Long Distance Voyager

By The Metric Maven

Bulldog Edition

When it comes to distance, the larger metric prefixes are generally neglected. Astronomers feel justified in using Astronomical Units to describe distances within the solar system. When distances become large enough, the ubiquitous light-year is then employed with great relish and awe. One of the arguments offered for the absence of the larger metric prefixes in astronomy, is that the distances are just too large, and the metric system is overwhelmed. The distances are just too astronomical for the metric system to handle!—or even convey their vastness! Generally, this manner of argument masks a provincial desire by a specialty of engineering or science to have its “own” special measurements. It is also stated that people can only relate to Km and smaller metric measures because the other distances are outside of their everyday experience.

I have had the privilege of working with some incredibly talented engineers, including the Engineer, who designed the high gain dish antenna which resides on the front of the Voyager spacecraft. His name is Michel, and I once shared an office with him. The Voyager antenna would at one time have been within millimeters of Michel, it was then moved about 4000 Kilometers away from him so it could be launched into space on September 5, 1977 (1977-09-05). It ascended from our planet, which has a circumference of 40 Megameters. Michel’s antenna then passed the orbit of the moon which is about 384 Megameters from Earth. One could argue that the Voyager spacecraft was now in the realm of the solar system. At that point, its distance from the sun might be a more meaningful reference point to describe its distance from us. The Earth is approximately 150 Gigameters from the sun.

Gigameters is a useful length to describe the distances of our planets from the sun, as well as the current location of the Voyager spacecraft (2014-04-04). Michel’s antenna is part of the singular human-constructed object we call Voyager 1, and is further away from the Earth than any other space probe in history—and likely to remain so. Despite the fact that Voyager is now beyond our solar system, its distance is still readily describable in terms of Gigameters. Below is a table of planetary distances and Voyager 1 and 2:

I don’t recall any astronomers ever using Gigameters in school or on television, even though it is a convenient unit. Astronomers define their own “yardstick” which they call an astronomical unit. This astronomical unit is defined as the distance from the earth to the sun, therefore 1 AU = 150 Gigameters. I don’t see why modern astronomers, by which I mean astronomers who have been born after 1960, don’t use Gigameters instead. The prefix Giga was officially adopted in 1960. A Gigameter is certainly as convenient of a unit as an AU, and it’s tied to the meter, which is the universal measurement length used by science, and by 95% of the worlds population. When a person, even an American, sees the symbol Km, they see kilometers. The lack of use of the designation Gm for Gigameters by astronomers makes it unfamiliar and seemingly awkward. It is only the lack of general use which makes this so.

When Astronomers begin to describe distances outside of our solar system, they generally turn to another unit they coined which is unique to astronomers—the light-year. Wikipedia gives the definition of  a light-year as:

1 light-year     = 9460730472580800 metres (exactly)

This is where, if I were forced to write it in meters, I would use the three digit space convention to parse it. The three digit grouping allows a person to identify the appropriate metric prefixes with ease:

1 light-year     = 9 460 730 472 580 800 metres (exactly)

This expression allows one to immediately recognize the metric prefixes as one moves from right to left as: one, Kilo, Mega, Giga, Tera, Peta, and determine that 1 light-year = 9.461 Petameters (Pm). In my view the light-year is more of a “gee whiz” measurement metaphor than an actual length. It is like the kilowatt-hour. There is a metric prefix which is of sufficient magnitude to describe distances which have magnitudes in terms of light-years and it is Peta. The hypothetical Oort cloud is believed to be about 7.5 Petameters away, which when compared with stars, it not  far away.

Almost everyone knows that alpha-centari is the star closest to Earth (other than the sun). It is 4.366 light-years distant. This is 41.4 Petameters. So even when we are discussing the distances to stars, there is a sufficient metric prefix. The light year is not required, at least not after 1975, when Peta was adopted as a metric prefix. Here is a list of nearby stars, and a more distant one in Petameters:

Constellation of Orion Betelgeuse is the upper left star which is about 6 Em from Earth. Rigel is on the lower right and about 8 Em from Earth — Click to enlarge                    (Wikimedia Commons)

Betelgeuse is a red giant which is in the upper left corner of the constellation Orion. On a clear night in Montana, when I lived far away from the city lights, I could clearly see its red color. Stars beyond Betelgeuse are at distances that may require the introduction of another metric prefix.  This would be the prefix Exa.  One could categorize stars which are “near” earth as those up to 1000 Pm and those beyond 1 Em (Exameter) as “far away” stars. This would make Alpha-Centari, Barnard’s Star and Sirius all nearby stars. Far away stars would include Betelgeuse (6.1 Em) and Rigel (7.7 Em). The farthest currently known star which is still inside of the Milky Way Galaxy is  UDF 2457. It is 558 Em distant.

