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# Parallax And Magnitude

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• 1. Parallax and Magnitude
• 2. Proper Motion Stars stay fixed against the rest of the sky however they have individual motions - proper motions - over long periods of time. Barnard’s star (in the constellation of Ophiuchus) has an annual proper motion of 10.3” against its background. It would take 190 years to cover a distance equal to the apparent diameter of the Moon in the sky (its angular size).
• 3. Parallax Nearby stars appear to shift relative to the stellar background as we orbit the Sun. The distance between the Sun and the Earth is defined as 1 astronomical unit,1 AU (150 million km). If the angular shift from the centre (the parallax) is 1” , the distance to the star is 3.26 lyrs (31 x 10 12 km), now redefined as 1 parsec ( 1 pc ).
• 4. Parallax The binary system 61 Cygni (in the constellation of Cygnus) has a parallax of 0.292”. Now 1” gives a distance of 1 parsec . A smaller parallax means the star is further away. So the distance to 61 Cygni is: 1/0.292 = 3.424 pc (11.16 lyrs). Alpha Centauri (in the southern hemisphere) has a parallax of 0.76”. This gives a distance of 1.31 pc (4.3 lyrs).
• 5. Parallax Beyond 200 - 300 lyrs the parallax shifts are too small to be measured so different methods are used to determine the distances of stars. The star’s luminosity (energy per second) and apparent brightness (luminosity/area of a sphere, 4πD 2 ) are used to determine its distance, D. When doing this loss of light (by absorption) through the interstellar medium has to be taken into account. ISM
• 6. Apparent Magnitude Apparent magnitude (m) is a scale that measures how bright a star appears to be relative to others in the sky. It gives no indication of the actual luminosity of the star; a star may look bright because it is close or because it happens to be very luminous. Two stars differing by 5 magnitudes differ in apparent brightness (b) by a factor of 100 . A 1 magnitude difference is equivalent to 5 √100 = 2.512 ; a 5 magnitude difference is 2.512 5 = 100. So b 1 /b 2 = 2.512 m2 - m1
• 7. Apparent Magnitude The smaller the value of m, the brighter the object. magnitude of Sun = -26.8 magnitude of Sirius (brightest star in sky) = -1.43 magnitude of Venus (when at its brightest) = -4.4 Faintest stars still visible to the naked eye have a magnitude of +6 .
• 8. Apparent Magnitude Sirius (in the constellation Canis Major) has a magnitude of -1.5 . It appears to be brighter than Rigel (in the constellation Orion), m = +0.1 . Sirius has a luminosity 26 x greater than that of the Sun, however Rigel’s luminosity is 60 000 x L sun . Sirius appears brighter because it is closer ( 8.6 lyrs ) whereas Rigel is 900 lyrs away. We see Sirius as it was in 2000, however Rigel looks as it was 900 years ago (at the time of William the Conqueror!). Sirius Rigel
• 9. Absolute Magnitude The absolute magnitude of a star (M) is the apparent magnitude (m) it would have at a distance of 10 pc (32.6 lyrs). This is a better indication of how bright stars actually are relative to each other. M = 5 + m - 5logD D in parsecs E.g. A star 100 pc away has an apparent magnitude, m = 8. What is its absolute magnitude, M? M = 5 + 8 - 5log100 M = 13 - (5 x 2) = +3 A logarithm of base 10 takes a number and finds the power that 10 has to be raised to to get that number: log 10 100 = 2, so 10 2 = 100
• 10. Absolute Magnitude The smaller the value of M, the brighter the object. absolute magnitude of Sun = +4.8 absolute magnitude of Sirius (brightest star in sky) = +1.4 absolute magnitude of Venus (when at its brightest) = +28
• 11. http: //radmila-topalovic . blogspot .com