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Intro to astrophysics nis grade 11 by mr marty, visible brightness = apparent magnitude ‘m’, absolute magnitude
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Intro to astrophysics nis grade 11 by mr marty, visible brightness = apparent magnitude ‘m’, absolute magnitude

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History of magnitude scales; brightness, luminosity, and Power of a star; Stefan-Boltzmann Law; Stellar Parallax; and Wien's Displacement Law of blackbody radiation.

History of magnitude scales; brightness, luminosity, and Power of a star; Stefan-Boltzmann Law; Stellar Parallax; and Wien's Displacement Law of blackbody radiation.

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  • The Magnitude Scale
  • The Inverse Square Law
  • Luminosity
  • Stellar Parallax
  • Units for Stellar Distances
  • The Surface Temperatures of Stars

Transcript

  • 1. Intro to Astrophysics NIS Grade 11 Physics By Mr. Marty Visible Brightness = Apparent magnitude ‘m’, Absolute Magnitude ‘M’, Luminosity and Star classification
  • 2. Objectives: • Understand that stars are classified by luminosity which relates to their brightness and measured in terms of apparent magnitude • define apparent and absolute magnitude in terms of “m” • define absolute magnitude “M” of a star as the apparent magnitude ‘m” it would have if the star is at 10 parsecs
  • 3. Apparent Magnitude • Introduced by the Greek astronomer Hipparchus – Based on naked eye observations – Hipparchus used 6 levels of brightness that he called magnitudes. • Brightest stars – first magnitude • Half as bright – second magnitude • Dimmest stars – sixth magnitude • Apparent magnitude decreases as brightness increases!
  • 4. The Apparent Magnitude Scale “m” • The Apparent Magnitude was formalized in 1856 with exact numerical basis of how bright a star “appears” to a person on Earth. It is an extension of Hipparchus’ original magnitude scale. • This magnitude scale is backwards, larger number in magnitude means the star is dimmer. • Our Sun has m = -26, the dimmest star seen by the unaided eye has m = 6 and the faintest objects observable in visible light have m = 36
  • 5. Apparent Magnitude “m”, a measure of brightness as seen from Earth • The scale is logarithmic, because first magnitude stars are 100 times brighter than sixth magnitude stars, a magnitude difference of ‘1’ corresponds to brightness difference factor of 2.512 = (5 100)√ • The brightness of a star is defined as the amount of energy per second (power) striking a unit area at the Earth’s surface. • Also called the ‘Intensity’ of light hitting the Earth. • Sometimes it is called the flux (flow per unit area), in astronomy the it is the flow of radiant energy coming to the Earth’s surface per meter squared per second.
  • 6. Absolute Magnitude, “M” • Absolute Magnitude “M”: the magnitude a star would appear to have if it is placed at a distance of 10 parsecs from Earth. • m-M = 5 log(d) – 5 where d = distance to the star in parsec This formula does not need to be known by learners, although they should know: stars closer than 10 pc, M is less bright and has a larger number absolute magnitude than apparent magnitude, M > m  stars further than 10 pc, M is more bright and has smaller number absolute magnitude than apparent magnitude, M < m stars at 10 parsecs have absolute magnitude equal to apparent magnitude, M = m
  • 7. Absolute Magnitude of our Sun Our Sun would have a magnitude of 4.8 if it were at 10 pc, so its absolute magnitude is 4.8! Apparent magnitude = -26 Absolute Magnitude = 4.8 Image comparison is estimated
  • 8. Brightness of a Star Depends on 1. Distance and 2. Power or Luminosity of the star
  • 9. The Inverse Square Law The brightness of a star depends on both its luminosity and its distance. The farther away a star is, the dimmer it will appear. The brightness decreases as the square of the distance, the same principal as Newton’s Law of Universal Gravitation.
  • 10. Luminosity • The luminosity of a star represents the Power of the star (amount of energy a star emits per second). • Astronomers specify luminosity using the same magnitude scale that they use for brightness.
  • 11. Luminosity = Power Output The apparent brightness of a star is inversely proportional to the square of its distance and its Power is equal to Sigma x Area x Temperature4 (Kelvin). b = L /(4πd2 ) and B = σ T4 , because b=B when d=r L = 4πr2 σT4 → P = σA T4 → Stefan’s law where: b=apparent brightness , B=absolute brightness, L=luminosity, P=Power , d=distance to star, r=radius of star, T=temperature in Kelvin and σ = 5.67 x 10-8 Wm-2 K-4 , is Stefan’s constant
  • 12. Most stars have low luminosity
  • 13. How do Astronomers measure distances to stars and galaxies?
  • 14. Stellar Parallax • Stellar parallax is a direct trigonometric technique for measuring distance by taking observations from 2 locations. • Definition: A parallax angle is the shift, relative to the background, caused by a shift in the observer’s position.
