Seeing What Can’t Be Seen



What do I mean by seeing what can’t be seen?  What I mean is simply this: that one of the amazing things about stars is that all of them (except for our own Sun) are too small to be seen; nevertheless, we can see them.  Well, what do I mean by “too small”?  They are hundreds of thousands, if not millions, of miles across; how can they be too small to be seen?

Say for example that your twenty year-old six-foot-tall son is standing near you.  Well, he looks to be six feet tall.  If he steps back so that he’s twenty feet away from you, he still appears to be six feet tall, even if he takes up less space in your mind’s eye.  And if he steps away so that he’s a block away from you, you may be able to imagine that he’s still six feet tall, but he takes up even less of what your eye can take in at that distance.  You can imagine that there is a distance that is so far from you that you can no longer see him.  Will you go along with me that he will be too small to see if you’re in New York City and he’s standing in Paris (flat Earth assumed!), some 5000+ miles away?  Good.  Because at that distance, he “subtends an angle” (when something is so far away from you that you cannot possibly measure how big it is, the only way you can measure it is by the size of the angle defined by a) the top of the object, b) your eye, and c) the bottom of the object; thus, the object subtends an angle of some size, measured in trigonometric terms, degrees) that is less than 1% of one second of arc (1 second of arc = 1/3600th of a degree).  He is now far “too small to be seen.”

But what is the smallest thing that an eye can see?  Expensive art magazines use a printing process that resolves (distinguishes) 3000 dots per inch.  The human eye cannot resolve that small a single dot, but it is probably near what we can see at our best.  At two feet away, a likely distance to view such a magazine, one of these dots “subtends an angle” of 3 seconds of arc, pretty good if you can make it out but not good enough to be able to see a star with!

The nearest star from the Sun is 4 light years (24 trillion miles, is that any clearer?  At these unimaginable distances nothing really makes sense) away from us and is roughly the size of our Sun.  This star “subtends an angle” that is roughly 1% of one second of arc, 300 times smaller than that magazine dot, and about the size of the basketball your son is holding 5000 miles away!  Thus, the nearest nighttime star is “too small to be seen.”

Rigel, a very large star in Orion, is some 910 light years away from us, some 225 times as far from us as our nearest neighbor (see above).  It is also some 35 times as large (in diameter) as our Sun.  Rigel, therefore, subtends an angle a bit larger than 1/10th of 1% of a second of arc, a rather small object, wouldn’t you say.  It is ten times smaller than our neighbor star above; it is like seeing the pingpong ball your son is holding in Paris!  Yet, when Rigel is up in the night sky, you will never fail to see it, as it will be one of the brightest celestial objects out that night!  Rigel is 3000 times too small to see, 3000 times as small as that magazine dot!

So, what’s the trick?  Light is the trick.  It seems that light is so remarkable that even if it is “too small to be seen” you will be able to see it!  Go figure!