Reprinted from the "IAU Style Manual" by G.A. Wilkins, Comm. 5, in IAU Transactions XXB (1989), which may be consulted for further details (download PDF file, 4.7MB)

# SI Units

The international system (SI) of units, prefixes, and symbols should be used for all physical quantities except that certain special units, which are specified later, may be used in astronomy, without risk of confusion or ambiguity, in order to provide a better representation of the phenomena concerned. SI units are now used to a varying extent in all countries and disciplines, and this system is taught in almost all schools, colleges and universities. The units of the centimetre-gram-second (CGS) system and other non-SI units, which will be unfamiliar to most young scientists, should not be used even though they may be considered to have some advantages over SI units by some astronomers.

General information about SI units can be found in the publications of national standards organisations and in many textbooks and handbooks.

There are three classes of SI units: (a) the seven base units that are regarded as dimensionally independent; (b) two supplementary, dimensionless units for plane and solid angles; and (c) derived units that are formed by combining base and supplementary units in algebraic expressions; such derived units often have special names and symbols and can be used in forming other derived units. The units of classes (a) and (b) are listed in Table 1. The units of class (c) of greatest interest to astronomers are given in Table 2 for those with simple names and symbols, and in Table 3 for those with compound names and symbols. In forming compound names division is indicated by per, while in the corresponding symbols it is permissible to use either a negative index or a solidus (oblique stroke or slash); thus the SI: unit of velocity is a metre per second and the corresponding symbol is m s-l or m/s.

The space between the base units is important in such a case since m/s could be interpreted as a frequency of 1000 Hz; a space is not necessary if the preceding unit ends in a superscript; a full stop (period) may be inserted between units to remove any ambiguity; the solidus should only be used in simple expressions and must never be used twice in the same compound unit.

Table 1. The names and symbols for the SI base and supplementary units.

 Quantity SI Unit: Name Symbol length metre m mass kilogram kg time (1) second electric current ampere A thermodynamic temperature kelvin K amount of substance mole mol luminous intensity candela cd plane angle radian rad solid angle steradian sr

1 The abbreviation sec should not be used to denote a second of time.

Table 2. Special names and symbols for SI derived units.

 Quantity SI Unit: Name Symbol Expression frequency hertz Hz s-l force newton N kg m s-2 pressure, stress pascal Pa N m-2 energy joule J N m power watt W J s-l electric charge coulomb C A s electric potential volt V J C-l electric resistance ohm Omega V A-l electric conductance siemens A V-l electric capacitance farad F C V-l magnetic flux weber Wb V s magnetic flux density tesla T Wb m-2 inductance henry H Wb A-l luminous flux lumen lm cd sr illuminance lux lx lm m-2

Table 3. Examples of SI derived units with compound names.

 Quantity SI unit: Name symbol density (mass) kilogram per cubic metre kg m-3 current density ampere per square metre A m-2 magnetic field strength ampere per metre A m-l electric field strength volt per metre V m-l dynamic viscosity pascal second Pa s heat flux density watt per square metre W m-2 heat capacity, entropy joule per kelvin J K-l energy density joule per cubic metre J m-3 permittivity farad per metre F m-l permeability henry per metre H m-l radiant intensity watt per steradian W sr-l radiance watt per square metre per steradian W m-2 Sr-l luminance candela per square metre cd m-2

Table 4. SI prefixes and symbols for multiples and submultiples.

 Submultiple Prefix Symbol Multiple Prefix Symbol 10-1 deci d 10 deca da 10-2 centi c 102 hecto h 10-3 milli m 103 kilo k 10-6 micro mu 106 mega M 10-9 nano n 109 giga G 10-12 pico p 1012 tera T 10-15 femto f 1015 peta P 10-18 atto a 1018 exa E

Note: Decimal multiples and submultiples of the kilogram should be formed by attaching the appropriate SI prefix and symbol to gram and g, not to kilogram and kg.

