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When a Ruler Is Too Short

Surveyors are often seen in the middle of the street making careful measurements of angles with their transits, and distances with their steel tapes. For points than can be easily reached, such a survey is convenient. But when the target is inaccessible – a mountain summit or a distant star – known distances can be combined with measured angles to determine a distance or altitude. The method relies on parallax, the way an object appears to move, relative to a more distant background, when viewed from different angles. In 1838, Friedrich Wilhelm Bessel became the first to successfully apply this method to a star, measuring an angle of <0.5 second of arc for the summer star 61 Cygni. (One second of arc is the angle you get when you divide one degree into 3600 equal parts. For comparison, the Moon’s diameter as seen from Earth is about 0.5 degree, or 1800 arcsec.) A new NASA mission, SIM PlanetQuest, applying the same technique to determine stellar distances, will measure angles to an accuracy of one microsecond (one millionth of a second) of arc!

Stephen J. Edberg
Date Accepted: 2005-08-25 Grade Group: High School (9-12) Benchmarks: M3.3.9 M3.3.11 M3.3.17 M3.4.3 M4.3.3 M4.3.7 M4.4.4 M4.4.6 S15.3.3 S15.4.4 Keywords: star distances parallax trigonometry geometry triangle distance angle small angle approximation estimation Microsoft Word: 04_28_05_1.docx PDF Document: 04_28_05_1.pdf