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The Celestial Sphere the Celestial Sphere

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The Celestial Sphere the Celestial Sphere The Celestial Sphere The Celestial Sphere Engraving displayed in Flammarion's `L'Atmosphere: Meteorologie Populaire (Paris, 1888)' The Celestial Sphere: Great Circle A great circle on a sphere is any circle that shares the same center point as the sphere itself. Any two points on the surface of a sphere, if not exactly opposite one another, define a unique great circle going through them. A line drawn along a great circle is actually the shortest distance between the two points (see next slides). A small circle is any circle drawn on the sphere that does not share the same center as the sphere. The Celestial Sphere: Great Circle • A great circle divides the surface of a Pole of Great Circle sphere in two equal parts. • A great circle is the largest circle that fits on the sphere. • If you keep going straight across a sphere then you go along a great circle. • A great circle has the same center C as the sphere that it lies on. Primary Great Circle Great Circle • The shortest route between two points, measured across the sphere, is part of a great circle. The Celestial Sphere: Great Circle How many great circles do you need to define your coordinate? Pole of Great Circle Every great circle has two poles. A single great circle doesn’t define a coordinate system uniquely (cf: rotation). ® We need a secondary great circle to define a coordinate system. Primary Great The secondary great circle is a Circle Great Circle great circle that goes through the poles of a primary great circle The Celestial Sphere: North and South Poles The celestial equator is an extension of the Earth’s equator to the surface of the celestial sphere The north/south celestial pole is an extension of the Earth’s north/south pole. The Celestial Sphere: Earth’s Latitude & Longitude Two perpendicular great circles: the equator & Greenwich longitude circle Toronto: 43.7°N (latitude) & 79.4°W (longitude) Note: 1 hour is 15 degrees in longitude and Toronto is 5 (NRAO is located hours behind London at Charlottesville.) The Celestial Sphere: Horizon, Meridian, & Celestial equator A horizon (plane) is a plane tangent to the Earth’s surface at the observer’s feet. The Celestial Sphere: Horizon, Meridian, & Celestial equator The North Celestial Pole (near Polaris) is at altitude of your location’s latitute. The Equatorial Coordinate: (R.A. & decl.) RA: extension of the longitude to the celestial sphere DEC: extension of the latitude to the celestial sphere (vernal equinox) Note: RA & DEC: fixed on the celestial sphere. (Latitude, Longitude) vs. (R.A., decl.) (Latitude, Longitude) (R.A., decl.) • Earth equator for LAT; • Celestial equator for decl.; • A vertical circle to the • A vertical circle to the equator containing a equator containing a reference location for LON; reference location for decl.; • The reference location is • The reference location is Greenwich observatory, a vernal equinox, a fixed fixed location on earth. location on the celestial sphere. The Equatorial Coordinate: (R.A. & decl.) (R.A., decl.) and Vernal Equinox Vernal equinox is the ascending node of the Sun on the ecliptic plane when it meets with the celestial equator. Ecliptic is the circle the Sun sweeps around the Celestial Sphere over a year. It is tilted by 23.5 degrees from the equator due the Earth’s tilt. (R.A., decl.) and Vernal Equinox Equinoxes are where the Sun meets the celestial equator (Vernal equinox for spring; Autumn equinox for autumn) Motion of the Sun through the year on Vernal Equinox: the ecliptic plane. ascending node of the ecliptic on the equator (R.A., decl.) and Vernal Equinox The Sun Right Ascension Declination Vernal Equinox 0h 0° Summer Solstice +6h +23.5° Autumn Equinox +12h 0° Winter Solstice +18h -23.5° The Celestial Sphere at the Poles The Celestial Sphere at the Equator The Celestial Sphere at the Latitude LAT At the northern hemisphere Star at less than LAT from the NCP: “Never sets.” Star at less than LAT from the SCP: “Never rises.” The Celestial Sphere at the Latitude LAT Observer’s horizon (At the northern hemisphere) The Celestial Sphere at the Latitude LAT ● Objects on the Celestial Equator: Due East ® Due West 12 hours above horizon ● Objects of the North Circumpolar Region: North of the Due East/West more than 12 hours above horizon ● Objects of the South ● North Circumpolar Region: Circumpolar Region: (90o – LAT) < DEC < 90o South of the Due ● South Circumpolar Region: East/West less than 12 – 90o < DEC < – (90o – LAT) hours above horizon Al/tude'and'Azimuth'' • It&is&also&useful&to&define&a& coordinate&system&that&are&local&to& the&observer& – These&coordinates&are&dependent&on& the&observer’s&laCtude&and&longitude& • Al/tude&is&the&shortest&angular& distance&from&the&object&to&the& horizon&(0&to&90°)& • Azimuth&is&defined&in&angles& measured&eastward&from&North& around&the&horizon&(0&to&360°)& • Hour'angle'specifies&the&number&of& hours&from&the&meridian&a&source&is,& HA'='LST'X'RA' therefore&defines&visibility' Sidereal'Time' • The&local'sidereal'/me'(LST)&is&the&current&right& ascension&that&passes&directly&over&your&locaCon&at&the& meridian& • Since&the&Earth&rotates&about&its&axis&as&well&as&around& the&Sun,&a&source&crosses&your&meridian&4&minutes& earlier&each&day&(or&change&of&1&degree)& • This&means&an&Earth&day&(24&hours)&is&defined&by&the& locaCon&of&the&Sun& 3& Posi/on'1'to'2:&Globe&rotates&360°&& 2& &(Sidereal&Day:&23&hours,&56&mins)& Posi/on'1'to'3:&Globe&repoints&to&Sun&& &(Solar&day:&24&hours)& 1& Not&to&scale!& Determining'“transit”'/me' • At&sunset&tonight&the&local&sidereal&Cme&is&20h& 25m,&then&how&many&hours&and&minutes&is&it& unCl&the&Andromeda&galaxy&(RA=&00h&42m&and& Dec=+41°&16’)&transits?& • Is&Andromeda&observable&from&the&MP& telescope&at&sunset&tonight?& A:&The&hour&angle&of&Andromeda&at&sunset&will&be&4&hours& and&17&mins&(HA&=&LST&–&RA).&Andromeda&will&be&above&the& horizon&and&observable&but&with&a&large&airmass.& Proper'Mo/on' • Objects&in&our&solar&system,&galaxy,&and&extragalacCc& sources&have&their&own&velociCes& – Closer&the&source&and&higher&the&velociCes&the&greater& moCon&on&the&projecCon&of&the&sky,&which&is&known&as& “proper&moCon”& • Typical&proper&moCon&of&nearby&stars&is&0.1”&per&year& • Typical&proper&moCon&of&main&belt&asteroids&is&~0.5G1’&per&hour& • NEO’s&can&move&have&as&fast&as&2.5°&per&day& Arcturus)radial)velocity) Δt& Radial&velocity& μ& Star’s&velocity& Sun& Proper&moCon& Barnard’s)star,)10.3”)per)year) Lab #3: Astrometry • Reduce 2D CCD data of a sky image • Measure positions of stars • Match these stars with a catalog of stars with known sky positions • Compute the plate constants (i.e. translation between pixel position and RA/DEC) • Measure the sky coordinate of an asteroid over many nights .
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