How Fast (Or Slow) Is The Speed Of Light?

A Little Background

The first recorded discussion regarding the speed of light was in and around 300 B.C. where Aristotle quotes Empedocles as theorizing that the light from the sun must take some time to reach the Earth. Almost two millennia later during the Scientific Revolution (circa 1620 A.D.), Descartes theorized that light was instantaneous. At about the same time, Galileo gave a more general thought that light was much faster than sound but not instantaneous, offering up some ideas as to how it might be tested using lanterns and telescopes. At what point would these theories actually be tested and how?

About half a century after Descartes and Galileo, the Danish astronomer Ole Römer began measuring the actual speed of light through observation of Io, one of Jupiter’s moons. He recognized that as the Earth and Jupiter moved in their orbits, the distance between them varied. The light from Io (reflected sunlight) took time to reach the earth, and took the longest time when the earth was furthest away.  When the Earth was furthest from Jupiter, there was an extra distance for light to travel.  The observed eclipses were furthest behind the predicted times when the earth was furthest from Jupiter.  By measuring the difference in time and using a little math, the speed of light could essentially be calculated.

From that point forward, numerous scientists tackled this quest through a diverse set of accompanying theories and experiments. The speed of light would be more accurately determined, leading to wide applications in optics, astronomy, and physics. For example, in the early 1900’s, the speed of light became a foundational component of Einstein’s theories (general and special) of relativity, proven to relate energy to mass (E=m*c^2 where c = speed of light). As a result of these applications, the calculation of the speed of light was a major platform for new scientific discovery and enlightenment.

So How Fast Is It?

Well, the measured speed of light in a vacuum is exactly 299,792,458 meters per second, often approximated as 300,000 kilometers per second (3.0 * 10^8 m/s or 3.0 * 10^5 m/s) or 186,000 miles per second. Outside of a vacuum where there might be atoms and molecules that act as impeding forces, the speed of light slows down based on the refractive index of the material. For a given substance with refractive index (n), the actual speed of light (v) is given by v=c/n where c is the constant speed of light in a vacuum. Of note:

v(air) = 299,704,764 m/s (n=1.0002926 at standard room temperature)
v(water) = 224,900,568 m/s (n=1.3330)
v(salt) = 194,166,100 m/s (n=1.544)
v(diamond) = 123,932,392 m/s (n=2.419)

Let’s put the speed of light, in air, in a bit of context…

The circumference of the Earth is about 40,000 km on average. That means that light could travel around the Earth 7.5 times in a second.

The distance between the Earth and its moon is about 380,000 km on average. It takes light about 1.27 seconds to travel from one to another. Click here for a demonstration.

On the size of our solar system, it takes light from the sun about 8 seconds to reach Earth, 43 minutes to reach Jupiter, and nearly 7 hours to pass the orbit of Pluto.

On the size of our galactic realm, the Milky Way is a spiral galaxy. Our solar system is located on what is called Orion’s arm, about 25,000 light years from the center of the Milky Way’s center. One light year is the distance light travels in one Earth year. In more earthly terms, that’s about (3*10^5 km/s)*(60 s/min)*(60 min/hr)*(24 hrs/day)*(365 days/yr) = 9,460,800,000,000 kilometers. And I thought a marathon was far.

Beyond our Milky Way galaxy and looking at our Local Group of galaxies, it extends about 4 million light years across. That means for light to run from a galaxy one side of our Local Group to a galaxy on the other side of our Local Group, it takes 4 million years. Yikes.

And our Local Group of galaxies is part of a larger “supercluster” that is 150 million light years across. The dinosaurs roamed Earth from 230 million to 65 million years ago. In other words, light from the Ursa Major and Virgo galactic clusters still hasn’t reached us if it was emitted during the extinction of dinosaurs. Makes light seem pretty slow now, no?

Whether quick relative to earthly distances or slow through vast cosmic voids, even light has meaning. It provides perspective, foundation, discovery, and well, light.

For more on the speed of light and the depths of the universe and time, I highly recommend Bill Bryson’s A Short History of Nearly Everything (it’s my favorite book).