Hubble's Law relates the speed of a galaxy from its distance to us. If you assume Hubble's constant to be 23 km/s/10⁶ ly, then what is the distance of a galaxy that is traveling at 10% the speed of light away from us? A) It is not possible for a galaxy to travel so fast! B) 1.3 × 10¹⁰ ly C) 1.3 × 10⁹ ly D) 1.3 × 10¹¹ ly E) 1.3 × 10⁸ ly

Question

Quizplus · Accepted Answer

Hubble's Law states that the velocity of a galaxy relative to us is proportional to its distance from us. Mathematically, this can be expressed as v = H0 d, where v is the velocity of the galaxy, d is its distance from us, and H0 is Hubble's constant. We are given H0 as 23 km/s/10^6 ly. To find the distance of a galaxy traveling at 10% the speed of light (which is 0.1c), we first convert H0 to units of km/s/Mpc (megaparsec) by dividing by 3.086 × 10^19 km/Mpc:

H0 = 23 km/s/10^6 ly ÷ 3.086 × 10^19 km/Mpc 
= 0.00745 km/s/Mpc

Now we can use the formula v = H0 d, but we need to convert the velocity to km/s first:

v = 0.1c ÷ 1.609 × 10^6 km/s/c 
= 0.622 × 10^8 km/s

d = v ÷ H0 
= (0.622 × 10^8 km/s) ÷ (0.00745 km/s/Mpc) 
= 8.35 × 10^9 Mpc

Finally, we convert Mpc to ly:

8.35 × 10^9 Mpc × 3.26156 × 10^6 ly/Mpc ≈ 1.3 × 10^19 ly

Therefore, the best choice is C, 1.3 × 10^19 ly.

Hubble's Law Relates the Speed of a Galaxy from Its