(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c0.9c.
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Final Answer
  1. 2.0×105 km/s2.0\times 10^{5}\textrm{ km/s}
  2. 0.670.67

Solution video

OpenStax College Physics for AP® Courses, Chapter 34, Problem 7 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We are going to measure the speed at which a galaxy that is located at the greatest possible distance that we can observe from us and we are gonna multiply Hubble's constant by this distance of 10 gigalight-years and we'll convert the gigalight-years into units of megalight-years since Hubble's constant contains megalight-years in the denominator. And this works out to 2.0 times 10 to the 5 kilometers per second and our units are kilometers per second since Hubble's constant has kilometers per second here. So the megalight-years cancel and as do the gigalight-years leaving us with kilometers per second. And as a fraction of the speed of light, we convert that into meters per second since I have the speed of light in meters per second memorized— 2.998 times 10 to the 8 meters per second— and this works out to 0.67 so this is two-thirds the speed of light is the recessional velocity of this galaxy from us.