# Recommendations concerning Units

```Reprinted from the "IAU Style Manual" by G.A. Wilkinson, Comm. 5, in
IAU Transactions XXB (1987), which may be consulted for further details.

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NOTE:

In this section all SUPERSCRIPTS and EXPONENTS are written as numbers
preceded by a sign in the same line. Hence 10-1 = 1/10, 10+3 = 1000, etc.

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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	        s
electric current           ampere	        A
thermodynamic temperature  kelvin	        K
amount of substance	   mole	                mol
luminous intensity 	   candela	        cd

(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	        S	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 unite 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
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	10+2	hecto	h
10-3	milli	m	10+3	kilo	k
10-6	micro		10+6	mega	M
10-9	nano	n	10+9	giga	G
10-12	pico	p	10+12	tera	T
10-15	femto	f	10+15	peta	P
10-18	atto	a	10+18	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 =3D 365.25 d
angle (2)	second of arc	  "	        (pi/648 000) rad
angle	        minute of arc	  '	        (pi/10 800) 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 10+30 kg
mass	        atomic mass unit  u	        1.660 540 x 10-27kg
energy	        electron volt	  eV	        0.160 2177 aJ
flux density	jansky (4)	  Jy	        10-26W 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	        A	      10-1Om = 0.1 nm
length	              micron	        mu            10-6 m
length	              fermi		              1 fm
area	              barn	        b	      10-28 m+2
volume	              cubic centimetre	cc	      10-6 m+3
force	              dyne	        dyn	      10-5 N
energy	              erg	        erg	      10-7 J
energy (2)	      calorie	        cal	      4.1868 J
pressure	      bar	        bar	      10+5 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 10+8 / frequency in hertz
or		  =3D 1.239 842 4 x l0-6 / 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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