Stellar Magnitude and Celestial Sphere

Stellar Magnitude and Celestial Sphere - Stellar Magnitude...

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Unformatted text preview: Stellar Magnitude The Magnitude Scale Lower right corner of equatorial chart: Magnitude Scale: A description of the relative brightness of the stars. The Magnitude Scale First introduced by Hipparchus (160 - 127 B.C.): • Brightest stars: ~1st magnitude • Faintest stars (unaided eye): 6th magnitude More quantitative: • Symbol, mv. • 1st mag. stars appear 100 times brighter than 6th mag. stars (by definition of the scale). • 1 mag. difference gives a factor of 2.512 in apparent brightness (higher magnitude number ⇒ fainter object!) The Magnitude Scale The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint objects): Sirius (brightest star in the night sky): mv = -1.42 Full moon: mv = -12.5 Sun: mv = -26.5 The Magnitude Scale Table 2-1, Page 17. (Horizons) The Magnitude Scale (Example) mv Star A = 4, mv Star B = 2 Difference = 4 – 2 = 2 From Table 2-1: Difference of 2 ⇒ ratio of 6.3 We receive 6.3 times more light energy from Star B than from Star A. The Magnitude Scale (Example) mv Star C = –1, mv Star D = 3 Difference = 3 – (–1) = 4 From Table 2-1: Difference of 4 ⇒ ratio of 40 We receive 40 times more light energy from Star C than from Star D. The Magnitude Scale (Example) ^Extreme mv Sun = –26, mv Hubble = +29 Difference = +29 –(–26) = 55 = 5 x 11 i.e. difference of 5, 11 times Difference of 5 ⇒ ratio of 100 (by definition) i.e. ratio of 100, 11 times Ratio = 10011 = 1022 = 10,000,000,000,000,000,000,000 (ten sextillion) The Magnitude Scale (Example) ^Tutorial Tutorial I-13 “Apparent Magnitude” Star A, m = 4.4: Star B, m = 1.7. Difference in magnitude is ∆m = 4.4 – 1.7 = 2.7 From the Lecture-Tutorial table: ∆m = 2.0 => 6.31 ∆m = 0.7 => 1.91 Ib/Id = 6.31 x 1.91 = 12.1 (12.0521) The Magnitude Scale Do tutorial I-13 “Apparent Magnitude” LecTut.pdf page 13. Here are some example answers for the table: Star A Star B Brighter? |∆m| IA/IB 0 +5 Star A 5 100 ... ... ... ... ... +2 +2.5 Star A 0.5 1.58 ... ... ... ... ... The Celestial Sphere A transparent sphere, big enough that the Earth is insignificant. North Celestial Pole: Directly above Earth’s North Pole. South Celestial Pole: Directly above Earth’s South Pole. Shared axis of rotation – once per day, east to west. Celestial Equator: Directly above Earth’s Equator, 90° from the poles. Ecliptic: Apparent path of the Sun against the background stars. The Celestial Sphere Celestial Equator: Directly above Earth’s Equator, 90° from the poles. Created by the equatorial plane passing through the center of the Earth, perpendicular to the poles. Ecliptic: Apparent path of the Sun against the background stars. Created by the ecliptic plane – the plane of the Earth’s orbit around the Sun. These two planes are inclined by 23.5° – the tilt of the Earth. The Celestial Sphere Special points along the ecliptic – the solstices and the equinoxes – the beginning of the seasons (North America). Winter Solstice (Dec 21) Summer Solstice (Jun 21) Autumnal Equinox (Sep 21) Vernal Equinox (Mar 21) Reversed for the southern hemisphere. The Celestial Sphere Do tutorial I-14 “Celestial Sphere” LecTut.pdf pages 14, 15. The Celestial Sphere (Viewing) The Celestial Sphere Zenith = Point on the celestial sphere directly overhead Nadir = Point on the c.s. directly underneath (not visible!) The Celestial Sphere Local Meridian = A line from due north, through your zenith, to due south. Antimeridian = A line from due north, through your nadir, to due south. Notice the intersections of the celestial equator with the horizon and with the local meridian. The Celestial Sphere Azimuth = Measured along the horizon. Horizon Coordinate System Altitude = Measured from the horizon to the object. Altitude: -90° to +90° Horizon = 0° Zenith = 90° Azimuth: 0° to 360° North = 0° East = 90° South = 180° West = 270° Alcumentar: A circle of constant altitude. Main disadvantage: Motion of the earth changes coordinate values. The Celestial Sphere Do tutorial I-15, “LecTut.pdf” pages 16, 17. The Celestial Sphere Do tutorial I-16, Prather Book (black book) pages 19, 20. The Celestial Sphere Rule: The altitude of the north celestial pole (NCP) is equal to the observer’s latitude. The latitude of Grand Rapids is, λ = 43° In Grand Rapids, the horizon coordinates of the NCP are: azimuth = 0° altitude = 43° At southern latitudes, the NCP’s altitude becomes negative. The Celestial