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WebAssign troubles. If you cannot log in, you probably enrolled very recently and are not in the roster yet. Just give me your SID.
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WebAssign troubles • If you cannot log in, you probably enrolled very recently and are not in the roster yet. Just give me your SID. • If you don’t find webassign card in your book, you may have bought the book only (ISBN 0-495-01578-4), not a bundle with webassign (ISBN 0-495-26588-8). You can buy an access separately for $25.
Classification of objects on the sky • Description of motions of these objects • Understanding 1 and 2
International Astronomical Union (IAU) http://www.iau.org/IAU/Activities/nomenclature/const.html Names and Standard Abbreviations of Constellations The following list of constellation names and abbreviations is in accordance with the resolutions of the International Astronomical Union (Trans. IAU, 1, 158; 4, 221; 9, 66 and 77). The boundaries of the constellations are listed by E. Delporte, on behalf of the IAU, in, Delimitation scientifique des constellations (tables et cartes), Cambridge University Press, 1930; they lie along the meridians of right ascension and paralleIs of declination for the mean equator and equinox of 1875.0. 88 constellations
SIRIUS: "scorching" in Greek (?) Other Names: Canicula; Dog Star; Aschere. Alpha Canis Majoris HR 2491 HD 48915 Sirius is rising in dawn at the hottest days of the year, “dog days”. It is the time for the summer break (“canicular days”)
Wobbling motion of Sirius A Detecting the presence of an unseen companion, Sirius B by its gravitational influence on the primary star, Sirius A.
Sirius B is very hot: surface temperature 25,000 K Yet, it is 10,000 times fainter than Sirius A It should be very small: R ~ 2 Rearth Its mass M ~ 1 Msun It should be extremely dense! M/R3 ~ 106 g/cm3
Hipparchus of Rhodes Born: 190 BC in Nicaea (now Iznik), Bithynia (now Turkey)Died: 120 BC in probably Rhodes, Greece Catalogue of 850 stars Discovered precession of the Earth’s orbit Determined the distance to the moon Compiled trigonometric tables For thousands of years, discoveries in math and science were driven by astronomical observations!
Claudius Ptolemy Born: about 85 in EgyptDied: about 165 in Alexandria, Egypt Almagest • A treatise in 13 books • Mathematical theory of the motions • of the Sun, moon, and planets • Catalogue of 1022 stars and 48 constellations • Introduced minutes and seconds • Geocentric system Shares with Euclid's "Elements" the glory of being the scientific text longest in use.
Original book title is Syntaxis • Translated to Arabic as Almagest (al majisti) and then to Latin • That is why stars have Arabic names Venice: Petrus Liechtenstein, 1515.
OFFICIAL STAR-NAMING PROCEDURES Bright stars from first to third magnitude have proper names that have been in use for hundreds of years. Most of these names are Arabic. Examples are Betelgeuse, the bright orange star in the constellation Orion, and Dubhe, the second-magnitude star at the edge of the Big Dipper's cup (Ursa Major). A few proper star names are not Arabic. One is Polaris, the second-magnitude star at the end of the handle of the Little Dipper (Ursa Minor). Polaris also carries the popular name, the North Star. A second system for naming bright stars was introduced in 1603 by J. Bayer of Bavaria. In his constellation atlas, Bayer assigned successive letters of the Greek alphabet to the brighter stars of each constellation. Each Bayer designation is the Greek letter with the genitive form of the constellation name. Thus Polaris is Alpha Ursae Minoris. Occasionally, Bayer switched brightness order for serial order in assigning Greek letters. An example of this is Dubhe as Alpha Ursae Majoris, with each star along the Big Dipper from the cup to handle having the next Greek letter. Faint stars are designated in different ways in catalogs prepared and used by astronomers. One is the Bonner Durchmusterung, compiled at Bonn Observatory starting in 1837. A third of a million stars are listed by "BD numbers." The Smithsonian Astrophysical Observatory (SAO) Catalogue, the Yale Star Catalog, and The Henry Draper Catalog published by Harvard College Observatory are all widely used by astronomers. The Supernova of 1987 (Supernova 1987a), one of the major astronomical events of this century, was identified with the star named SK -69 202 in the very specialized catalog, the Deep Objective Prism Survey of the Large Magellanic Cloud, published by the Warner and Swasey Observatory. These procedures and catalogs accepted by the International Astronomical Union are the only means by which stars receive long-lasting names.
