Parallax Measurements

 

Parallax is the apparent shift in an object’s position (with respect to its background) as seen by a moving observer (or by an observer who shifts positions).  It is what gives our vision the three-dimensional stereoscopic effect of depth perception when we have both eyes open.

 

Try this:  With one eye open, try to grab a pencil held vertically by a friend a few feet away from you.  It is not easy.  Now try to grab it as you move your head from side to side, keeping only one eye open.  It is much easier, because you are giving your brain the information of depth by moving your head from side to side. 

This is parallax at work.  Since most humans have two eyes, we do not need to move our head from side to side to gather depth information—it is automatic.

 

Things to notice:  As you walk outside, notice the objects closer to you seem to move quicker then objects fixed at a distance, like the mountains.  The angular shift in position of closer objects is thus greater than those that are far away.

 

Try this:  Look at your thumb with your arm outstretched.  Now relax your eyes into the distant horizon until you see two images of your thumbs.  The angle between your thumbs should be about ¾ of a hand width, or about 7.5° of angle (about 7 ½ pinky widths at arm’s length, in other words).  Now have your friend hold a pencil vertically about 2 to 8 paces from you.  Blink one eye, then the other, to see a shift in the pencil’s position (or, keep both eyes open and focus on the distant horizon to see two images of the pencil).  Approximate the apparent shift in angle of the pencil by using your pinky (remember, one pinky width at arm’s length is about 1° angle).  It should be less than the 7.5° angle shift that your thumb made.  Divide the 7.5° by the angular shift made by the pencil.  The resulting number should be the approximate distance (in “arm lengths”) to the pencil.  It is not an exact value*, but will provide a close approximation of the pencil’s distance.

 

A similar method was used to measure the size of the Moon’s diameter (using two cities and the Moon’s position amongst the fixed stars) and the distances to objects in the local Solar System (using two Earth positions and the object’s position amongst the fixed stars).  Distances to stars could not easily be found using parallax.  Why?

 

(*It works for small angles, because for small angles, the tangent of the angle is approximately the value of the angle itself.  You don’t need to know this, but if you happen to take trigonometry later, this will make more sense to you.)