It was natural for humans to use their own dimensions as a basis to measure distances. Thus arose the inch, the width of a thumb; the span, the width of the palm of the hand with spread fingers; the foot, the length of a human foot; the cubit, the distance from the elbow to the tip of the middle finger; the fathom, the distance between the two hands with outstretched arms; the pace, the distance between the two feet while walking; and so on.
This system of measurement has two problems. The first: that these lengths depend on each person. The second: that they are not simple multiples of one another. To solve the first problem, standard values were introduced. To solve the second problem, some of the measurements were slightly modified. Thus, in England, the inch was approximated by one-twelfth of a foot. This introduced a third problem, because each country chose different standard values and made approximations in its own way.
The first to suggest the desirability of adopting a
unified and international system of measurement was a French mathematician,
Gabriel Mouton, who did so in 1670. However, his suggestion was only adopted over
one century later, during the French Revolution, because the revolutionaries
believed that a new era was beginning and wanted to break with the constraints
of the past. Therefore, they invented a new calendar, which failed, and a new
system of measurement, which, due to its simplicity, soon spread throughout
almost all of Europe.
The fundamental unit of the new system was called
the meter
(measure). Multiples and sub-multiples of the fundamental unit were obtained by
multiplying or dividing by powers of ten. For this reason, its full name became
the decimal metric system.
The meter was defined as one
ten-millionth of the quadrant of the Earth's meridian passing through Paris. This is the same as assigning, by definition, to
the circumference of the Earth a length of 40,000 kilometers (40 million
meters). This definition had the problem that accurately measuring such a
length is very difficult, and although expeditions were undertaken to remote
locations, considerable errors accumulated. Therefore, the First General
Conference on Weights and Measures in 1889 (I GCWM) changed the definition of
the meter to this:
The length
of the meter is the length of the international prototype deposited in the
Archives of France, made of platinum alloyed with 10% iridium.
This alloy was chosen because its length is very
little affected by environmental conditions (humidity and temperature). Each
country obtained a copy of the standard meter, whose error, compared to the
original, was less than 0.01 millimeters.
During the 20th century, the precision of
measurements increased, and new definitions of the meter were needed. The 11th GCWM
in 1960 established the following definition, which increased precision a
thousandfold:
The meter
is the length of 1,650,763.73 wavelengths in a vacuum of the radiation of the
transition between the 2p10 and 5d5 levels of the
krypton-86 atom.
But this precision also fell short, and in 1983 the
17th GCWM adopted the following definition of the meter, which remains in force
and provides a precision 25 times greater than that of the previous definition:
The meter
is the length of the path traveled by light in a vacuum during 1/299,792,458 of
a second.
To this must be added the prefixes for multiples
and sub-multiples, which since the latest addition of the 27th GCWM in
2022, go from 10-30 to 1030. With them, the definition of
the meter is useful for all practical applications that can be carried out on
Earth and in the solar system, but it isn’t used for the distances that
separate us from stars and other galaxies, for which two other units were
invented. The first is called a light-year,
and is the distance traveled by light in one year. Since the speed of light is
299,792,458 meters per second, to calculate the length of a light-year, simply
multiply that speed by the number of seconds in a year (60×60×24×365.2422),
which gives the following result:
1
light-year = 9.46 petameter
Where 1 petameter is 1015 meters or one
trillion kilometers.
The second unit of measurement for astronomical
distances is called a parsec,
short for parallax-second, which means a parallax of 1 second, and is the distance from which the radius of the
Earth's orbit around the Sun would be seen at an angle of one arcsecond:
1 parsec =
3.26 light-years
The parsec is, therefore, a unit of measurement
quite close to the light-year. The choice between one or the other is a matter
of preference.
 |
| Milky Way |
Within our galaxy (the Milky Way), these two units are very useful, as its diameter
measures around 100,000 light-years. But as soon as we move to other galaxies,
the distances reach millions of light-years (or megaparsec), and for the most distant ones, billions of
light-years (gigaparsec). There's no need to go any further, since the
maximum distance we can see (the cosmic microwave background radiation) is
located approximately 46 billion light-years away, equivalent to about 14.11
gigaparsec, or about 435 yottameter (1024 meter).
Recall that the light that emerged from the cosmic
microwave background radiation about 13.8 billion years ago has had to travel
through an expanding universe, which has extended its wavelength into the
microwave region, and the distance it has traveled through has lengthened until
it is now more than three times longer. Therefore, the radius of the visible
universe from our location is equal to about 46 billion light-years.
Thematic Thread on Science and History: Previous Next
Manuel Alfonseca
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