Redshift measurements on a galaxy show that it is receding from us with a velocity of 7240 km/s.Estimate how far away the galaxy is if the Hubble constant is 22 km/s per million light-years.(c = 3.00 × 10⁸ m/s,1 ly = 9.461 × 10¹⁵ m,1 y = 3.156 × 10⁷ s) A) 3.1 × 10²⁴ m B) 1.2 × 10²⁶ m C) 1.2 × 10²⁴ m D) 4.1 × 10²³ m E) 2.0 × 10²² m

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To find the distance to the galaxy, we use the formula $v = H_0 \times d$, where $v$ is the velocity of the galaxy, $H_0$ is the Hubble constant, and $d$ is the distance to the galaxy. Rearranging the formula to solve for $d$, we get $d = \frac{v}{H_0}$. Given $v = 7240$ km/s and $H_0 = 22$ km/s per million light-years, we first convert $H_0$ to the same units as $v$ by noting that 1 million light-years is the distance light travels in a million years. Using the speed of light $c = 3.00 \times 10^{8}$ m/s and the definition of a light-year, we can calculate the distance:$$d = \frac{7240 \, \text{km/s}}{22 \, \text{km/s per million light-years}} = 329 \, \text{million light-years}$$To convert this distance into meters, we use the conversion factor $1 \, \text{light-year} = 9.461 \times 10^{15} \, \text{m}$:$$d = 329 \times 10^6 \times 9.461 \times 10^{15} \, \text{m} = 3.1 \times 10^{24} \, \text{m}$$

Redshift Measurements on a Galaxy Show That It Is Receding