A quasar is observed to have a redshift of about 0.06, with a recessional velocity about 6% of the speed of light. Approximately what distance, in light-years, does the Hubble law give for this object? The Hubble constant is about 70 kilometers per second per megaparsec.

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Quizplus · Accepted Answer

The Hubble Law states that the recessional velocity of a galaxy (v) is proportional to its distance from us (d), with the proportionality constant being the Hubble constant (H0). The formula is v = H0 * d. Given that the recessional velocity is about 6% of the speed of light, we convert this to km/s: 0.06 * 300,000 km/s = 18,000 km/s. The Hubble constant is given as 70 km/s/Mpc. Rearranging the formula to solve for distance, we get d = v / H0 = 18,000 km/s / 70 km/s/Mpc = 257.14 Mpc. Converting megaparsecs to light-years (1 Mpc ≈ 3.26 million light-years), we get 257.14 Mpc * 3.26 million light-years/Mpc ≈ 838 million light-years, which rounds to approximately 800 million light-years.

A Quasar Is Observed to Have a Redshift of About