# Constants (astropy.constants)¶

## Introduction¶

astropy.constants contains a number of physical constants useful in Astronomy. Constants are Quantity objects with additional meta-data describing their provenance and uncertainties.

## Getting Started¶

To use the constants in S.I. units, you can import the constants directly from the astropy.constants sub-package:

>>> from astropy.constants import G


or, if you want to avoid having to explicitly import all the constants you need, you can simply do:

>>> from astropy import constants as const


and then subsequently use for example const.G. Constants are fully-fledged Quantity objects, so you can easily convert them to different units for example:

>>> print(const.c)
Name   = Speed of light in vacuum
Value  = 299792458.0
Uncertainty  = 0.0
Unit  = m / s
Reference = CODATA 2014

>>> print(const.c.to('km/s'))
299792.458 km / s

>>> print(const.c.to('pc/yr'))
0.306601393788 pc / yr


and you can use them in conjunction with unit and other non-constant Quantity objects:

>>> from astropy import units as u
>>> F = (const.G * 3. * const.M_sun * 100 * u.kg) / (2.2 * u.au) ** 2
>>> print(F.to(u.N))
0.3675671602160826 N


It is possible to convert most constants to cgs using e.g.:

>>> const.c.cgs
<Quantity   2.99792458e+10 cm / s>


However, some constants are defined with different physical dimensions in cgs and cannot be directly converted. Because of this ambiguity, such constants cannot be used in expressions without specifying a system:

>>> 100 * const.e
Traceback (most recent call last):
...
TypeError: Constant u'e' does not have physically compatible units
across all systems of units and cannot be combined with other
values without specifying a system (eg. e.emu)
>>> 100 * const.e.esu
<Quantity 4.8032045057134676e-08 Fr>


## Collections of constants (and prior versions)¶

Constants are organized into version modules. The constants for Astropy 1.3 can be accessed in the astropyconst13 module. For example:

>>> from astropy.constants import astropyconst13 as const
>>> print(const.e)
Name   = Electron charge
Value  = 1.602176565e-19
Uncertainty  = 3.5e-27
Unit  = C
Reference = CODATA 2010


Physical CODATA constants are in modules with names like codata2010 or codata2014:

>>> from astropy.constants import codata2010 as const
>>> print(const.h)
Name   = Planck constant
Value  = 6.62606957e-34
Uncertainty  = 2.9e-41
Unit  = J s
Reference = CODATA 2010


Astronomical constants defined (primarily) by the IAU are collected in modules with names like iau2012 or iau2015:

>>> from astropy.constants import iau2012 as const
>>> print(const.L_sun)
Name   = Solar luminosity
Value  = 3.846e+26
Uncertainty  = 5e+22
Unit  = W
Reference = Allen's Astrophysical Quantities 4th Ed.

>>> from astropy.constants import iau2015 as const
>>> print(const.L_sun)
Name   = Nominal solar luminosity
Value  = 3.828e+26
Uncertainty  = 0.0
Unit  = W
Reference = IAU 2015 Resolution B 3


The astronomical and physical constants are combined into modules with names like astropyconst13 and astropyconst20. To temporarily set constants to an older version (e.g., for regression testing), a context manager is available, as follows:

>>> from astropy import constants as const
>>> with const.set_enabled_constants('astropyconst13'):
...     print(const.h)
Name   = Planck constant
Value  = 6.62606957e-34
Uncertainty  = 2.9e-41
Unit  = J s
Reference = CODATA 2010
>>> print(const.h)
Name   = Planck constant
Value  = 6.62607004e-34
Uncertainty  = 8.1e-42
Unit  = J s
Reference = CODATA 2014


Warning

Units such as u.M_sun will use the current version of the corresponding constant. When using prior versions of the constants, quantities should be constructed with constants instead of units.

## Reference/API¶

### astropy.constants Package¶

Contains astronomical and physical constants for use in Astropy or other places.

A typical use case might be:

>>> from astropy.constants import c, m_e
>>> # ... define the mass of something you want the rest energy of as m ...
>>> m = m_e
>>> E = m * c**2
>>> E.to('MeV')
<Quantity 0.510998927603161 MeV>


The following constants are available:

Name Value Unit Description
G 6.67408e-11 m3 / (kg s2) Gravitational constant
N_A 6.02214086e+23 1 / (mol) Avogadro’s number
R 8.3144598 J / (K mol) Gas constant
Ryd 10973731.6 1 / (m) Rydberg constant
alpha 0.00729735257   Fine-structure constant
atm 101325 Pa Standard atmosphere
b_wien 0.0028977729 m K Wien wavelength displacement law constant
c 299792458 m / (s) Speed of light in vacuum
e 1.60217662e-19 C Electron charge
eps0 8.85418782e-12 F/m Electric constant
g0 9.80665 m / s2 Standard acceleration of gravity
h 6.62607004e-34 J s Planck constant
hbar 1.0545718e-34 J s Reduced Planck constant
k_B 1.38064852e-23 J / (K) Boltzmann constant
m_e 9.10938356e-31 kg Electron mass
m_n 1.67492747e-27 kg Neutron mass
m_p 1.6726219e-27 kg Proton mass
mu0 1.25663706e-06 N/A2 Magnetic constant
muB 9.27400999e-24 J/T Bohr magneton
sigma_T 6.65245872e-29 m2 Thomson scattering cross-section
sigma_sb 5.670367e-08 W / (K4 m2) Stefan-Boltzmann constant
u 1.66053904e-27 kg Atomic mass
GM_earth 3.986004e+14 m3 / (s2) Nominal Earth mass parameter
GM_jup 1.2668653e+17 m3 / (s2) Nominal Jupiter mass parameter
GM_sun 1.3271244e+20 m3 / (s2) Nominal solar mass parameter
L_bol0 3.0128e+28 W Luminosity for absolute bolometric magnitude 0
L_sun 3.828e+26 W Nominal solar luminosity
M_earth 5.97236473e+24 kg Earth mass
M_jup 1.89818717e+27 kg Jupiter mass
M_sun 1.98847542e+30 kg Solar mass
R_earth 6378100 m Nominal Earth equatorial radius
R_jup 71492000 m Nominal Jupiter equatorial radius
R_sun 695700000 m Nominal solar radius
au 1.49597871e+11 m Astronomical Unit
kpc 3.08567758e+19 m Kiloparsec
pc 3.08567758e+16 m Parsec

#### Functions¶

 set_enabled_constants(modname) Context manager to temporarily set values in the constants namespace to an older version.

#### Classes¶

 Constant A physical or astronomical constant. EMConstant An electromagnetic constant.