Other than derogatory comments made by colleagues in university physics departments on the strange non-standard units that astronomers used, my first unpleasant experience involved the Catalog of Infrared Observations published by NASA (Gezari et al., 1993). In the introduction, a table is given of the 26 different flux units used in the original publications from which the catalogue was compiled – no attempt was made to unify the flux measures. The difficulties of many different ways of expressing absolute and apparent flux measures when trying to combine observations made in different parts of the electromagnetic spectrum became all too apparent to me when preparing a paper (Dodd, 2007) for a conference on standardizing photometric, spectrophotometric and polarimetric observations. This work involved plotting X-ray, ultraviolet, visible, infrared and radio frequency measurements of selected bright stars in the open cluster IC2391 as spectra with common abscissae and ordinates. Several participants at the conference asked if I could prepare a ‘credit card’ sized data sheet containing the conversion expressions I had derived. As is usually the case, I was otherwise engaged at the time in comparing my newly derived coarse spectrophotometry with a set of model stellar atmospheres, so the ‘credit card’ idea was not acted upon. However, the positive response to my paper did make me realize that there was a need in the astronomical community for a reference work which, at the least, converted all the common astronomical measurements to a standard set.

Using SI units in astronomy

The target audience for a book on using SI units in astronomy has to be astronomers who teach and/or carry out astronomical research at universities and government observatories (national or local) or privately run observatories. If this group would willingly accept the advantages to be gained by all astronomers using the same set of units and proceed to lead by example, then it should follow that the next generation of astronomers would be taught using the one set of units. Since many of the writers of popular articles in astronomy have received training in the science, non-technical reviews might then also be written using the one set of units. Given the commitment and competence of today's amateur astronomers and the high-quality astronomical equipment they often possess, it follows that they too would want to use the one set of units when publishing the results of their research.

As to why one set of units should be used, a brief search through recent astronomical literature provides an answer. Consider the many different ways the emergent flux of electromagnetic radiation emitted by celestial bodies and reported in the papers listed below and published since the year 2000, is given.

1. Józsa et al. (2009) derived a brightness temperature of 4 × 105K for a faint central compact source in the galaxy IC2497 observed at a radio frequency of 1.65 GHz.[…]

SI definition of the ampere

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per metre of length.

The dimension of electric current is [I], its unit is the ampere and its symbol is A.

Possible future definition of the ampere

Under discussion at the present time is the redefining of the unit of electric current in the following way:

The ampere is a unit of electric current such that the elementary charge is exactly 1.602 176 53 × 10-19 C, where 1C (coulomb) = 1 A .s (ampere second).

Definition of electricity

Funk & Wagnalls New Standard Dictionary of the English Language (1946) gives a general definition of electricity as:

And as a physics-related definition of electricity:

Definition of magnetism

Funk et al. (1946) give, as a general definition of magnetism:

SI definition of the kilogram

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

The dimension of mass is [M], its unit is the kilogram and its symbol is kg.

The International Prototype Kilogram

The original definition (1795) of the kilogram was a mass equal to that of a cubic decimeter of pure air-free water at the temperature of melting ice (273.15 K). This was altered four years later to the mass of water in the same volume but at the temperature at which water has its maximum density (which occurs at 277.13 K; Kaye & Laby, 1959). An all-platinum prototype with the same mass as the cubic decimeter of water was manufactured the same year and designated the Kilogramme des Archives. The current standard kilogram mass, a cylindrical platinum–iridium alloy, made in 1879 and accepted as the standard since 1889, is known as the International Prototype Kilogram, (IPK). It is now the only SI standard which is a manufactured artifact. The IPK and six replicas are stored at BIPM in a controlled environment. Further copies, known as replicas, were manufactured for distribution to other national metrology laboratories throughout the world.

The stability of the International Prototype Kilogram

As the IPK has, by definition, a mass of one kilogram, it has a zero measurement error. However, when the mass of the IPK is compared with the masses of the replicas, the IPK is apparently losing mass relative to all of them.

Definition of taxonomy

Taxonomy is defined as the science of classification and is derived from the ancient Greek word, ταξις, meaning arrangement, order, regularity (Liddell & Scott, 1996).

