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I brought some of the questions from the Korean SAT. In the context of Hubble's law, galaxies A, B, and C appear like pictures. (The $y$-axis is the recessional speed, and the $x$-axis is the distance)

This problem compares the recessional velocity of galaxy C with the galaxy C 2 billion years ago. The problem explanation explains: “2 billion years ago, it would have been closer than the current distance, so recessional speed 2 billion years ago would have been smaller.”

I point out the following errors: First, this problem did not take into account the Hubble constant value 2 billion years ago. Second, the recessional velocity 2 billion years ago is that deceleration expansion, acceleration expansion, and constant velocity expansion should be considered depending on the universe model. Like the picture below.

enter image description here

Do you think the recesional velocity of galaxy c from 2 billion years ago would be less than the current value?

So I think we should discuss that the velocity was greater or smaller 2 billion years ago, depending on the expansion model of the universe, rather than simply because the distance was smaller. Am I right?

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  • $\begingroup$ Is your SAT is a high-school exam? $\endgroup$
    – mike stone
    Commented Dec 21, 2021 at 21:47
  • $\begingroup$ @mike stone It's a Korean high school exam. Students have learned how their proper distace changes over time. $\endgroup$
    – teacher
    Commented Dec 22, 2021 at 7:03
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    $\begingroup$ I feel like the accelerated expansion is an unnecessary complication when calculating something of that precision over a 2 billion year scale. it's not asking how the situation would have been 14 billion years ago, that would be a different story, but over 2 billion years i would simply neglect dark energy $\endgroup$
    – rfl
    Commented Dec 22, 2021 at 9:33
  • $\begingroup$ @rfl So, how would you interpret speed change on a scale scale of 2 billion years? In the end, I think the distribution of speed between 11.7 billion and 13.7 billion years out of 13.7 billion years should be presented directly. The approach to this test is simply that if the distance is small, the speed is smaller. I think this is wrong. $\endgroup$
    – teacher
    Commented Dec 22, 2021 at 10:07
  • $\begingroup$ well, that's exactly the Hubble law... which I would think is all that question is asking about. $\endgroup$
    – rfl
    Commented Dec 23, 2021 at 15:50

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