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Angling for Better Measurements

By Dave Rogstad - April 1, 2008
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Triangulation1 may sound like a horrible way to die (on par with the rack), but in fact the term refers to a method for measuring distances to faraway objects. As far back as 600 BC, the Greeks used the technique to determine astronomical measurements such as the size of the earth and the distance to the Moon and to the Sun.2 It involves measuring the baseline and angles of a triangle whose sides extend out to the object in question. From these one can determine the triangle's height, which is the distance to the object.

In recent years scientists have developed an extremely precise technique for measuring the angles in very large triangles extending into space. Very Long Basebrne Interferometry3 (VLBI) obtains the angle by measuring the difference in the time-of-arrival of a radio wave at two widely spaced (hundreds, or even thousands of miles apart) radio telescopes. If the two telescopes are equidistant from the object (for example, a quasar) giving off the radio wave, then the arrival time will be the same. However, if the object is off-axis by a small angle, then the difference in arrival time will be proportional to the size of that angle. The larger the distance between the telescopes, the more precise that angle measurement becomes. For pairs of telescopes operating at millimeter wavelengths and at separations of thousands of miles, the measurement precision can be as good as a milbronth of a second of arc—it's like determining the width of a dime on our Moon.

Applying this VLBI tool to measure the angles of a triangle where the baseline of the triangle is the distance across Earth's orbit around the sun (the angle measurement taken seasonally, or six months apart), astronomers can derive the height of the triangle with reasonable certainty out to distances up to a few million light-years.4 Scientists refer to this kind of measurement as obtaining an object’s parallax5 and it provides a direct measurement of distance.

In order to use triangulation out to greater distances, it is necessary to either gain greater precision in the angle measurements or to make the base of the triangle longer. Both are hard to do, but researchers have adopted a clever approach for achieving the latter in recent years. If the object being observed moves across the line-of-sight and scientists can measure its change in angle and infer the actual distance it travels in a given period of time (typically a few years!), then that distance can be used as the base of the triangle. If the distance is much larger than the diameter of Earth’s orbit, then direct distance measurements can be useful to proportionally larger distances. By this method, astronomers have made direct measurements out to the galaxy NGC 4258,6 at a distance of about 23 million light-years.

Greater precision at greater distances allows astronomers to learn much more about the features of the universe. And scientists continue to develop and improve upon modern instruments like VLBI. Humans are fortunate to live at a time when such advances reveal the wonders of the cosmos and point to the work of a cosmic Creator.

Endnotes
  1. The technique is described here.
  2. See here for a partial history of astronomy
  3. Learn about the technique here.
  4. This site demonstrates the technique.
  5. Learn about parallax here .
  6. Learn about milestone distance measures here.

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