  • 15. Other Units for Stellar Distances • One unit frequently used for stellar distances is the light year (ly), the distance light travels in one year (about 10 trillion kilometers). • Astronomers use the parsec (pc), the distance from which the size of Earth’s orbit around the Sun would appear to be 1 arcsecond. A parsec is 3.26 light years.
  • 16. • Parallax is denoted by ‘p’. • Distance (d) is measured in parsec. • d = 1 parsec = the distance at which a star has a parallax (p) of 1 arc second. 1 parsec = 3.26 light years. Also d = 1/p Closest star, Proxima centauri, p = 0.772 arc seconds. Hence distance ‘d’ in parsec is d = 1/p = 1/0.772 = 1.3 parsec = 4.2 light years
  • 17. The Limits for Measuring the Distance to Stars by Parallax • The nearest star is 4.2 ly (1.29 pc) away. Thus its parallax is less than 1 arcsecond. • The smallest parallax which can be accurately measured is about 0.01 arcseconds. This corresponds to a distance of 100 pc or 326 ly. • Our Milky Way galaxy is about 100,000 ly across, so stellar parallax can be accurately measured for only the nearest stars.
  • 18. Distances to farther away stars Calculation techniques require the use of • Apparent Magnitude (m) • Absolute Magnitude (M) • Luminosity (L) • Inverse Square Law
  • 19. The Surface Temperatures of Stars •A star’s color reveals the surface temperature. Blue stars are hotter than white stars and white stars are hotter than red stars. • The Wien's Displacement Law state that the wavelength carrying the maximum energy is inversely proportional to the absolute temperature of a black body. λmax T = b λmax = Wavelength of maximum intensity ( meters ) T = Temperature of the blackbody ( kelvins ) b = Wien's displacement constant = 2.8977685 ± 51 × 10-3 meters·kelvins Reference: http://www.physicshandbook.com/laws/wienlaw.htm • A star’s spectrum reveals the surface temperature, and additionally the chemical composition, atmospheric pressure, and rotation rate.
  • 20. Thermal Radiation: Temperature and color of radiation Hot……. Hotter…... Hottest!
  • 21. Must Watch video for Homework: • Our simulation Lab on Mon/Tue will give you an experience with Wien’s Displacement Law which relates the Wavelength emitted by a blackbody to its temperature. • The temperature and composition of stars: • http://www.youtube.com/watch?v=01U7ZUKVW8o
  • 22. Black Body Radiation and Wien’s Law http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html
  • 23. Black Body Radiation and Wien’s Law http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c2
  • 24. Surface Temperature and Apparent Color of Stars
  • 25. Vocabulary Terms of Astrophysics Astronomy Term Definition Russian Kazakh Absolute Magnitude “M” The apparent magnitude a star would have at 10 parsecs (32.6 light years) Абсолютная величина "М" Apparent Magnitude brightness “m” Each division is 2.51 times brighter than the next magnitude, sun has m= -26 Кажущаяся яркость Магнитуда "м" Apparent Magnitude scale A modern version of Hipparchus scale Полная шкала Магнитуда Intensity Power per unit area at the observer: I=P/4πr2 интенсивность Luminosity Total power radiated by a star (joules/sec=watts), depends on the temperature and distance between the star and the observer. L≈ d2 T4 светимость Parallax Angle The shift, relative to the background, caused by a shift in the observer’s position. Параллакс Угол Parsec The distance at which one AU subtends an angle of one arc second (1/3600th of a degree), 1 pc = 3.26 light years парсек Relative Brightness scale A scale created by in 120 BC where 1 is the brightest star and 6 is the dimmest star Относительная шкала Яркость Spectral Class A classification of a star based on features of its spectrum which also indicate its surface temperature and chemical composition Спектральный класс Wein’s Displacement Law Defines a relationship between the peak radiation emitted by a star and its temperature. Объем Закон Wein в
  • 26. References: • Wien’s Law from Physics Handbook: • http://www.physicshandbook.com/laws/wienlaw.htm • Astronomy General Topics Page with links to specific topics: http://www.astro.cornell.edu/academics/courses/astro201/topi cs.html • Windows to the Universe from National Association of Earth Science Teachers: • http://www.windows2universe.org/the_universe/Stars/magnit ude_scale.html • Spectral Classes of Stars: • http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/staspe.html • Wien’s and Stefan-Boltzman Laws explained: • http://csep10.phys.utk.edu/astr162/lect/light/radiation.html
  • 27. References 2: • Brightness, Luminosity and Radius: • http://science.howstuffworks.com/star3.htm • Luminosity and how far away things are: • http://zebu.uoregon.edu/~soper/Light/lumin osity.html • Properties and Classification of Stars: • http://www2.astro.psu.edu/~mce/A001/lect 13.html