Expert: Courtney Seligman - 7/1/2010

Question
I usually hear that the speed of light is 186,000 miles per second vs the exact 186,282 miles per second.  Is not the more exact measurement used vs the general rounded off measurement?  Also, for some reason I thought that the speed of light was 186,400 miles per second.  Did I just imagine that or was that used to be the figure given?

Answer
Whether the more exact measurement is used depends upon the accuracy needed. The rounded off value is only off by one sixth of a percent, so for many purposes, it's perfectly reasonable to use the rounded off value. For instance, the average distance of the Earth from the Sun is about 93 million miles. Using the rounded off speed of light, it would take light about 500 seconds to go from the Sun to the Earth. Using the exact speed of light (which is defined as 299,792.458 km/sec (exactly), or about 186,282.397 mi/sec), it would take 499 seconds and a bit over. So in this case, it would be reasonable to say it takes about 8 minutes and 20 seconds for light to go from the Sun to the Earth, particularly since the changing distance of the Earth from the Sun during the year would change the time by about 15 seconds, which is far larger than the one second error.

However, if a NASA engineer was using the arrival times of radio waves (which travel at the speed of light) to follow the motion of a distant spacecraft, he would (or at least should) use the exact value of the speed of light (in km/sec), to ensure as accurate results as possible.

As far as the 186,400 mi/sec figure, that is what I recall it's being quoted as, when I was much younger (in fact, I think that was the figure I quoted, when I started teaching). I was surprised when I found it was off by more than a hundred miles per second. I don't know the reason for the error. Perhaps some textbook had a typographical error, and other textbooks copied it, without looking up the original value. Or perhaps at some early stage, that was the best value available, and it "stuck" in people's minds long after more accurate values were available.