Triangulation is a method used to measure vast distances like between Earth and Alpha Centauri. It involves using two observers located a few kilometers apart who measure the base angles to an object. By knowing the baseline distance between the observers and using trigonometry, the distance to the object can be calculated from a scaled drawing. However, for very distant stars the angles appear the same from both points, and with too short a baseline the method is limited.

1. Triangulation

2. How can we measure vast distances, like the
distance between earth and Alpha Centauri?
Triangulation
?
?
?

3. Triangulation
?
To do this, two observers are located at 'A' and
'B' separated by a few kilometers (baseline)
A B
baseline

4. Triangulation
?
A B
The base angles at A and B can be measured
with a protractor or theodolite.
baseline
x y

5. ?
Theodolite:
Triangulation

6. Triangulation
?
By knowing the baseline distance, the distance D can
be worked out with a simple scaled drawing
A B
baseline
D
x y

7. Triangulation
?
For example:
A B
5 m
D
50 55
How do you make a scaled drawing?

8. Triangulation
?
For example: How do you make a scaled drawing?
5 cm
1) Draw the bottom line to scale (ex. 1 cm = 1 m)

9. Triangulation
?
For example: How do you make a scaled drawing?
5 cm
50 55
2) Draw the two angled lines

10. Triangulation
?
For example: How do you make a scaled drawing?
5 cm
D
50 55
3) Measure distance D

11. Triangulation
?
?
Limitations:
1 km
Stars are so far away that the angles appear to be
90 , as if the star is straight up for both observers

12. Triangulation
?
Limitations:
1 m
D
Similar problem exists when two observers stand
too close (baseline is too short)

13. Triangulation
?
Solution:
To solve this
problem, astronomers use
trigonometric
parallax, where they use
photography to measure the
vertex angle of the triangle

14. Triangulation
?
Solution:
D
You can solve this problem by standing farther apart.