The units used in astronomy are a confusing mixture of SI, imperial and one-offs. Keith Atkin suggests some improvements. As in the other physical sciences, the units used in astronomy have evolved over time. Fifty years ago, a mixture of imperial and metric units was to be found in almost all textbooks but, as the years rolled by, we have said farewell to feet, inches, miles, pounds and degrees Fahrenheit, with the welcome introduction of SI units. But this transition has not been complete. Although physics teaching and research have largely embraced SI, the change has been less comprehensive in astronomy. Indeed, many of the units used by practising astronomers constitute an unfortunate confusion of imperial, old CGS (centimetre–gram–second), SI, together with a number of entirely redundant units peculiar to astronomy. Here I suggest that simpler logical units would help both within the subject and in multidisciplinary research. Astronomical lengths The units of length currently in astronomical and astrophysical usage include the mile, the foot and the inch, especially among American astronomers who are influenced by the “customary” units of day-to-day life in the US. The US represents about 4% of the population of the Earth; almost all other countries are essentially metric. In the UK we have a situation which is particularly confusing: the process of metrication, although started some decades ago, is still incomplete. Young people in this country are taught mathematics, science and engineering using metric (SI) units, but are then expected to deal with a muddle of imperial and metric units – pints, litres, miles, metres – in the outside world (Atkin 2015). Students who have learned their physics using SI units and start to take an interest in astronomy will, on joining an astronomical society, commonly find people talking about “six-inch” telescopes or hear enthusiastic descriptions of spacecraft travelling at “thousands of miles per hour”. Professional astronomers are not immune to this muddle as the astronomical unit (au), the light-year (ly), and the parsec (pc) are widely regarded as respectable and useful. In actuality, these units are redundant and serve no useful purpose. My bête noire is the megaparsec – a clumsy and ugly fusion of an SI prefix and a non-SI unit. The answer to the problem is, of course, to encourage the use of SI units of length in all astronomical work: all distances and lengths should be based on, and simply related to, the metre. The metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. The definition of the astronomical unit is most simply expressed as the mean distance from the Earth to the Sun, in itself a variable term. The definition has evolved over the years and seen a number of technical reforms (Dodd 2012), leading to its modern definition in terms of the metre, as 1 au = 1.495 978 714 64 × 1011 m. This is indeed based on the metre, but not simply. The light-year has been defined as the distance that light, travelling at 299 792 458 m s−1 covers in one Julian year of exactly 3.155 76 × 107 s, i.e. 1 ly = 9.460 730 472 580 8 × 1015 m. The parsec has been defined as the distance, D, at which one astronomical unit subtends an angle of one arcsecond. It is the reciprocal of the parallax, p, expressed in arcsecond of a celestial body, i.e. D = 1/p. Evaluating this in terms of the metre, we find that 1 pc = 3.085 677 6 × 1016 m. It should be clear that, in view of the above definitions of the au, ly and pc in term of the metres they represent, there is no logical need to retain them. Simple multiples of the metre can be used instead. Metric multiples As can be seen, the au has a magnitude ∼1011 m and the ly and pc are both ∼1016 m. These quantities can be expressed neatly using the SI prefix system. Table 1 shows the set of currently approved SI prefixes, along with an unofficial set which was suggested by Mayes (1994). 1 SI-approved and unofficial prefixes 1048 ultra U 1045 quinsa Q 1042 cata C 1039 astra A 1036 vela V 1033 besa B 1030 sansa S 1027 nava N 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 10−3 milli m 10−6 micro μ 10−9 nano n 10−12 pico p 10−15 femto f 10−18 atto a 10−21 zepto z 10−24 yocto y 10−27 tiso t 10−30 vindo v 10−33 weto w 1048 ultra U 1045 quinsa Q 1042 cata C 1039 astra A 1036 vela V 1033 besa B 1030 sansa S 1027 nava N 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 10−3 milli m 10−6 micro μ 10−9 nano n 10−12 pico p 10−15 femto f 10−18 atto a 10−21 zepto z 10−24 yocto y 10−27 tiso t 10−30 vindo v 10−33 weto w List of SI-approved prefixes (between the lines) and the unofficial prefixes suggested by Mayes (above and below the lines). View Large The important consideration when discussing distances in the universe is that of scale and this should be emphasized when introducing beginners to astronomy. Instead of trying to impress students with big numbers (e.g. “billions of light-years away”), attention should be given to a sensible choice of units appropriate to the scale of the situation under discussion. So I propose that the megametre (1 Mm = 106 m) should be used for distances at planetary scales. For distances within the solar system and other planetary systems, the gigametre (109 m) and the terametre (1012 m) would be useful (see tables 2 and 3), while the petametre (1015 m) and exametre (1018 m) conveniently express distances to stars within the galaxy. For galactic distances and beyond, there is the zettametre (1021 m) and yottametre (1024 m). 