When we approach the dimensions of the Milky Way Galaxy, we may want to describe the distances from the galactic center. The diameter of our galaxy dwarfs the distance from the sun to Betelgeuse. It is 1 000 000 Petameters across or, shifting metric prefixes, is approximately 1 Zettameter (Zm) in extent. From this information, we know that no star within our galaxy is more than a zettameter away.

The Andromeda Galaxy is 24 Zm from Earth and is visible with the unaided eye.                      (Wikimedia Commons)

Interestingly, we can directly see a distance which is much farther than the dimension our galaxy with the unaided eye. The nearest spiral galaxy is Andromeda, and it can be viewed with the “naked eye.” The Andromeda Galaxy is 2 540 000 light-years away or approximately 24 Zettameters (Zm). This is rather close. It is only 24 times the diameter of our galactic disk. The Andromeda galaxy is expected to collide with our Milky Way Galaxy in 3.75 billion years and form a large elliptical galaxy. Andromeda is not the nearest galaxy overall. The Sagittarius Dwarf Elliptical Galaxy is actually a satellite Galaxy of the Milky Way, that is, it orbits our galaxy. It is only 0.77 Zettameters from our galaxy (or 766 Exameters). This places it just a couple of hundred Exameters beyond the farthest known star within the Milky Way Galaxy.

Here is a short list of local group galaxies which are over one Zettameter away:

The Sombrero Galaxy is 265 Zm from Earth (Wikimedia Commons)

Sextans B is near the end of what is known as the local group of galaxies. The local group encompasses a diameter of about 100 Zettameters (Zm). Clearly there are lots of galaxies which are further away, so which one is the farthest known? The current candidate for the furthest galaxy is MACS0647-JD which is a whopping  125 825 Zettameters (Zm). We can see that we are well beyond a 1000 difference. Has the metric system let us down because of this astronomical distance? No, it has not, at least not since 1991. In 1991 both the Zetta prefix, and the Yotta prefix were added. The Yotta prefix allows us to write the distance to the farthest confirmed galaxy as 126 Yottameters (Ym). The end of the observable universe is approximately 435 Yottameters (Ym). The diameter of the universe is 870 Ym. Astronomical distances do not crush the metric system. There is no need for astronomers to resort to a light-year or AU or parsecs to describe astronomical dimensions. The metric system can in fact be useful to classify astronomical distances. For instance:

— click to enlarge

Neil deGrasse Tyson — Host of Cosmos

The latest incarnation of Cosmos has been interesting to watch, but I can only wince when I hear Neal deGrasse Tyson use miles, billions of kilometers, astronomical units, and light-years to describe the cosmos. This archaic measurement usage seems like a lack of respect for the metric system on the part of the Cosmos producers. It is 34 years after the original series was aired. When the original Cosmos aired, the Zetta and Yotta prefixes had not been added to SI. One could see why metric might not have been invoked. Indeed, SI was not large enough to encompass the universe, but like the universe, it expanded. Unfortunately, the root cause for the lack of the metric system in Cosmos could possibly have an even less desirable origin—it could just be unawareness. It is even possible it is the product of a culturally encouraged unfamiliarity. This culturally sanctioned ignorance, if that is the root source, was fortified at the same time as the first airing of Cosmos in 1980. It was in that year that Ronald Reagan quashed any possibility of measurement reform in the US, by disbanding the metric board. This disbanding was an attack on modernity and efficiency, mantled in a red herring of cost savings. It was a narcotic of intellectual flattery perpetrated by a cultural embargo, which has numbed the minds of the American public to the spectrum of metric prefixes, and in turn, it has cost lives. If there is another edition of Cosmos 34 years from now, I can only hope, that by then, it uses the metric system.

This essay was edited on 2016-10-15 to conform with The Elements of Bile.

19 thoughts on “Long Distance Voyager

  1. Agreed, good article (except maybe for the last paragraph). The Metric Board was SO useless as constructed that it probably did more to prevent than to cause metrication in the US. It perhaps should have been fixed instead of abolished, but lets be honest, Congress controls the purse strings and the legislative process and has never “walked the talk.” Congress defunded it, Reagan recognized reality. I think you demonize the wrong person. You should look at the people appointed (several anti-metric), the lack of meaningful authority or responsibility, the defunding, and who really controlled those decisions

    Back to astronomy. Their special units are confusing. Sure a lightyear is how far light goes in a year, but there are common years, leap years, Julian years, Gregorian years, tropical years (and the length of the year changes slowly over time. Turns out the IAU uses the Julian year, 365.25 days of 86 400 SI seconds to define it. The nice thing about using metric prefixes is that it doesn’t look so different in “full decimal dust” and “reasonably rounded” modes:
    9.460 730 472 5809 Pm or 9.461 Pm.

