# Computing the Age of the Universe

## Introduction

While in the lunch room at work, I often look at the paper. The paper one day this week had an article on the farthest object that has yet been observed by astronomers. One of the guys in my group was there and we started to talk about computing the Earth's age and computing the age of the universe. Since I have already covered calculating the age of the Earth in a previous post, I thought it would be worth documenting calculating the age of the universe as well. It is a shorter subject, at least for this level of detail.

## Calculation

The only piece of data needed is Hubble's constant. We can see the linear relationship between the recessional velocity and distance from the chart shown in Figure 1 (Source). Note the linearity of the characteristic. Figure 1: Recessional Velocity Versus Distance.
I believe the bulge in the middle of the curve is the data from various galaxy clusters (e.g. Virgo), which also have a rotational component to their motion.

I show in Figure 2 that the reciprocal of Hubble's constant equals the age of the universe. Figure 2 is a screenshot of my Mathcad worksheet (I like to use Mathcad's unit checking).

## Conclusion

Pretty straightforward. I first got interested in the subject while listening to an audio book called "Horizons of Cosmology" by Silk. It is a great listen and worth your time if you are interested in that sort of thing.

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### 2 Responses to Computing the Age of the Universe

1. Basil says:

Interesting calculation. This calculation doesn't seem to involve a changing expansion factor. For example, if you were blowing up a balloon the distance between objects would increasingly get farther after time, making a linear calculation inappropriate. I also think it is interesting to note how time relativity plays a part in this measurement. The book Genesis and the Big Bang relate these two together.

• mathscinotes says:

Until recently, measurements have indicated that Hubble's constant is linear. The question of the linearity of Hubble's constant is an interesting one. The book "Horizons of Cosmology" does a good job describing some recent measurements that indicate that very distant objects appear to be accelerating. No one really understands what is going on. The acceleration is usually attributed todark energy" and the cosmological constant. So the calculation for the age of the universe may change as more is discovered.