English 233: Introduction to Western Humanities - Baroque & Enlightenment

Glossary of Terms:

Parallax

Parallax itself is something that can be observed (though it amounts to at least what we might call a composite observation, since it involves a comparison of two separate observations made at two different locations (and sometimes at two different points in time). Taken together with the principle that two objects that show different parallax stand at different distances from the observer, the parallax of an object is a basis for inferring the distance of the object from the observer.

An easy way to appreciate this is to consider what is known as BINOCULAR PARALLAX. This is the apparent difference in the position of an object as seen by one eye from its position as seen by the other eye while the head is kept in a fixed position. (It is the same as the angle - sometimes called the optic angle - between the optic axes of the two eyes when directed to a single point.) Try this:

Extend your arm and point your thumb upwards so that you are looking at your thumbnail, directly in front of your face (i.e., not out to one side or the other). Now close one eye. Through your open eye, notice where your thumb is positioned against the background in your field of vision (the furniture on the other side of the room or the building out across the lawn, as the case may be). Now, keeping your head and thumb steady, close that eye and open the other. What do you notice about the position of your thumb against the background (which has also remained stationary)?

Now let's bring your thumb in towards your face, to a point let's say about a foot in front of the midpoint between your eyes. Repeat the same procedure. Again you note the way your thumb appears to jump from side to side against the stationary background. In which case did it appear to jump further?

The difference in the apparent displacement of an objects sighted from the same pair of standpoints varies in a regular way with the distance of those objects from the observer. This means relative apparent displacement can be used to calculate distance.

The same principle can be used to measure distances far beyond what we can register with binocular parallax. Our eyes are only a couple of inches apart. But if we increase the base the triangle formed by the two points of observation and the object observed from two inches to (say) the distance between London and Rome, we can register much greater distances. (When people finally accepted the Copernican hypothesis, it was possible to use the diameter of the earth's orbit at its widest extent, by taking two measurements at half-year intervals!)  Using trigonometry, astronomers calculate angle at the apex (the observed object) of the triangle formed by the sighted object and the two observatories. Since this angle gets progressively more acute the farther the object is from the earth, its size can be translated into a measurement of the distance from the earth of the various heavenly bodies (with the exception of the fixed stars, which as are at such a distance as to show no parallax with the instrumentation available to Tycho Brahe, although with telescopes some of them do eventually begin to reveal that they are closer to us than others).  This diagram may be useful to help you visualize how the idea works.

  Go to discussion of Tycho Brahe's use of parallax measurements.


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      Contents copyright 1999 by Lyman A. Baker

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      This page last updated 01 February 1999.