Hipparchus: classified stars into 6 classes with faintest stars in the 6th class This was only classification. How can we measure the brightnesses of the stars?
In the 19th century astronomers introduced the magnitude scale roughly following the Hipparchus’s classes and related them to the light intensities Please wake up, it’s becoming serious!
Intensity: light energy that hits 1 square meter per second Lv[J/s] R Iv = Lv/(4R2)
Relationship between magnitudes and intensities Define the magnitude scale so that two stars that differ by 5 magnitudes have an intensity ratio of 100.
Log10(y) y
Apparent visual magnitudes mv of some objects Note that only the differences in mv are defined. The zeroth magnitude had to be picked arbitrarily.
Apparent visual magnitude: The guy to blame The mathematical form of the magnitude scale came from Norman Pogson at Oxford, who in 1854 suggested that the brightness ratios then measured were, to available accuracy, close to a factor of 100 for the difference between first and sixth magnitude. We, and generations of college students, have Pogson to thank for the notion that the ratio of intensities that corresponds to a difference of one magnitude is the fifth root of 100, or 2.512.... Mayer describes how the scale was standardized by E. C. Pickering at the Harvard College Observatory, with the zero-point fixed by setting Polaris at magnitude 2.1. (Mayer, A. 1992, "On the History of the Stellar Magnitude Scale," J. AAVSO, 15, 283.) by Jay M. PasachoffWilliams College — Hopkins ObservatoryThe Astronomy Education Review, Issue 2, Volume 2:162-165, 2003 http://aer.noao.edu/AERArticle.php?issue=4§ion=5&article=1
Pogson's magnitude scale is logarithmic. As Young (1990) and Hearnshaw (1992, 1996) describe, the eye's sensitivity was long thought to be largely logarithmic, based on 19th-century work by Gustav Fechner in 1858 and 1860, but Ernst Zinner in 1926, Knut Lundmark in 1932, and Andrew T. Young in 1984 differed. The psychologist S. S. Stevens concluded in the 1940s (and reviewed in 1961) that the eye's sensitivity is a power law rather than a logarithmic law, going back to John Herschel's suggestion from 1849. Hearnshaw (private communication 2003) writes, "In a paper analysing the Almagest scale and comparing with modern photoelectric magnitudes, I came to the conclusion that the earlier critics of Pogson and Fechner, who claimed the scale was not really logarithmic, were in fact erroneous. You can find this analysis in a paper by D. Khan and me in Southern Stars 36, 169 (1995). The reason for the conclusions of a non-logarithmic scale relate to huge selection effects in the plot of Almagest magnitude vs. modern photoelectric mag, in that Ptolemy included stars really brighter than sixth mag which he listed as being mag 6, but not fainter than sixth mag and listed as brighter. In other words the distribution of errors is severely skewed, because of the eye's limiting magnitude."
The Magnitude Scale: Love It or Hate It by Steve White My final complaint seems negligible by comparison, but it reveals another important feature of the magnitude scale. How bright, exactly, is magnitude zero? I have mentioned that the star Sirius shines at -1.5. There are three other stars bright enough to have negative magnitudes (Canopus at -0.7, Alpha Centauri at -0.3, and Arcturus at -0.1), as well as the Sun (at -26.5!), the Moon (around -12 when full), and five planets (Mercury, Venus, Jupiter, and sometimes Mars and Saturn). Apart from these eleven objects and the occasional bright comet or meteor, everything else in the sky has a positive magnitude. The Sun, Moon, and planets are fairly unique, but is there anything special about these four bright stars? Not at all. Interestingly, the fifth brightest star in the night sky, Vega, has a magnitude of exactly 0.00, and represents the "zero point" of the magnitude scale. Why Vega? Why not Sirius? I haven't been able to find a good answer to that one, and I've been digging. As any field of science progresses, patterns and idiosyncrasies that get started arbitrarily can be adopted by enough people so that they stick, and cannot be changed. There's plenty of this in astronomy, and the magnitude scale is a perfect example. What can we do? Look on the bright side. The magnitude scale is unnecessarily complicated and awkward, but once you learn it, you have a valuable tool that turns all those strange numbers into meaningful information. If you are interested in astronomy, it is worth the effort! - Steve WhiteObserving Guide, Nightly Observing Program Kitt Peak Visitor Center http://www.noao.edu/outreach/nop/nophigh/steve6.html Return to NOAO Home Page
The celestial sphere The entire sky appears to turn around imaginary points in the northern and southern sky once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon.
