hours Altitude above horizon Altitude of Middle-Dark-Time Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Airmass Finding charts: important for weak objects or crowded fields http://catserver.ing.iac.es/dss1/ What about moving objects? http://ssd.jpl.nasa.gov/horizons.cgi 51 Asteroid Ceres La Silla 1 – 10 august 2014 one per hour 52 53 Sidereal time Trip to OPD http://www.lna.br/distempo/17i/intro.html Trip to OPD • • • • • Do you have a laptop ? Linux ? IRAF ? Warm clothes ? Sunglasses ? Flashlight (light from cell phone is OK) ? Good tennis or trekking shoes, as you have to walk many stairs at night, and perhaps you may want to walk around the observatory 56