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The recessional velocity is 9,771,241 m/s.
Step 1: The redshift of a faraway galaxy is determined by measuring the shift of its spectral lines compared to similar lines from nearby galaxies. The redshift is usually expressed as a ratio in terms of how much the wavelength of each line has shifted from its original value.
Step 2: The hydrogen alpha emission line has a known rest wavelength of 6562 angstroms. This means that the observed wavelength of 6782 angstroms is shifted from its rest wavelength by a factor of 1.03.
Step 3: The redshift of a galaxy can be converted into a recessional velocity in km/s by using the Hubble Law, which states that the recessional velocity of a galaxy is proportional to its redshift.
Step 4: To calculate the recessional velocity, the formula V = H0 x z is used, where V is the recessional velocity, H0 is the Hubble Constant, and z is the redshift.
Step 5: The Hubble Constant is currently estimated to be 70 km/s/Mpc, so using the formula, the recessional velocity of the faraway galaxy is 70 km/s/Mpc x 1.03 = 71.1 km/
Recessional velocity is the speed at which an object is moving away from an observer. This is typically measured in kilometers per second and is used to measure the expansion of the universe. It is calculated by measuring the wavelength shift of an object's light, which increases as the object moves away from the observer.
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