Using triangulation to measure size of large objects
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
14 January 2024
After reading the
article of 31st December 2023 about the scale of the
universe, Joseph Maina wrote in with a simple question: “Scientists
believe that the universe is 13 billion years old; how do they arrive at
such large numbers? Who was there at the beginning to record the date of
birth of the universe?!”
Well, the first
things first: science is not concerned with people’s beliefs; it is
about measurements. So, the question needs to be rephrased thus: how is
the age of the universe measured? The answer is in trigonometry – the
geometry of triangles.
A triangle is an
intrinsically rigid shape. If you know two of its angles, then you can
evaluate the third one. And, if you know if you know two lengths and the
angle between them, you can work out the third length as well as the
remaining two angles.
To understand how
this knowledge of triangles is applied in measurements of the universe,
let us start with something more down to earth. How can one measure the
height of a mountain? How do we know that the highest peak of Mt Kenya,
for example, is 5,199m above sea level?
We start by looking
at the peak from some (unknown) distance away and measure the angle
between our line of site and the horizontal plane. Next, you move a
closer to (or farther away from) the mountain and measure the distance
moved accurately – say one kilometer. Now we view the peak again and
determine the new angle between the line of site and the horizontal
plane.
Now we can form a
triangle with three points: our starting position, the peak of the
mountain and our final position. In this triangle, two angles have been
measured: from you first and final positions. Therefore, its third angle
(at the peak) can be calculated by trigonometry.
The horizontal
distance to the centre of the mountain can also be calculated, and, with
that value, we can evaluate the height of the mountain above our
position. With similar measurements, we can determine our elevation
above sea level and add that to the height of the peak above our
location to get the measurement above seal level.
Try and visualise
these steps over the coming week and, next week we shall see how similar
principles are applied in astronomical measurements…and how these relate
to the age of the universe.
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