2 Scales and distances in the inner solar system body equatorial radius (Mm) mean distance from Sun (Gm) Mercury 2.42 57.9 Venus 6.08 108 Earth 6.37 150 Mars 3.37 228 body equatorial radius (Mm) mean distance from Sun (Gm) Mercury 2.42 57.9 Venus 6.08 108 Earth 6.37 150 Mars 3.37 228 View Large 3 Scales and distances in the outer solar system body equatorial radius (Mm) mean distance from Sun (Gm) Jupiter 71.4 0.778 Saturn 60.4 1.43 Uranus 23.6 2.87 Neptune 22.3 4.50 body equatorial radius (Mm) mean distance from Sun (Gm) Jupiter 71.4 0.778 Saturn 60.4 1.43 Uranus 23.6 2.87 Neptune 22.3 4.50 View Large The speed of light in vacuum to three-figure precision is easily remembered as 300 Mm s−1 while the mean Earth–Moon distance to the same precision can be written as 384 Mm. It is then immediately obvious that the light travel time between the Earth and Moon is just over one second. Arithmetical advantages The petametre (1015 m) and exametre (1018 m) are convenient units for expressing stellar distances. The distance to the nearest star, Proxima Centauri, is about 40 Pm. For those who are reluctant to give up the light-year, a nice observation is that the light travel time (in years) from a star can be found to within a few percent by dividing the distance in petametres by ten. So it follows that the light travel time from Proxima Centauri is approximately 4 years. Figure 1 shows some typical distances. The SI prefix system can easily cope with distances out to the most remote object detected, the protogalaxy UDFj-39546284. 1 View largeDownload slide Some astronomical distances using SI units. 1 View largeDownload slide Some astronomical distances using SI units. The mass of the Sun is 1.98 × 1030 kg and is commonly used (denoted by M⊙) as a standard by which to express the mass of all stars. This is understandable: the solar mass is enormous compared with the kilogram. But 1030 kg = 1033 g and so, using one of Mayes's unofficial prefixes, besa (1033), we can write 1 solar mass = 1.98 Bg. So, by use of this (albeit unofficial) prefix, we can neatly write stellar masses in besagrams rather than solar masses, and thus obtain a unit that has a simple relation to the kilogram, i.e. 1 Bg = 1030 kg and the mass of the red supergiant Betelegeuse is 15 Bg. Energy and time The electron volt (eV) is commonly regarded as a convenient energy unit in both physics and astronomy, and is related to the joule via an unwieldy factor: 1 eV = 1.602 177 33 × 10−19 J. Using the SI prefix atto (10−18), we find that 1 eV = 0.160 217 733 aJ, suggesting that the attojoule is a convenient substitution (aJ). For example, the ground state of the hydrogen atom, traditionally written as −13.6 eV, can be expressed as −2.18 aJ, enabling a simple power-of-ten connection with the joule. It follows that we can also ditch the MeV, GeV and TeV. Thus a high-energy cosmic-ray particle with an energy of 3 × 1020 eV can be expressed simply as an energy of 48 J. The eV and its multiples serve only to confuse. While considering measures of energy, it is hard to believe that the erg (10−7 J) is still in use. But it does appear from time to time in some astrophysical papers. The persistent use of this anachronistic unit serves no purpose other than to limit access to otherwise worthy academic articles. Non-SI units such as the hour, day and year are in regular use in astronomy and difficult to replace, especially when used to record the time of events. But it is possible – and, I think, desirable – to minimize the inclusion of some time-based non-SI derived units, such as those used for speed. For example, a commonly quoted value for the Earth's surface escape speed is 40 320 km h−1. It would be far better to encourage use of the SI version, 11 km s−1. The degree is presumably here to stay, but it might be an advantage to discontinue use of the arcminute and arcsecond. These are commonly used by astronomers but serve no real purpose. Angles can just as well be expressed in decimal format. The radian is the SI unit of angle and its increased use in astronomy would simplify both presentation and practice of the subject. For example, the declination of the star Capella is traditionally written σ = 45° 59′ 52.8″. This cumbersome sexagesimal measure would be far better replaced by σ = 45.9979° or even σ = 0.802816 rad, using the SI units. Outlook It is surely desirable to improve our practice rather than cling to outdated units. Traditional usages evoke nostalgia but have no place in the thinking of the astronomical researcher and educator. Removal of obsolete metrological clutter would certainly improve our subject. I recognize that these changes will not happen overnight. As a colleague recently observed: “Andromeda will be a good deal closer to the solar system than it is now, before we read of its distance in zettametres.” However, even if only some of these changes can be made, this will surely benefit understanding and communication within astronomical circles and between astronomy and related sciences. REFERENCES Atkin J K 2015 Physics Education 50 608 CrossRef Search ADS Dodd R 2012 Using SI Units in Astronomy ( Cambridge University Press) 75 Mayes V 1994 Quart. J. Roy. Astron. Soc. 35 569 © 2018 Royal Astronomical Society
Astronomy & Geophysics – Oxford University Press
Published: Apr 1, 2018
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