F=ma, the Inverse-Square Law, and Other Sound Principles that Don’t Seem to Hold Up (Part 3)

Today’s Astronomy Picture of the Day is a brilliant image of the constellation Orion. The photograph boasts some of the brightest stars in the sky and serves as a shining roadmap for finding famous stars and planets. The presence of stars in the sky brings us to the Inverse-Square Law.

An inverse-square law is a description of physical phenomena in which the strength of the phenomenon is inversely proportional to the square of distance from its source.  If you want to test out this intensity factor, turn off all of the lights in a room but one, then stand with your eyes one centimeter away from the one lamp.  As a matter of fact don’t do that, just imagine the experience and avoid the pain and potential vision loss.   The intensity of the lamp from this distance would be extreme. If you spent any amount of time at this distance the heat from the lamp would likely burn your eyes and face and the light would drown out anything else in your field of vision.

Now imagine that you move to a distance of 10 cm from the light. At this distance the light would still be bright, but not unbearable.  Again, don’t try this, just imagine the difference.  While you have only moved 10 cm from the source the intensity has dropped 100 times.  The calculation according to the inverse-square law looks like this.

Intensity = 1/10² = 1/100

Now move 100 cm away from the lamp. Go ahead and do this one, it should be safe. The intensity of the light is now 1/1000 of the intensity at 1 cm and may be bright but hardly uncomfortable. From this distance you can easily read a book or magazine because the light is bright enough to perform tasks but not too bright to cause you to turn away. 

Within the distance of an arm’s length or the depth of a refrigerator, the light’s intensity has transitioned from unbearable to useful. Continue moving away from the light and the intensity continues to decline exponentially.  On the far side of the room you might begin to strain to see the words on the page and from a city block away the words would fade into the surrounding darkness as you view the point of light that shines in the distance.

The inverse-square law relentlessly degrades the intensity of the light to a point that it appears insignificant, without impact, arbitrary.

So when does the inverse square law stop holding up? More later.

Special thanks to my pal Tim who introduced me to http://apod.nasa.gov/apod/ and expertly narrated the captured night sky shown in today picture.