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The Trigonometric Parallax

0. The Trigonometric Parallax. B. d. p. d = (1/p[arcsec]) parsec. B = 1 AU = 1.496*10 13 cm. 1 pc = 3.26 LY ≈ 3*10 18 cm. 0. The Moving Cluster Method. v. q. v f. v r. q. f. x. 0.

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The Trigonometric Parallax

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  1. 0 The Trigonometric Parallax B d p d = (1/p[arcsec]) parsec B = 1 AU = 1.496*1013 cm 1 pc = 3.26 LY ≈ 3*1018 cm

  2. 0 The Moving Cluster Method v q vf vr q f x

  3. 0 The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint objects): Sirius (brightest star in the sky): mv = -1.42 Full moon: mv = -12.5 Sun: mv = -26.5

  4. 0 Color and Temperature Stars appear in different colors, from blue (like Rigel) via green / yellow (like our sun) to red (like Betelgeuze). These colors tell us about the star’s temperature. Orion Betelgeuze Rigel

  5. 0 Blackbody Radiation (I) The light from a star is usually concentrated in a rather narrow range of wavelengths. The spectrum of a star’s light is approximately a thermal spectrum called Blackbody Spectrum.

  6. 0 Blackbody Radiation Fsurf = s Teff4 s = 5.67*10-5 erg/(cm2 s K4) Wien’s displacement law: lmax≈ 0.29 cm / TK (TK = temperature in Kelvin).

  7. 0 The Color Index (I) B band V band The color of a star is measured bycomparing its brightness in different wavelength bands: The blue (B) band and the visual (V) band. We define B-band and V-band magnitudes just as we did before for total magnitudes.

  8. 0 Optical Wavelength Bands U: l0≈ 3650 Å B: l0≈ 4400 Å V: l0≈ 5500 Å

  9. 0 The Color Index We define the Color Index B – V (i.e., B magnitude – V magnitude) The bluer a star appears, the smaller the color index B – V. The hotter a star is, the smaller its color index B – V. B - V Temperature

  10. 0 Example: For our sun: Absolute V magnitude: 4.83 Absolute B magnitude: 5.51 => Color index: B – V = 0.68 From standard tables: B – V = 0.68 => T ≈ 5800 K.

  11. 0 The Color-Color Diagram B0 -1.0 -0.5 Blackbody 0.0 A0 U - B F0 G0 0.5 K0 1.0 M0 1.5 -0.5 0.0 0.5 1.0 1.5 2.0 B - V

  12. 0 The Hertzsprung-Russell Diagram Log(L) Most stars are found along the Main Sequence M Zero-Age Main Sequence (ZAMS) Teff B - V

  13. 0 Radii of Stars in the Hertzsprung-Russell Diagram Rigel Betelgeuze 10,000 times the sun’s radius Supergiants Polaris Giants 100 times the sun’s radius Sun White Dwarfs As large as the sun 100 times smaller than the sun

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