The lengths scientists go to define units of measuring distance
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
16 June 2019
Last week we saw how
the nautical mile was initially defined in terms of the size of arc on
the surface of the earth. It was intended to be equivalent to one minute
of arc of a latitude; that is one-sixtieth of a degree.
Of course, such a
definition encounters an immediate challenge because it depends on where
on the earths surface this measurement is taken. For that reason, the
international community agreed to fix the definition to exactly 1,852m.
This is was a good
move because the metre is defined in a way that doesn’t depend on the
location of the experimenter. You can be anywhere in the universe and
the definition will give the exact same result!
One metre is the
distance that a beam of light travels in a 299,792,458th of a second;
and one second is the duration that elapses during 9,192,631,770 cycles
of a cesium-133 atomic clock. Complex, isn’t it?
Well, it hasn’t
always been like that. One meter was initially defined as a 10,000,000th
(ten millionth) of the distance from the North Pole, through the town of
Dunkirk in France, to the equator.
Now since that
journey is a quarter of the way around the earth, this definition put
the circumference of the planet at 40 million metres, that is, 40,000km.
That’s not very far off from the current average distances measured by
satellites - about 40,008km.
The major challenge
is that, measurements of the of the earth’s circumference will always
have a margin of error – however small – and it is not desirable to define
a standard unit using a quantity that has errors. Hence the current
definition using the movement of a beam of light.
There is another unit
of measuring distance that borrows a leaf from the nautical mile –
defined in terms of the size of an arc. This is the parsec used by
astronomers.
To understand what it
is, imagine drawing a very large, right-angled triangle whose base is a
line joining the earth to the sun – a distance of approximately 150
million kilometres.
The third point of
this triangle is located some great distance in space in a way that the
angle at the sun is 90 degrees. Close your eyes and visualise it…
Now, how far would
this third point have to be in order for the angle its location to be
one second of an arc? As a reminder, one degree is divided into 60
minutes of arc, and each minute of arc is split into 60 seconds.
Thus, one second of
arc is 3,600th of a degree – very small indeed. Applying basic secondary
school geometry, it is easy to establish that the third point of this
astronomical triangle will be about 31 trillion kilometres in space.
Unfortunately, again,
the basic input in this definition varies greatly. The distance from
earth to the sun is not constant – it changes from about 147 million to
152 million kilometres during the year.
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