<p>Here is some remarks on the issue, straight from Ryden:</p>

<blockquote>
  <p>If galaxies are currently moving away from each other, then it implies
  they were closer together in the past. Consider a pair of galaxies
  currently separated by a distance $r$, with a velocity $v = H_0r$
  relative to each other. If there are no forces acting to accelerate or
  decelerate their relative motion, then their velocity is constant, adn
  the time that has elapsed since they were in contact is</p>
  
  <p>$t_0 = \frac{r}{v} = \frac{r}{H_0r} = H_0^{-1}$, </p>
  
  <p>independent of their current separation $r$.</p>
</blockquote>

<p>Which part of this are you confused about? I can edit my answer once I better understand your question.</p>

CC BY-SA 3.0
2018-04-23T21:23:51.193Z
2018-04-23T21:23:51.193Z
pretzlstyle
<p>Hubble's constant is estimated at 15km/s at a distance of million light years, without considering effects of mutual gravity, relativity, etc.
I am trying to calculate the characteristic expansion time of the universe.
Its formula is given as reciprocal of the Hubble constant, because time is distance by velocity. But:</p>

<p>$$v=kx$$</p>

<p>This implies that velocity and distance are exponential functions of time and so time cannot simply be calculated by dividing 1 million light years by 15km/s.
So what am I missing? Why is the characteristic expansion time simply the reciprocal of Hubble's constant?</p>

CC BY-SA 3.0
2018-04-23T20:13:51.623Z
Please [edit] for spelling. Put capital letters at the start of sentences, names of people and the word "I", and the correct spelling is "because" not "cuz"
James K
CC BY-SA 3.0
2018-04-24T18:37:37.293Z
15 km/s/Mlyr is somewhat off — **21** km/s/Mlyr is more correct. If you divide 1 Mlyr with 21 km/s, you get roughly 14.3 Gyr, which is pretty close to the 13.8 Gyr inferred from Planck measurements.
pela
<big-bang-theory><hubble-constant>
calculation of characteristic expansion time of the universe
Dhruv Gupta
# calculation of characteristic expansion time of the universe

(Asked by: username_0 on 2018-04-23)

Hubble's constant is estimated at 15km/s at a distance of million light years, without considering effects of mutual gravity, relativity, etc.
I am trying to calculate the characteristic expansion time of the universe.
Its formula is given as reciprocal of the Hubble constant, because time is distance by velocity. But:

$$v=kx$$

This implies that velocity and distance are exponential functions of time and so time cannot simply be calculated by dividing 1 million light years by 15km/s.
So what am I missing? Why is the characteristic expansion time simply the reciprocal of Hubble's constant?

**Tags:** big-bang-theory, hubble-constant
> **Comments:**
> **username_1**: Please [edit] for spelling. Put capital letters at the start of sentences, names of people and the word "I", and the correct spelling is "because" not "cuz"  
> **username_2**: 15 km/s/Mlyr is somewhat off — **21** km/s/Mlyr is more correct. If you divide 1 Mlyr with 21 km/s, you get roughly 14.3 Gyr, which is pretty close to the 13.8 Gyr inferred from Planck measurements.  

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## 1 answers

### Answer by username_3 on 2018-04-23. Score: 3

Here is some remarks on the issue, straight from Ryden:

> If galaxies are currently moving away from each other, then it implies
> they were closer together in the past. Consider a pair of galaxies
> currently separated by a distance $r$, with a velocity $v = H\_0r$
> relative to each other. If there are no forces acting to accelerate or
> decelerate their relative motion, then their velocity is constant, adn
> the time that has elapsed since they were in contact is
>
> $t\_0 = \frac{r}{v} = \frac{r}{H\_0r} = H\_0^{-1}$,
>
> independent of their current separation $r$.

Which part of this are you confused about? I can edit my answer once I better understand your question.


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