Astrophysics of Life

# Apparent brightness and inverse square law light

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Apparent brightness and inverse square law Light appears fainter with increasing distance If we increase our distance from the light source by 2, the light energy is spread out over four times the area (area of sphere = 4pid^2) Flux = luminosity / 4pid^2 To know a star’s luminosity we must measure its apparent brightness (flux) and know its distance. Then, Luminosity = Flux x 4pid^2 The Magnitude Scale

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2 nd century BC, Hipparchus ranked all visible stars – brightest = magnitude 1 faintest = magnitude 6 To our eyes, a change of one magnitude = a factor of 2.5 in flux Hence, the magnitudes scale is logarithmic A change of 5 magnitudes means the flux 100 x greater Our eyes use logarithmic Apparent magnitude – star’s apparent brightness when seen from its actual distance Absolute magnitude – apparent magnitude of a star as measured from a distance of 10 pc Sun’s apparent magnitude (if seen from a distance of 10 pc) is 4.8 This is then the absolute magnitude of the Sun Starlight: Who Cares? We do! Primary source of “life energy” on Earth Many living things convert sunlight to energy Most other living things eat them (or eat things that eat them, or . . .) Also, heat/temperature Living things want liquid phase Need the right star/distance combination for this Also, want STABLE temperatures for long time (i.e. millions, or better yet, BILLIONS of years) H – red, turquoise, violet He – red, yellow, aquamarine, violet Stellar Temperature: Color You don’t have to get the entire spectrum of a star to determine its temperature Measure flux at blue (B) and yellow (“visual”=V) wavelengths Get temperature by comparing B-V color to theoretical blackbody curve Stellar Temperature: Spectra 7 stars with same chemical composition
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