Title: triangulation
1Triangulation
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.
2Triangulation
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.
3Triangulation
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.
4Triangulation
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
5Triangulation
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 boxesthat is, 575 meters. We have
solved the real problem by modeling it on paper.
6Triangulation
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 trianglethat
is, by lengthening the baselinebut there are
limits on how long a baseline we can choose in
astronomy.
7Triangulation
This illustrates a case in which the longest
baseline possible on EarthEarths diameter, from
point A to point Bis used. Two observers could
sight the planet from opposite sides of Earth,
measuring the triangles angles at A and B.
However, in practice it is easier to measure the
third angle of the imaginary triangle. Heres
how.
8Triangulation
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 objects apparent displacement, or shift,
relative to the distant, undisplaced stars.
9Triangulation
parallax The apparent motion of a relatively
close object with respect to a more distant
background as the location of the observer
changes.
10Triangulation
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 objecta 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 walla
large parallax.
11Triangulation
The amount of parallax is inversely proportional
to an objects distance. Small parallax implies
large distance, and large parallax implies small
distance