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How To Calculate the Age of the Universe

How To Calculate the Age of the Universe
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  • 0:02 Estimating Age
  • 0:39 Important Equations
  • 2:38 The Age of Our Universe
  • 4:38 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
This lesson will explain to you how old our universe is and how we calculate it thanks to the Hubble law and Hubble constant as well as one other simple equation.

Estimating Age

How do you estimate age? For people, you probably look at their face and make a judgment. For a tree, you count tree rings. For a fossil, you can do carbon dating. In any case, you can see there are many different ways we can determine the age of something. But how do we determine the age of something as vast as the universe? How old is the universe anyways?

Spoiler alert! The answer is: the age of the universe is about 13.7 billion years old. And we'll use math to show you how and why that's the case in this lesson.

Important Equations

About 13.7 billion years ago, the Big Bang occurred. The Big Bang is an explanation of how the universe began from an infinitely compact state, and it thus marks the age of our universe. The universe has expanded ever since the Big Bang. I know that you can picture two galaxies within the universe flying apart as it expands. That's easy to do. But we can just as easily reverse this and imagine them flying back towards one another as we rewind the animation on your screen (please see the video beginning at 01:11).

Thus, we can calculate the time it would take for these galaxies to collide back to where they started out from. In a simple way, the time (T) it would take for them to collide is equal to the distance (d) divided by velocity (v). We can then modify this equation by using the Hubble law. The Hubble law is a direct (linear) relationship between a galaxy's velocity of recession and its distance.

You can see on screen that the Hubble law is where velocity (v) is equal to the Hubble constant (H) multiplied by distance (d):

Hubble Law
hubble law equation

The average value of the velocity of recession divided by distance is the Hubble constant.

Therefore, if we replace the velocity in our original equation with the Hubble law, we get what you see on screen:

The ds in this equation cancel out.
hubble equation

Since a d in the denominator and numerator cancel each other out, you're left with T equal to 1 divided by the Hubble constant. One divided by the Hubble constant is known as Hubble time and is equal to the age of the universe assuming it has expanded at a constant rate since the Big Bang.

The Age of Our Universe

This means that T is actually the same for all galaxies. This makes sense because at one point all the galaxies were sort of compressed together, if you will, at the Big Bang.

Now, although this varies just slightly based on estimations, the Hubble constant value we'll use for this lesson is 73 km/s/Mpc. Going back to our equation, T is equal to the reciprocal of the Hubble constant. But it's not as simple as that; we have to convert the units of time we use. So, take a look at the conversion we use on screen to see what we're doing here:

Calculation for conversion
conversion for hubble equation

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