Lost in Unit Space


By The Metric Maven

Bulldog Edition

When I saw the initial episode of Lost in Space, one moment which captured my attention was when they showed the destination planet. I thought I recalled a sun and numerous planets, but the image to the left shows it was just a fuzzy circular smudge. When viewed from the mid-1960s, the world of 1997 still had desks with ashtrays and physical inboxes on their surface, but no computers.  It was also a time when the best images of the known planets in our solar system were but blotches of color with fuzzy details. When Voyager 1 took photos of Jupiter and revealed its swirling colors that resemble the marbling on the inside covers of antique books, it was astonishing. The rest of the planets followed during that “grand tour” era, all but Pluto. It would be reclassified as a Kuiper Belt object or at best a “dwarf planet” before it was imaged with a spacecraft. In 1978 James Christy noted a periodic elongation of Pluto and hypothesized that it had a moon. The images were fuzzy and lacking in detail, only a sort of bump could be seen. Until the New Horizons space probe produced crisp images in 2015, Pluto was only seen as ill-defined regions of light and dark brown areas.

I was quite enraptured when I saw this image on Gizmoto in the article: Incredible Photo Shows an Exoplanet Orbiting Around its Host Star I mistakenly thought it was the first planet ever imaged directly, but it is not. Bad Astronomer, and Bad Metric User, Phil Plait set me straight. Neil de Grasse Tyson may be your personal astrophysicist, but Phil appears to be the hardest working astrophysicist. He posts a prolific number of essays on his blog and they are quite interesting.

Six years back, on June 30 2010 (2010-06-30) Plait’s Bad Astronomy blog is titled: Another Direct Picture of a Planet Orbiting an Alien Star Confirmed! Exoplanet 1RXS 1609b was the first planet imaged with a ground-based telescope. The first exoplanet to be imaged, according to the Bad Astronomer, is 2M1207b shown below:

2M1207b and its star

Plait indicates:

It orbits the star at about 1.5 times the distance Pluto orbits from the Sun. The two are close by as these things go: just 70 parsecs (230 light years) from here.

I’m fine with a comparison to Pluto’s orbit, but it would have been nice if he used the metric system for the distance from us. In the case of the first star mentioned Plait offers:

..we know the planet 1RXS 1609b has about 8 times the mass of Jupiter, orbits the star 45 billion km (27 billion miles) from its star — 300 times the Earth-Sun distance …

Forty Five billion Kilometers? I’m sure that Phil Plait is of the view that Kilometers are a distance that is “everyday” and so saying there are a billion of them (using an Olde English “prefix”) is much more expressive to the public than 45 000 Gigameters. There seems to be no astronomer exception for AUs and parsecs for the public, so why is there for metric?

Rather than using astronomical argot like parsecs, AUs and light-years, let’s sort all of this out using the metric system and Naughtin’s Laws (as much as possible). Wikipedia does not assert that 2M1207b was the first exoplanet imaged, but we will assume it is. 2M1207b is currently thought to orbit at about 6000 Gigameters from its star. Pluto is at about 5914 Gm so exoplanet 2M1207b is at about the same distance out as Pluto. The star itself, 2M1207 is only around 1600 Petameters distant (a light-year is about 9.46 Pm). This star is very close to us. It makes sense we would first see an exoplanet around a nearby star rather than one that is farther away.

New Scientist TRAPPIST-1

There have been many planets that have been indirectly inferred to be orbiting other stars. In August of 2016 New Scientist (pg 8) mentions the ultracool star TRAPPIST has three potentially habitable planets orbiting the same star. See upper graphic.

The three planets are surprisingly close to TRAPPIST-1 ranging from 2-3 Gigameters or so. Mercury orbits at 58 Gigameters from the Sun. If they orbited our Sun, these planets would be well inside the orbit of Mercury.

Table 1  — Click To Enlarge

The above table helps put the information into context using metric prefixes. The planets orbiting TRAPPIST-1 are all very close to their star. Because it is ultracool (in the temperature sense) the orbiting planets are potentially cool enough for life as we know it to exist. The first imaged exoplanets 2M1207b and 1RSX1609b orbit at a distance about equal to Pluto in the first case, and  about 7.5 times that distance in the second. When mapped onto our solar system, none of these new planets orbit within the same range as our planets.

The only exoplanet in the table with an estimated diameter, 2M1207b, (210 Mm)  has a diameter larger than Jupiter (140 Mm). It would make sense that a planet would have to be about this size to allow for measurement of its extent. Distances to these stars are expressed with Petameters, which means they are very close to us. The extent of our Galaxy is about 1000 Exameters or 1 000 000 Petameters, so TRAPPIST-1 (370 Pm), 2M1207 (1608 Pm) and 1RXS 1609 (4440 Pm) are close to us when compared with our galaxy’s dimensions.

Astronomers appear to be generators of unit proliferation. When you look up the diameter of 1RXS 1609 in Wikipedia, its radius is listed as 1.35 solar radii. The brown dwarf 2M1207 is about 0.25 solar radii, but its orbiting planet 2M1207b is given as 1.5 Jupiter radii. Astronomers have chosen to express measurements using metaphorical units in terms of arbitrarily chosen objects in our solar system. Why not use the metric system directly?—and then offer an example for context?  Mass is expressed in terms of Jupiter’s mass, but the temperature of the planet is given in kelvin. Why is the temperature not in terms of Jupiter’s temperature?—just to stay consistent. Do astronomers have equipment that measures and outputs  values in Jupiter masses and radii?—I kind of doubt it—I hope.

