Transcript Triangulation

Triangulation
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
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
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
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
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
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
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
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.
Triangulation
parallax
The apparent motion of a relatively
close object with respect to a more
distant background as the location of
the observer changes.
Triangulation
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
The amount of parallax is inversely
proportional to an object’s distance.
Small parallax implies large distance, and
large parallax implies small distance