    Using prefixes “properly,” we could certainly express distances up to 999 Ym, or about 105 billion light years. Since the universe has been expanding at less than the speed of light for some 14 billion or so years, we’re covered, even if we don’t know EXACTLY how big or old the universe is.

    The earth’s orbit is elliptical and varies so the AU is more of an average distance, and it also changes slowly over time like the tropical year. It is accepted for use with the SI in table 7 of the SI Brochure although the value given there is out of date. The IAU went the adopted value route in 2012, setting the value at 149.597 8707 Gm exactly.

    Astronomers tend to actually measure long distances in parsecs and use the lightyear more for public consumption. The parsec is the distance at which 1 AU subtends an angle of 1 arc second (and assumes the tangent of theta equals theta for small angles). This works out to 648 000/pi astronomical units, 30.856 776 Pm or about 3.261 56 light years.

    • If the Universe is finite and expanding, then there must be a centre. So, where is the centre of the Universe?

  2. DeGrasse, recently…

    http://www.joyoftech.com/joyoftech/joyimages/1991.gif

    🙂

    Jokes apart, the AU, the light-year and the parsec are all based on Earth-centered and/or non-decimal units, such as the year and the arcsecond: ‘customary” units, thus; perhaps even intuitive, but not really coherent with the metric system, of course.

    BTW, Carl Sagan, IIRC, correctly used the metric system in the first Cosmos – but those were more progressive times, perhaps…? At least, the “future” still existed, in the collective imagination.

    Great article, BTW… 🙂

    DeGrasse of course is a good guy, but he must also “follow” the (perhaps not so good?) “times”, so to speak…

    • Just a correction: the parsec isn’t even “intuitive”, like the AU or lightyear…

      Of course, as said in the article, it would be much better to just use SI prefixes, both for the macro- and microcosmos.

      And also to have a decimal and SI-scalable time measurement, eventually, if possible…

      • One man’s “intuitive” is another’s “mind boggling complexity.” The parsec is pretty intuitive to astronomers actually measuring apparent displacement of nearer stars against galaxies on photographic plates to measure distance. However, it is not trivial to explain to the man on the street; hence the lightyear.

        • Yes, that’s of course true, too…

          But, anyway, the parsec is always based on Earth-centered measurements, which involve the year and the arcsecond, both non-decimally based (even if the “old” sexagesimal angular units could perhaps eventually be superseded by the turn, milliturn, and so on, or something similar): so, it doesn’t seem to be a so good unit, for example, for a future interplanetary, and above all interstellar society (à la Star Trek’s United Federation of Planets, Jack Vance’s Alastor Cluster, Isaac Asimov’s Galactic Empire, Frank Herbert’s Dune, etc. etc., just to name a few possibile future sci-fi scenarios…).

          The same is true for the lightyear, of course: it still involves the year, an Earth-pecuilar unit; but at least it doesn’t involve sexagesimal angular units…

          Anyway, the speed of light being an universal constant (at least, if our current physics is correct – but who knows, eventually…), it makes sense to base very long distances on it; but of course a coherent use of SI would be even better (well, also the meter was originally an Earth-based measure, but that isn’t actually so important, anymore…)!

  3. You have introduced another standard – that of ‘digit group separators’ which also leads us to the various decimal points. The use of the coma as a decimal point has caused many errors and the use of a space between groups also leads to errors.

    The unfortunate choice of the comma by some for a decimal point has made the use of a comma separator common to the USA problematic as 10,001 could be confused with 10.001 – not an error you would want your doctor to make. The other way is also a problem.

    The use of spaces, as you did above is also problematic as it is not clear if 22 888 means 22,888 or is two values. The medical community has standardized on the ‘thin space’ separator.

    so what is probably a format error above:
    1 light-year = 9 460 730 472 580 800 metres (exactly)
    Becomes
    1 light-year = 9 460 730 472 580 800 metres (exactly)

    The use of the thin space for numbers after the decimal point is a no brainer – I’m less happy about the change away from the comma separator for thousands.
    The comma vs point for the ‘decimal point’ should move to the ‘point’ or full stop – as the term seems to specify that already.

    Besides, what happens if we have 123,456 – is it 123 456 or 123.456 ? The coma decimal point should die.

    The use of the thin space is do-able (but not easy) in most word-processors, but the reality is we also write numbers with pencils – and if I need to list 123,456 and 234,567 next to each other, the chance of error becomes a concern.

    The point is there really need to be a usable international standard that works for both pen and keyboard for notating long numbers – not just something a standards group spits out, but one that will be used internationally and reduces errors.

    • Sorry, Karl, I have to disagree. At least in usage with SI data, neither the comma not dot may be used as a thousands separator, and both are accepted as a decimal marker (latest 2003 CGPM Res 10).

