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triangulation Method of determining distance based on the principles of geometry. A distant object is sighted from two well-separated locations. The distance between the two locations and the angle between the line joining them and the line to the distant object are all that are necessary to ascertain the object's distance. Triangulation

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Surveyors often use simple geometry and trigonometry to estimate the distance to a faraway object. By measuring the angles at A and B and the length of the baseline, the distance can be calculated without the need for direct measurement. Triangulation

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cosmic distance scale Collection of indirect distance-measurement techniques that astronomers use to measure the scale of the universe. baseline The distance between two observing locations used for the purposes of triangulation measurements. The larger the baseline, the better the resolution attainable. Triangulation

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To use triangulation to measure distances, a surveyor must be familiar with trigonometry, the mathematics of geometrical angles and distances. However, even if we knew no trigonometry at all, we could still solve the problem by graphical means Triangulation

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Suppose that baseline AB is 450 meters the angle between the baseline and the line from B to the tree is 52°. We can transfer the problem to paper by letting one box on our graph represent 25 meters on the ground. Drawing the line AB on paper, completing the other two sides of the triangle, at angles of 90° (at A) and 52° (at B), we measure the distance on paper from A to the tree to be 23 boxes—that is, 575 meters. We have solved the real problem by modeling it on paper. Triangulation

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Narrow triangles cause problems because it becomes hard to measure the angles at A and B with sufficient accuracy. The measurements can be made easier by "fattening" the triangle—that is, by lengthening the baseline—but there are limits on how long a baseline we can choose in astronomy. Triangulation

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This illustrates a case in which the longest baseline possible on Earth—Earth’s diameter, from point A to point B—is used. Two observers could sight the planet from opposite sides of Earth, measuring the triangle’s angles at A and B. However, in practice it is easier to measure the third angle of the imaginary triangle. Here’s how. Triangulation

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This imaginary triangle extends from Earth to a nearby object in space (i.e. planet). The group of stars at the top-left represents a background field of very distant stars. Hypothetical photographs of the same star field showing the nearby object’s apparent displacement, or shift, relative to the distant, undisplaced stars.

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parallax The apparent motion of a relatively close object with respect to a more distant background as the location of the observer changes. Triangulation

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The closer an object is to the observer, the larger the parallax. Do this now: Hold a pen vertically in front of your nose and concentrate on some far-off object—a distant wall. Close one eye, then open it while closing the other. You should see a large shift of the apparent position of the pencil projected onto the distant wall—a large parallax. Triangulation

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The amount of parallax is inversely proportional to an object’s distance. Small parallax implies large distance, and large parallax implies small distance Triangulation

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Cosmic Distances How do we determine the distance to celestial objects? No single method works at all distances… close, intermediate and far. Astronomers.

Cosmic Distances How do we determine the distance to celestial objects? No single method works at all distances… close, intermediate and far. Astronomers.

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