Sphere Rule: The transit altitude of the celestial equator (CE) is equal to 90° minus the observer’s latitude. The latitude of Grand Rapids is, λ = 43° In Grand Rapids, the horizon coordinates of the CE transit are: azimuth = 180° altitude = 90°-43°=47° The Celestial Sphere (Viewing) The Celestial Sphere Rule: The altitude of the north celestial pole (NCP) is equal to the observer’s latitude. The latitude of Grand Rapids is, λ = 43° In Grand Rapids, the horizon coordinates of the NCP are: azimuth = 0° altitude = 43° At southern latitudes, the NCP’s altitude becomes negative. The Celestial Sphere Rule: The transit altitude of the celestial equator (CE) is equal to 90° minus the observer’s latitude. The latitude of Grand Rapids is, λ = 43° In Grand Rapids, the horizon coordinates of the CE transit are: azimuth = 180° altitude = 90°-43°=47° The Celestial Sphere When standing on the North Pole, the north celestial pole (Polaris) is at your zenith and the celestial equator matches the horizon. The Celestial Sphere Do tutorial I-17, “LecTut.pdf” pages 19, 20. The Celestial Sphere When standing on the Earth’s equator, the north celestial pole is on the northern horizon, the south celestial pole is on the southern horizon and the celestial equator passes through the zenith. The Celestial Sphere Do tutorial I-18, “LecTut.pdf” pages 21, 22. The Celestial Sphere When standing at latitude 30° north, the north celestial pole (Polaris) is 30° above the northern horizon and the celestial equator crosses the local meridian at 60° off the southern horizon. The Celestial Sphere Do tutorial I-19, “LecTut.pdf” pages 23, 24. The Celestial Sphere When standing at latitude 30° south, the north celestial pole is below the horizon, the celestial equator crosses the local meridian at 60° above the northern horizon and the south celestial pole is 30° above the southern horizon. The Celestial Sphere Do tutorial I-20, “LecTut.pdf” pages 23, 24. Bug fixes: Part I ⇒ Tutorial 17 Part II ⇒ Tutorial 18 Part III ⇒ Tutorial 19 The Celestial Sphere Sky Motion Apparent Daily (Diurnal) Motion of The Celestial Sphere The celestial sphere appears to rotate around us. This is an apparent motion because it is the Earth that is rotating, not the sphere. At this point, this fact is irrelevant. All that matters is the relative motion between the Earth and the Sphere. Apparent Daily (Diurnal) Motion of The Celestial Sphere Circumpolar stars (constellations) never go below the horizon. Apparent Daily (Diurnal) Motion of The Celestial Sphere In the east, all objects rise at an angle equal to the culmination of the celestial sphere. In Grand Rapids, this is 47°. Apparent Daily (Diurnal) Motion of The Celestial Sphere Celestial Equator In the south, all objects rise in the southeast and set in the southwest. All daily (diurnal) sky motion is parallel to the celestial equator. There are some objects that never come above the horizon in Grand Rapids. The Celestial Sphere Drawings of sky motion. Northern hemisphere looking south. Southern hemisphere looking north. The Celestial Sphere Drawings of sky motion. Northern hemisphere looking north. The Celestial Sphere Drawings of sky motion. Southern hemisphere looking south. The Celestial Sphere Drawings of sky motion. Northern hemisphere looking east. Southern hemisphere looking west. The Celestial Sphere Drawings of sky motion. Northern hemisphere looking west. Southern hemisphere looking east. The Celestial Sphere Do tutorial I-21, “Position” Prather Book (black book) pages 1, 2. The Celestial Sphere Do tutorial I-22, “Motion” Prather Book (black book) pages 3 – 6. Precession At left, gravity is pulling on a slanted top. ⇒ Wobbling around the vertical. The Moon’s (and Sun’s) gravity is doing the same to Earth. The resulting “wobbling” of Earth’s axis of rotation around the vertical w.r.t. the Ecliptic takes about 26,000 years and is called precession. Precession As a result of precession, the celestial north pole follows a circular pattern on the sky, once every 26,000 years. It will be closest to Polaris ~ A.D. 2100. There is nothing all that special about Polaris (neither particularly bright nor nearby, but variable.) ~12,000 years from now, it will be close to Vega in the constellation Lyra. ...
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This note was uploaded on 01/31/2010 for the course AS 103 taught by Professor Millar during the Fall '08 term at Grand Rapids Community College.

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