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Some Quick Calculations with the Hubble Constant

By Steve Mencinsky

During the most excellent talk last Friday*, the concept of the expanding Universe was discussed at length. An integral part of this discussion was “Hubble’s constant”, which determines the rate of expansion of the Universe; and thus indirectly its age. “Hubble’s constant” is estimated to be between 50 km/s/Mpc and 100 km/s/Mpc**. Not the most convenient of units. What does this mean in more manageable terms? I have picked a middle-of-the-road value of 64 km/s/Mpc and converted it as per the following.

Speed of recession Distance Comment/Calculation
64 km/s 1 Mpc The definition
64 m/s 1 kpc Divide by 1000
64 mm/s 1 pc Divide by 1000 again
64 mm/s 3.2 ly Convert parsecs to light years
20 mm/s 1 ly Divide by 3.2

Thus, for every light year away from the Sun, the universe is expanding by approximately 20 millimetres per second. So, for example, space between us and Alpha Centauri at 4.2 light years is expanding at 84 millimetres per second. Not a lot.

What about planetary distances? Well, 20 mm/s per light year converts very conveniently to 20 mm per year per “light second”. So, the expansion of the universe is increasing the distance between Earth and the Moon at about “one inch per year”; and the distance between the Earth and the Sun (about 500 light seconds) at about 10 metres per year***.

Footnotes by Lesa Moore, 21st July 2012
I just loved this calculation when I first read it and it stuck in my mind all these years. I reproduced it from the original issue of Universe in which it appeared (that document no longer in my possession) and sent it in to ask for it to be put on the website (probably in 2006, the date on the electronic version in my computer). I have finally managed to accomplish this task today!

* Date of talk and original date of publication unknown.

** The Hubble Constant is now believed to be around 72 km/s/Mpc. Also, it is not constant, but is increasing with time, measuring an acceleration in the rate of expansion of the Universe (based on 1998 results of observations of distant Type 1a supernovae).

*** Technically, the space-time between the Earth, Sun and Moon is expanding at these rates, but gravity, stronger than the cosmic expansion, holds the Earth and Moon in their orbits. The Moon is, however, moving gradually away from the Earth due to tidal interactions, which are also slowing down the rate of Earth's spin in an exchange of angular momentum between the two bodies.

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