4.12 SI prefixes: Decimal multiples and submultiples of the SI: units, except the kilogram, are formed by attaching the names or symbols of the appropriate prefixes to the names or symbols of the units. The combination of the symbols for a prefix and unit is regarded as a single symbol which may be raised to a power without the use of parentheses. The recognised list of prefixes and symbols is given in Table 4. These prefixes may be attached to one or more of the unit symbols in an expression for a compound unit and to the symbol for a non-SI unit. Compound prefixes should not be used.

4.13 Non-SI units: It is recognised that some units that are not part of the international system will continue to be used in appropriate contexts. Such units are listed in Table 5; they are either defined exactly in terms of SI units or are defined in other ways and are determined by measurement. Other non-SI units, such as Imperial units and others listed in Table 6, should not normally be used.

Table 5. Non-SI units that are recognised for use in astronomny.

 Quantity Unit: Name Symbol Value time (1) minute min or " 60 s time hour h 3600 s = 60 min time day d 86 400 s = 24 h time year (Julian) a 31.5576 Ms = 365.25 d angle (2) second of arc " (pi/648 000) rad angle minute of arc ' (pi/10 800) rad angle degree o (pi/180) rad angle (3) revolution(cycle) c 2pi rad length astronomical unit au 0.149 598 Tm length parsec pc 30.857 Pm mass solar mass Mo 1.9891 x 1030 kg mass atomic mass unit u 1.660 540 x 10-27 kg energy electron volt eV 0.160 2177 aJ flux density jansky (4) Jy 10-26 W m-2 Hz-1

1 The alternative symbol is not formally recognised in the SI system.

2 The symbol mas is often used for a milliarcsecond (0".001).

3 The unit and symbols are not formally recognised in the SI system.

4 The jansky is mainly used in radio astronomy.

5 The degree Celsius (oC) is used in specifying temperature for meteorological purposes, but otherwise the kelvin (K) should be used.

5.14 Time and angle : The units for sexagesimal measures of time and angle are included in Table 5. The names of the units of angle may be prefixed by 'arc' whenever there could be confusion with the units of time. The symbols for these measures are to be typed or printed (where possible as superscripts) immediately following the numerical values; if the last sexagesimal value is divided decimally, the decimal point should be placed under, or after, the symbol for the unit; leading zeros should be inserted in sexagesimal numbers as indicated in the following examples.

2d 13h 07m 15.259s 06h 19m 05.18s 120o 58' 08".26

These non-SI units should not normally be used for expressing intervals of time or angle that are to be used in combination with other units.

In expressing the precision or resolution of angular measurement, it is becoming common in astronomy to use the milliarcsecond as the unit, and to represent this by the symbol mas; this is preferable to other abbreviations, but its meaning should be made clear at its first occurrence. The more appropriate SI Unit would be the nanoradian (1 nrad = 0.2 mas). In general, the degree with decimal subdivision is recommended for use when the radian is not suitable and when there is no requirement to use the sexagesimal subdivision. If it is more appropriate to describe an angle in terms of complete revolutions (or rotations or turns or cycles), then the most appropriate symbol appears to be a letter c; this may be used in a superior position as in 1c = 360o =2pi rad = 1 rev, but it may be used as in 1 c/s = 1Hz.

The use of units of time for the representation of angular quantities, such as hour angle, right ascension and sidereal time, is common in astronomy, but it is a source of confusion and error in some contexts, especially in formulae for numerical calculation. The symbol for a variable followed by the superscript for a unit may be used to indicate the numerical value of that variable when measured in that unit.

5.15 Astronomical units: The IAU System of Astronomical Constants recognises a set of astronomical units of length, mass and time for use in connection with motions in the Solar System; they are related to each other through the adopted value of the constant of gravitation when expressed in these units (IAU 1976). The symbol for the astronomical unit of length is au; the astronomical unit of time is 1 day (d) of 86 400 SI seconds (s); the astronomical unit of mass is equal to the mass of the Sun and is often denoted by Mo, but the special subscript makes this symbol inconvenient for general use.

An appropriate unit of length for studies of structure of the Galaxy is the parsec (pc), which is defined in terms of the astronomical unit of length (au). The unit known as the light-year is appropriate to popular expositions on astronomy and is sometimes used in scientific papers as an indicator of distance.