Classification in astronomy

Funk & Wagnalls New Standard Dictionary of the English Language (1946) defines classification as:

To classify, therefore, is to arrange in a class or classes on the basis of observed resemblances and differences. For this to proceed, two pieces of information are needed: an identity (the name of that which is to be classified) and an attribute (does the identified object have or could it have the necessary information for it to be classified as having the attribute), e.g., does Sirius (the identity – the name of the star) have a spectral type (the attribute or classification)? The answer is yes and the spectral type of Sirius is A1. It should be noted that the group of identifying names or definitions of a class of objects may also constitute a classification, e.g., the recent IAU definitions of types of bodies in the Solar System in which the new class, dwarf planet, contains the objects Pluto, Ceres and Eris.

SI definition of the second

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

This definition refers to a caesium atom in its ground state at a temperature of 0 K.

The dimension of time is [T], its unit is the second and its symbol is s.

Definition of time

Funk & Wagnalls New Standard Dictionary of the English Language (Funk et al., 1946) defines time, inter alia, as:

A system of reckoning or measuring duration; as solar time; sidereal time; mean time.

Systems of time or time scales

There are two major systems of time: those based on the Earth's rotation and the orbital motions of the Earth, Moon and planets, known as dynamical time; and those based on atomic clocks and known as atomic time.

A time system or scale may be specified by two numbers, the origin from which the time intervals are to be measured and the number of predefined unit scale intervals measured since the time of origin (Leschiutta, 2001).

Dynamical time

Dynamical time may be thought of as the independent variable in the equations that describe the motions of the bodies in the Solar System.

SI definition of the mole

1. The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12 (12C); its symbol is mol.

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

The dimension of amount of substance is [N].

Possible future definition of the mole

Presently under discussion is redefining the unit of amount of substance in the following way:

The mole is an amount of substance such that the Avogadro constant is exactly 6.022 141 5 × 1023 mol-1 (per mole).

Avogadro's constant and atomic masses

In keeping with the proposed new definition of the mole, Avogadro's constant may be defined as the number NA of elementary entities per mole of substance which has the (current) value 6.022 141 79 × 1023 mol-1 (Mohr et al., 2007). So the number of atoms in 0.012 kg of 12C is 6.022 141 79 × 1023.

Note that the dimension of Avogadro's constant is [N]-1 and its symbol mol-1.

Atomic and molar masses

In SI units, the atomic mass unit (amu) is defined to be exactly 1/12 the mass of one atom of the 12C isotope.

In SI units, the molar mass of a substance is defined to be the mass in kg of 1 mol of the elementary entities (e.g., atoms or molecules) composing the substance.

The name Système International d'Unités (International System of Units), with the abbreviation SI, was adopted by the 11th Conférence Générale des Poids et Mesures (CGPM) in 1960.

This system includes two classes of units:

1. - base units

2. - derived units,

which together form the coherent system of SI units.

The set of SI base units

There are seven well defined base units in the SI. They are: the second, the metre, the kilogram, the candela, the kelvin, the ampere and the mole, all selected by the CGPM and regarded, by convention, to be dimensionally independent. Table 2.1 lists the base quantities and the names and symbols of the base units. The order of the base units given in the table follows that of the chapters in this book.

The set of SI derived units

Derived SI units are those that may be expressed directly by multiplying or dividing base units, e.g., density (kg .m-3) or acceleration (m .s-2) or electric charge (A. s). Table 2.2 lists examples of SI derived units obtained from base units.

Special names have been assigned to selected derived units that are used to prevent unwieldy combinations of base SI names occurring. Table 2.3 gives some examples of such special names, with the derived unit expressed in terms of both other SI units and of base SI units only. Note that the radian and steradian were originally termed supplementary SI derived units.

SI definition of the metre

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

The dimension of length is [L], its unit is the metre and its symbol m.

The original definition of the metre was one ten millionth of the distance from the Earth's north pole to its equator, determined along a meridian arc that ran from Dunkirk in the north to Barcelona in the south. Observations were begun in 1792 by J. B. J. Delambre, who worked from Paris northwards and P. F. A. Méchain who made measurements from Paris to Barcelona. They completed their task in seven years and the metre thus determined was modelled in pure platinum as a one-metre-long bar (Alder, 2004).

Linear astronomical distances and diameters

The sizes of and the distances between astronomical bodies is generally extremely large by everyday terrestrial standards. This has resulted in astronomers inventing units such as the light year, the astronomical unit and the parsec, which are, at first sight, better able to deal with very large distances. The SI unit of length, the metre, used in conjunction with common prefixes is normally only used for measurements within the Solar System.

Size of the Earth

Were the Earth a perfect sphere it would follow from the original definition of the metre that its diameter would be 4 × 107/π m.