Astronomy 101 A Hubble’s Law: Work sheet for recording values and calculations if a spreadsheet is not used. Redshifted Wavelength values Galaxy ID (NGC number) Angular Size (milli-radians) Distance (Mpc) Calcium (CaII) K (rest λ=3933.7 Å) Calcium (CaII) H (rest λ=3968.5 Å) Hydrogen (Hα) (rest λ=6562.8 Å) Average redshift Velocity (km/sec) (22 kpc true size) Measured Redshift (z) Measured Redshift (z) Measured Redshift (z) Distance = true size / angular size z = (λmeasured- λtrue) λtrue z = (λmeasured-λtrue) λtrue z = (λmeasured-λtrue) λtrue v = average z × c Sample: 1.44 15 3946.7 0.0033 3982.3 0.0035 6585 0.0034 0.0034 1016 1357 1832 2276 2775 2903 3034 3147 3227 3245 33103368 3471 3516 3623 3627 3941 4472 4631 4775 5248 5548 5866 6181 6217 6643 6764 7469Relevant formulae: redshift = ! "measured#"true"true$ % & ' ( ) =vc= z Small angle formula approximation: a = s/d or d = s/a distance = actual size of the object ÷ angular size in radians (watch units – distance will come out in the same units as the actual size) Finding the steepest slope (rise over run) and shallowest slope (rise over run) allowed by your data in order to determine the uncertainty in your value of the Hubble constant: ! Hsteepest" H( )+ H " Hshallowest( )2= uncertainty in
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