      Either a space or thin space may be used as a thousands separator, preferably a thin space. However, in text (as opposed to tables) it may be more important to use a non breaking space. In many browsers, both the entry and display of high value Unicode characters can be problematic. The non-breaking, normal-width space may be a better choice. When writing with a pen, I use a space fat enough for me to be sure there is a space.

      Now with data in Customary units or financial data, the directives for proper usage of the SI have no real authority and are totally ignored.

      The Unicode Narrow Nonbreaking Space is U+202F, and I know how to enter in MS Word, but I frankly don’t know how to enter in IE. I believe it can be entered in Firefox and I could find where to look it up if I had to.

      The countries that use the decimal comma are no more going to give it up than we are going to give up meter and liter over metre and litre. Just go with the rule: neither is a thousands marker.

      • I like what the Swiss do: apostrophe! I write my numbers like: 12’345.67. Fixed! No confusion should someone use a comma radix sign. They do this because English uses a decimal point but German & French use a decimal comma. German uses dots for grouping but IIRC French & Italian use the small non-breaking space (HTML: ‘&nbsp’). Not sure if Italian uses a decimal comma too.

        Something else SI is good for is to get rid of the long/short scale confusion. Some languages use the long scale (Dutch?) but others (English these days) use the short scale. This can cause a lot of confusion. Is 10^12 a billion or trillion? Depends if you’re using long or short scale. 10^9 is a short billion but long milliard.

        • In Italy, the decimal comma is definitely used (even if some journalists sometimes use the decimal point – just to appear more “clever”? who knows…), and the point or apostrophe – as in Switzerland – as a thousands separator (while the ISO-recommended space would of course be better, as in France and Sweden, for example); and in all continental Europe, too, the decimal comma is used, except often for prices, where the point or the colon might be used (and also a dash for the “00” part): for example, in Sweden, 99.00 kronor would be simply “99:-“; while, in other countries, 99 euros might be “99.00” or “99.-“.

  4. Beyond yotta-, bronto- and geop- have been proposed for 10^27 and 10^30.

    Any update on this, or have these been proposed for use with just bytes, and so would only mean 2^90 and 2^100 instead?

    • Binary prefixes involve a “power of 10” SI prefix combined with the suffix “bi”. So, a kilobyte would be 1000 bytes, but a kibibyte would be 1024 bytes.

      So, if bronto and geop were to be added to the list of SI prefixes, the binary prefix would have to be something brontbi(1024^9) and geopbi (1024^10).

  5. I’ve made the point here and on Reddit that metric is improperly taught in most schools and is treated as a parallel unit collection to imperial/USC. Each of the prefixed units is treated as a separate unit when in fact they are not. There is only the metre for measuring distance.

    SI is composed of a set of measuring units and a set of scaling prefixes. No one is taught to pick the appropriate prefix for expressing a value, instead the distance units focus around kilometre (for mile), metre (for foot & yard), centimetre (for inch) and millimetre (for inch fractions).

    If everyone was actually taught and used SI properly, non-metric klingons would disappear over night.

  6. I absolutely agree with the Metric Maven about prefixes to the meter. I have been trying to make the same point for a long time now. The only argument against using Megameters and Gigameters and Petameters et cetera is that only a few people use them. Well I use them and write about them in my short book: An Educational Overview for Americans that is available at MetricPioneer.com. Great article! I love it!

    • Good points DP.

      However, consider this: The mass of the Higgs Boson is about 125 GeV, which is about 225 yg.

      Thus, a prefix, giga- (G), was used, but not in an SI way. Not long after the isolation of a Higgs particle was promulgated on 4 July 2012, we saw the point estimates in GeVs but rarely in yoctograms.

      Such is sort of silly as “grams” are much-more common than “electron volts” to the general public.

      • How can the mass of anything be measured in electron volts? Electron volts are a measure of energy, not mass. By definition, it is the amount of energy gained (or lost) by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, 1 J/C) multiplied by the elementary charge (e, or 1.602176565(35)×10^−19 C). Therefore, one electron volt is equal to 1.602176565(35)×10^−19 J. That is from Wikipedia.

        In order for it to be a mass unit, the electron volt has to be divided by c^2.

        This is a bad practice that is common to imperial and US, where parts of the unit is dropped. Cubic yards are often referred to as yards, pounds per square inch as just pounds, and btu/h as just btus.

        • What Ametrica writes just shows another reason why I wrote “Such is sort of silly”.

          Apparently, the 125 GeV point estimate is the energy-mass (rest-mass) equivalence from E = mc^2, in electron volts.

          Similarly, we could solve for m and substitute, giving the 225 yg, as Ametrica indicates, which is the way it should be…

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