The IAU has used the julian century of 36 525 days in the fundamental formulae for precession, but the more appropriate basic unit for such purposes and for expressing very long periods is the year. The recognised symbol for a year is the letter a, rather than yr, which is often used in papers in English; the corresponding symbols for a century (ha and cy) should not be used. Although there are several different kinds of year (as there are several kinds of day), it is best to regard a year as a julian year of 365.25 days (31.5576 Ms) unless otherwise specified.

It should be noted that sidereal, solar and universal time are best regarded as measures of hour angle expressed in time measure; they can be used to identify instants of time, but they are not suitable for use as precise measures of intervals of time since the rate of rotation of Earth, on which they depend, is variable with respect to the SI second.

5.16 Obsolete units: It is strongly recommended that the non-SI units listed in Table 6 are no longer used. Some of the units listed are rarely used in current literature, but they have been included for use in the study of past literature. Imperial and other non-metric units should not be used in connection with processes or phenomena, but there are a few situations where their use may be justified (as in "the Hale 200-inch telescope on Mount Palomar"). The equivalent value in SI units should be given in parentheses if this is likely to be helpful.

Table 6. Non-SI units and symbols whose continued use is deprecated.

 Quantity Unit: Name Symbol Value length angstrom Å 10-1O m = 0.1 nm length micron mu 10-6 m length fermi 1 fm area barn b 10-28 m2 volume cubic centimetre cc 10-6 m3 force dyne dyn 10-5 N energy erg erg 10-7 J energy (2) calorie cal 4.1868 J pressure bar bar 105 Pa pressure stand. atmosphere atm 101 325 Pa acceleration (grav.) gal Gal 10-2 m s-2 gravity gradient eotvos E 10-9 s-2 magnetic flux density gauss G corresponds to 10-4 T magnetic flux density gamma corresponds to 10-9 T magn. field strength oersted Oe corr. to (1000/4pi) A m-l

1 Non-metric units, such as miles, feet, inches, tons, pounds, ounces, gallons, pints, etc., should not be used except in special circumstances.

2 There are other obsolete definitions and values for the calorie.

The definitions of the SI units and an extensive list of conversion factors for obsolete units are given by Anderson (Physics Vade Mecum, American Institute of Physics 1981). In particular, wavelengths should be expressed in metres with the appropriate SI prefix; e.g., for wavelengths in the visual range the nanometre (nm) should be used instead of the angstrom (A), which is a source of confusion in comparisons with longer and shorter wavelengths expressed in recognised SI units. The notation of the form of a Greek Lambda foIlowed by a numerical value (which represents the wavelength in angstroms) should also be abandoned.

The name micrometre should be used instead of micron. In all cases, the spelling metre should be used for the unit, while the spelling meter should be used for a measuring instrument (as in micrometer). The word kilometre should be pronounced ki-lo-me-te, not kil-lom-e-ter.

If wavenumbers are used they should be based on the metre, not the centimetre; in any case the unit (m-l or cm-l) should be stated since they are not dimensionless quantities. The uses of frequency (in Hz) at radio wavelengths and energy (in eV) at X-ray wavelengths are appropriate for some purposes, but they serve to obscure the essential unity of the electromagnetic spectrum, and so it may be helpful to give the wavelength as well at the first occurrence; the correspondences between these units and wavelength are as follows:

wavelength in metres =2.997 924 58 x 108 / frequency in hertz

or = 1.239 842 4 x l06 / energy in electron-volts

5.17 Magnitude: The concept of apparent and absolute magnitude in connection with the brightness or luminosity of a star or other astronomical object will continue to be used in astronomy even though it is difficult to relate the scales of magnitude to photometric measures in the SI system. Magnitude, being the logarithm of a ratio, is to be regarded as a dimensionless quantity; the name may be abbreviated to mag without a full stop, and it should be written after the number. The use of a superscript m is not recommended. The method of determination of a magnitude or its wavelength range may be indicated by appropriate letters in italic type as in U, B, V. The photometric system used should be clearly specified when precise magnitudes are given.

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