We can define a useful coordinate system for locating objects on the celestial sphere by projecting onto the sky the latitude-longitude coordinate system that we use on the surface of the earth. The stars rotate around the North and South Celestial Poles. These are the points in the sky directly above the geographic north and south pole, respectively. The Earth's axis of rotation intersects the celestial sphere at the celestial poles. The number of degrees the celestial pole is above the horizon is equal to the latitude of the observer. Fortunately, for those in the northern hemisphere, there is a fairly bright star real close to the North Celestial Pole (Polaris or the North star). Another important reference marker is the celestial equator: an imaginary circle around the sky directly above the Earth's equator. It is always 90 degrees from the poles. All the stars rotate in a path that is parallel to the celestial equator. The celestial equator intercepts the horizon at the points directly east and west anywhere on the Earth.
The arc that goes through the north point on the horizon, zenith, and south point on the horizon is called the meridian. The positions of the zenith and meridian with respect to the stars will change as the celestial sphere rotates and if the observer changes locations on the Earth, but those reference marks do not change with respect to the observer's horizon. Any celestial object crossing the meridian is at its highest altitude (distance from the horizon) during that night (or day). The angle the star paths make with respect to the horizon = 90 degrees - (observer's latitude). During daylight, the meridian separates the morning and afternoon positions of the Sun. In the morning the Sun is ``ante meridiem'' (Latin for ``before meridian'') or east of the meridian, abbreviated ``a.m.''. At local noon the Sun is right on the meridian. At local noon the Sun is due south for northern hemisphere observers and due north for southern hemisphere observers. In the afternoon the Sun is ``post meridiem'' (Latin for ``after meridian'') or west of the meridian, abbreviated ``p.m.''.
If you are in the northern hemisphere, celestial objects north of the celestial equator are above the horizon for more than 12 hours because you see more than half of their total 24-hour path around you. Celestial objects on the celestial equator are up 12 hours and those south of the celestial equator are above the horizon for less than 12 hours because you see less than half of their total 24-hour path around you. The opposite is true if you are in the southern hemisphere. Notice that stars closer to the NCP are above the horizon longer than those farther away from the NCP. Those stars within an angular distance from the NCP equal to the observer's latitude are above the horizon for 24 hours---they are circumpolar stars. Also, those stars close enough to the SCP (within a distance = observer's latitude) will never rise above the horizon. They are also called circumpolar stars.
Here is a summary of the positions of the celestial reference marks (note that ``altitude'' means the number of degrees above the horizon): • Meridian always goes through due North, zenith, and due South points. • Altitude of zenith = 90° (straight overhead) always. • Altitude of celestial pole = observer's latitude. Observers in northern • hemisphere see NCP; observers in southern hemisphere see SCP. • Altitude of celestial equator on meridian = 90 - observer's latitude. • Celestial equator always intercepts horizon at exactly East and exactly West • points. • Angle celestial equator (and any star path) makes with horizon = • 90 - observer's latitude. • Stars move parallel to the celestial equator. • Circumpolar object's distance from celestial pole = observer's latitude.
To measure distances on the imaginary celestial sphere, you use ``angles on the sky'' instead of meters or kilometers. There are 360 degrees in a full circle and 90 degrees in a right angle (two perpendicular lines intersecting each other make a right angle). Each degree is divided into 60 minutes of arc. A quarter viewed face-on from across the length of a football field is about 1 arc minute across. Each minute of arc is divided into 60 seconds of arc. The ball in the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second across. The Sun and Moon are both about 0.5 degrees = 30 arc minutes in diameter. The pointer stars in the bowl of the Big Dipper are about 5 degrees apart and the bowl of the Big Dipper is about 30 degrees from the NCP. The arc from the north point on the horizon to the point directly overhead to the south point on the horizon is 180 degrees, so any object directly overhead is 90 degrees above the horizon and any object ``half-way up'' in the sky is about 45 degrees above the horizon. 1 degree = 60 arcmin = 3600 arcsec 180 degrees = radian p. 17
