Hubble's law: A galaxy is observed receding from Earth with a speed of 2800 km/s. If the Hubble constant is 22 km/s per million light-years, estimate how many years ago the light that we presently see from the galaxy actually left the galaxy. (c = 3.00 × 10⁸ m/s, 1 ly = 9.461 × 10¹⁵ m, 1 y = 3.156 × 10⁷ s) A) 1.3 × 10⁸ y B) 4.2 × 10⁸ y C) 4.2 × 10⁷ y D) 1.4 × 10⁷ y E) 4.2 × 10⁶ y

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Hubble's law states that the recessional speed of a galaxy is proportional to its distance from Earth. The Hubble constant is the proportionality constant. In this problem, we are given the recessional speed of the galaxy and the Hubble constant. We can use these values to calculate the distance to the galaxy. Once we know the distance to the galaxy, we can use the speed of light to calculate how long ago the light that we presently see from the galaxy actually left the galaxy.The distance to the galaxy is given by:$$distance = \frac{recessional \ speed}{Hubble \ constant}$$$$distance = \frac{2800 \ km/s}{22 \ km/s \ per \ million \ light-years}$$$$distance = 1.27 	imes 10^8 \ light-years$$The time it took for the light to travel from the galaxy to Earth is given by:$$time = \frac{distance}{speed \ of \ light}$$$$time = \frac{1.27 	imes 10^8 \ light-years}{3.00 	imes 10^8 \ m/s}$$$$time = 4.23 	imes 10^8 \ years$$Therefore, the light that we presently see from the galaxy actually left the galaxy 4.23 × 10^8 years ago.

Hubble's Law: a Galaxy Is Observed Receding from Earth with a Speed