Lest you think I believe there has been no metric progress, it appears that at least Wikipedia is slowly changing its ways, albeit inconsistently. If you look at the orbital distance of Pluto it is first listed in AU (astronomical units) and in parenthesis next to it are the same values in Gigameters. Metric is still in parenthesis as “the alternative” but at least it is there, and not expressed in millions of Kilometers. I’m rather sure that at one time I never saw Gm values on astronomy pages in Wikipedia, and so this is a positive change. The Equatorial and Polar radius of Pluto and Jupiter are first given in Km and below each value is an equivalent Earth value, 11.209 Earths and 10.517 Earths in the case of Jupiter, and 0.18 Earths for Pluto. The volume and mass also have metric first and a suggested context second. I see this as a very acceptable way to designate these values. The mean density of Jupiter is in grams per cubic centimeter rather than 1.326 g/mL or 1326 g/L, so while it may have metric units in the expression it’s still more cgs than SI. Saturn is 0.687 g/ml or 687 g/L and because it is below one g/mL in the first case and below 1000 g/L in the second, an average chunk of Saturn would, in principal, float in water. Overall it seems that I’m seeing more use of the larger metric prefixes in Wikipedia and I definitely see that as a millimeter of progress in a country that has Yottameters to go.

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Related essays:

Long Distance Voyager

The Expanding Universe


Doubling Down


By The Metric Maven

Bulldog Edition

When I lived in Mexico as a boy, it was pointed out by my peers, that rather than drink the more expensive Coke or Pepsi, one should buy a less expensive Cola they called Doblay Cola. I became used to  the pronunciation as Dob-lay and expected it was a Mexican product. Years later I was in the US and saw a bottle of Dob-lay Cola, but suddenly I realized it was actually called Double Cola, and is from the US. When I was surrounded with Spanish, I saw words as all being pronounced as they would be within that environment. The modern bottle of Double Cola shown on the upper left has the marketing copy: “Double Measure Double Pleasure.” In light of the information that follows, it struck me as rather prescient. Recently Amy Young brought an interesting web page to my attention, and again I was faced with an English-French version of what I had experienced with Double Cola.

The university web page has an English translation of the original 1795 metric decree in France. There are a number of declarations about measures, and they are mostly what I would expect, but it offered extra context. It is interesting that the millimeter does not appear to be mentioned, but not exactly shocking.  What did surprise me was item number eight:

8. In weights and measures of volume, each of the decimal measures of these two types shall have its double and  its half, in order to give every desirable facility to the sale of divers items; therefore,  there shall be double liter and demiliter, double hectogram and demihectogram, and so on with the others.

Suddenly, the origin of the incredible name proliferation found in a chart made by the American Metric Association in the 19th Century revealed itself. In my essay Familiarity Versus Simplicity I diagnosed the inclusion of the double gram, demi dekagram, dekagram, double dekagram, demi hectogram, hectogram, double hectogram, demi kilogram and kilogram as a vestigial inclusion of pre-metric thinking. I suspected it had been ad-hoc and was very suspicious that it was introduced by Americans. It had not occurred to me that double in English and double’ in French would both mean well—double or twice an amount. I then realized that double and demi were introduced as concatenation prefixes of sorts. This is not unlike the Ye Olde English prefixes used with metric, like one billion Kilometers or one million Kilometers. The prefix demi (in the linguistic sense) is from Latin dimidium or “divided in half,” via Old French and Middle English, it became demi.

Why on Earth was it so important to include a prefix that is a factor of two rather than ten at the time? We have 3 barleycorns to an inch, but often the inch is divided into halves, quarters, eighths and sixteenths. When moving upward using linear measure it’s 12 inches to a foot, 3 feet to a yard and so on. The interest in doubling and halving is not presented for linear measure in the early metric system. There is no double meter or demimeter offered in the 19th century chart. The value of masses and volumes are given double and half values in this metric chart. Why? Probably because it is fairly easy to use a beam scale to halve flour or sugar or beer or whatever. This binary approach would match our Ye Olde English measures right? Well—not exactly.

Isaac Asimov in his work Realm of Measure has this to say:


Binary relationships quickly breakdown in Ye Olde English linear measure, volume and weight. The Troy pound has 12 ounces and the Avoirdupois pound has 16 ounces. Those who claim our Ye Olde English measures are consistent and binary are simply wrong. What is interesting is that the first draft of the metric system had provisions for doubling and halving values. I can only speculate at this point that this inclusion was an attempt to encompass a binary set of measures as a kind of reform of earlier measures that might have been more useful if they had strictly stayed with doubling and halving. This reform was developed at a time before modern scales with analog or digital readouts. When continuous reading scales were introduced, the idea of using a balance scale for everyday measures was moot. There was little reason to use the double or demi designations. I discuss the importance of the creation of a measurement continuum in my essay The Count Only Counts—He Does Not Measure. Modern measurement instruments are more than likely the reason that binary measures began to vanish. When one was no longer chained to binary quantities, it opened up a world where any measure for a product could be realized. Just look at any set of supermarket shelves.

Section 6 of the document calls for the prefix cluster around unity and the myriameter:

6. One-tenth of a meter shall be called a decimeter; and one one-hundredth thereof, a centimeter.

A measure equal to ten meters shall be called a decameter, which furnishes a very convenient measure for surveying.

Hectometer shall signify the length of 100 meters.

Finally, kilometer and myriameter shall be the lengths of 1,000 and 10,000 meters, and shall designate principally the distances of roads.

The incredibly useful millimeter is not listed in the document. The liter is defined and is asserted to be for both dry and liquid measure, as it is to this day.

The original formulation of the metric system as presented in this document illustrates how far we have come in simplifying and thereby  increasing the utility of this ubiquitous system of measures—well ubiquitous outside of the United States.

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Related essay:

Familiarity versus Simplicity