How To Calculate The Age Of The Universe

Astronomy Tutorial

How To Calculate The Age Of The Universe

Intro

Have you ever wondered how astronomers calculate the age of the universe? In this tutorial, you will learn about the astronomical theories that allow astronomers to make such calculations, including the Big Bang theory and the expansion of the universe. You will also learn about several key astronomical observations that serve as evidence for these theories, including Edwin Hubble’s original observations and more recent data from the WMAP and Planck spacecrafts.

Sample Problem

Question source

What is the age of the universe?

84.5 million years


12.7 million years


13.8 billion years


6000 years


13,000 years


Solution

Hubble’s Law and the Big Bang Theory

Let’s begin with Edwin Hubble in 1929. Hubble was an astronomer at the Mount Wilson Observatory who had recently used standard candles, specifically Cepheid variable stars, to collect evidence suggesting that the Milky Way was but one of many galaxies in the universe. This discovery would change our cosmological perspective forever, but Hubble was just getting started.

In 1929 Hubble combined his measurements of galaxy distances with previous measurements of galaxy redshifts. A redshift occurs when light is shifted towards the red-end of the spectrum, typically caused by an object moving away from the observer. Hubble’s analysis revealed a surprising relationship: redshift increased as distance increased. This relationship is now referred to as Hubble’s Law.

Hubble’s Law implies that the more distant a galaxy, the faster it is moving away from us, in all directions! It’s as if we’re at the center of a cosmic explosion pushing the entire universe away from us. Or as if we’re “it” in a cosmic game of “tag.” Or as if we forgot to brush our teeth. Why should the universe behave in such a peculiar way?

Hubble’s Law is a fantastic result that led to fantastic interpretations, including the one which has best stood the test of time: the Big Bang theory. Originally proposed by the Belgian Catholic priest and physicist Georges Lemaître, the Big Bang theory asserts that the universe is expanding in all directions.

Calculating the Age of the Universe

Hubble’s Law can be written as follows, where v is the velocity a galaxy is travel away from us, D is the distance of the galaxy from us, and H_0 is what’s known as Hubble’s constant.

    \[v=H_0*D\]

H_0 is a constant that must be empirically determined by measuring the velocity and distance of many galaxies. This work was Hubble’s contribution, though the value for H_0 has been refined over the years, including most recently by the WMAP and Planck space probes. The current best estimate, as of 2016, is H_0=67.31\pm0.96\mbox{ km} / {\mbox{Mpc}}\cdot\mbox{s}. We’ll address those funky units in a bit.

But how do we use Hubble’s Law to calculate the age of the universe? Well suppose you knew a car was traveling at a constant speed and you knew the distance it traveled over some time period. The relationship is similar to Hubble’s Law.

    \[v=\frac{D}{t}\]

You can solve for t to see that the time is \frac{D}{v}.

Well the universe is pretty similar to that car. Pick any distant galaxy and it has been traveling at a constant speed away from us since the beginning of the universe and is now some distance away. So we again have the following.

    \[v=\frac{D}{t}\]

And the time is again \frac{D}{v}, which in this case is the age of the universe. Now let’s rearrange Hubble’s Law to piece it all together.

    \[v=H_0*D\]

    \[\frac{v}{D}=H_0\]

    \[\frac{D}{V}=\frac{1}{H_0}\]

Now substitute t=\frac{D}{v}.

    \[t=\frac{1}{H_0}\]

Thus, the age of the universe is equal to one over Hubble’s constant!

To get an actual value of the age of the universe, plug in H_0=67.31\pm0.96\mbox{ km} / {\mbox{Mpc}}\cdot\mbox{s}, then do the necessary unit conversions. You need to know that 1\mbox{ Mpc} = 3.08\times10^{19}\mbox{ km} and 1\mbox{ yr} = 31,557,600\mbox{ s} (be sure to use 365.25 days per year to account for leap years).

    \[t=13.813\mbox{ billion years}\]



About The Author

2 reviews

Math Expert And SAT Instructor
Jared, founder of The Knowledge Roundtable, is passionate about the advancement of knowledge. He has a B.S. in astronomy and physics from UMass and an MBA in Advanced Financial Analytics, also from UMass. He has a day job as a Big Data Analyst in Boston. He has over 500 hours of tutoring experien...
Send Email
31 Subjects
KnowRo Tutor
4 Tutorials
$50
Quincy, MA
Learn

Suggested Tutors for Astronomy Help

Ad

Varsity Tutors

(855) 475-5132 - Award-Winning Academic & Test Prep Tutors

Ad

Air Tutors

One-on-One Ivy Tutoring Partners 24/7

Mackenzie H

Manassas, VA

Writing Enthusiast

Rizan S

Haymarket, VA

Future Teacher

Leave a Comment

Your email address will not be published. Required fields are marked *

^