Lost in Unit Space

Alpha-Centara-Centauri-CroppedBy 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-1There 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.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essays:

Long Distance Voyager

The Expanding Universe


The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.


Take It With 64.798 91 Milligrams of Salt

Grains-of-SaltBy The Metric Maven

Bulldog Edition

I have often made a point that a pound of feathers weighs more than a pound of gold, and that an ounce of feathers weighs less than an ounce of gold. This is because A troy pound is equal to 0.822 857 1 avoirdupois pounds. Feathers are weighed in avoirdupois pounds and gold is measured with troy when using medieval units. The Troy pound is divided into 12 ounces and the avoirdupois pound is divided into 16 ounces.

At one time I made the incorrect assumption that because the troy pound is defined as 5760 grains and the avoirdupois pound is 7000 that the value of a troy grain and avoirdupois grain were different. To my surprise, the common weight definition for pounds in Ye Olde English is the grain. The same grain is used to define the 5760 grains of a troy pound and the 7000 grains of an avoirdupois pound.

Recently I was watching an episode of the 1960’s mini-series The Prisoner. A discussion took place concerning how much of a drug had been given to the main character and what should be done when the effects were not as predicted:

Number 86: “I gave him eight grains of mitol. Suspicion, doubt, these are factors of aggression. The drug should preclude all such reactions.”

Number 2: “….go to him now repeat the dose.”

Number 86: “Now? But sixteen grains of mitol is quite impossible.”

Number-86The values are all in grains. What struck me as I thought about this exchange is the concern that some literary Lilliputians have that our clichés will suffer at the hands of a metric switch-over. The one phrase I don’t recall being discussed in this context is: “you better take that with a grain of salt.” It means that one should view a statement with some skepticism. The origin of the phrase is a bit apocryphal and is possibly from a Latin phrase. I realized that I had never interpreted the phrase “properly” until I saw that old episode of The Prisoner. The invention of the microscope around 1610 or so soon allowed humans to look at individual “grains” of salt. These grains vary, but a reasonable estimate is about 60 micrograms per salt crystal “grain.” I always took the meaning of taking something with a grain of salt as adding in an infinitesimal amount of salt to make it more palatable. When I thought of the phrase I thought of the microscopic salt crystals of NaCl and not the approximately 1000 of them that make up the Ye Olde English unit called the grain. when I think of a grain of sand I don’t think of 64.798 91 milligrams of sand, I think of a single particle of sand, which is on the order of 15 milligrams.

The grain as a unit is so unfamiliar to Americans as to be intellectually invisible. One has to remind people that some aspirin in the US are also labeled in grains, and if one asked how many grains are in an ounce they would not realize that it is 473.5 grains for an avoirdupois ounce and 480 in a troy ounce. The grain is as devoid of meaning for the average person as is a coomb.

The grain was defined in 1572 long before our modern notion of mass was developed. The pound was not uniquely defined as a mass or a force, and because of its pre-scientific heritage it continues to act as a barrier to a scientific understanding of our world by the average person, and often educated engineers and scientists. When we stand on a bathroom scale and read off the value in pounds, it is often assumed to be a mass. But the word pound is used interchangeably for weight or the force gravity exerted on the mass of the object. We in the US still say pounds per square inch when discussing pressure, which in terms of mass does not seem to make any sense. An object with mass is a three dimensional object and not a two dimensional area. Using the identical name pound for pound-mass and pound-force traps citizens in the US into a medieval view of the world. It also traps engineers and scientists.

Recently I was watching an episode of the highly enjoyable program Impossible Engineering. It dealt with the design of the World’s Biggest Cruise Ship. In the program Physicist Dr. Andrew Steele sets out to demonstrate the amount of drag or opposing force that different hull shapes of boats produce, as first mathematically expressed by engineer William Froude (1810-1879) in the 19th century. Dr. Steele attached a spring scale using rope to each example and then described the amount of force (hydrodynamic drag) they each exert. The value is read from the scale in Kilograms (mass) and not in newtons (force). Dr. Steele is British, which produces a sort of double irony. When a person is conditioned to see pounds as both mass and force, it is a short step for an average person, or a PhD, to substitute Kilograms for newtons and blur the modern distinction. The retention of medieval units brings along their pre-scientific baggage in a world where the public understanding of science is of existential importance.

When you see scientific explanations on popular television programs, remember to take them with a grain of salt.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page


The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.