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# Constants (`astropy.constants`)

## Introduction

`astropy.constants` contains a number of physical constants useful in Astronomy. A `Constant` is a |Quantity| object with additional metadata describing its provenance and uncertainty.

## Getting Started

You can import a `Constant` directly from the `astropy.constants` sub-package:

    >>> from astropy.constants import G
    >>> print(G)
      Name   = Gravitational constant
      Value  = 6.6743e-11
      Uncertainty  = 1.5e-15
      Unit  = m3 / (kg s2)
      Reference = CODATA 2018

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

    >>> from astropy import constants as const
    >>> print(const.G)
      Name   = Gravitational constant
      ...

Constants can be used in Arithmetic operations and NumPy Functions just like any other |Quantity|:

    >>> 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

## Unit Conversion

Explicitly Converting to Different Units is often not necessary, but can be done if needed:

    >>> print(const.c)
      Name   = Speed of light in vacuum
      Value  = 299792458.0
      Uncertainty  = 0.0
      Unit  = m / s
      Reference = CODATA 2018

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

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

It is possible to convert most constants to Centimeter-Gram-Second (CGS) units using, for example:

    >>> 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` 2.0 can be accessed in the `astropyconst20` module. For example:

    >>> from astropy.constants import astropyconst20 as const
    >>> print(const.e)
      Name   = Electron charge
      Value  = 1.6021766208e-19
      Uncertainty  = 9.8e-28
      Unit  = C
      Reference = CODATA 2014

The version modules contain physical and astronomical constants, and both sets can also be chosen independently from each other. Physical CODATA constants are in modules with names like `codata2010`, `codata2014`, or `codata2018`:

    >>> from astropy.constants import codata2014 as const
    >>> print(const.h)
      Name   = Planck constant
      Value  = 6.62607004e-34
      Uncertainty  = 8.1e-42
      Unit  = J s
      Reference = CODATA 2014

Astronomical constants defined (primarily) by the International Astronomical Union (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

However, importing these prior version modules directly will lead to inconsistencies with other subpackages that have already imported `astropy.constants`. Notably, `astropy.units` will have already used the default version of constants. When using prior versions of the constants in this manner, quantities should be constructed with constants instead of units.

To ensure consistent use of a prior version of constants in other `astropy` packages (such as `astropy.units`) that import `astropy.constants`, the physical and astronomical constants versions should be set via `ScienceState` classes. These must be set before the first import of either `astropy.constants` or `astropy.units`. For example, you can use the CODATA2010 physical constants together with the IAU 2012 astronomical constants:

    >>> from astropy import physical_constants, astronomical_constants
    >>> physical_constants.set('codata2010')
    <ScienceState physical_constants: 'codata2010'>
    >>> physical_constants.get()
    'codata2010'
    >>> astronomical_constants.set('iau2012')
    <ScienceState astronomical_constants: 'iau2012'>
    >>> astronomical_constants.get()
    'iau2012'

Then all other packages that import `astropy.constants` will self-consistently initialize with these prior versions of constants.

The versions may also be set using values referring to the version modules:

    >>> from astropy import physical_constants, astronomical_constants
    >>> physical_constants.set('astropyconst13')
    <ScienceState physical_constants: 'codata2010'>
    >>> physical_constants.get()
    'codata2010'
    >>> astronomical_constants.set('astropyconst13')
    <ScienceState astronomical_constants: 'iau2012'>
    >>> astronomical_constants.get()
    'iau2012'

If `astropy.constants` or `astropy.units` have already been imported, a `RuntimeError` will be raised:

    >>> import astropy.units
    >>> from astropy import physical_constants, astronomical_constants
    >>> astronomical_constants.set('astropyconst13')
    Traceback (most recent call last):
        ...
    RuntimeError: astropy.units is already imported

## 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 | 6.6743e-11 | m3 / (kg s2) | Gravitational constant
N_A | 6.02214076e+23 | 1 / (mol) | Avogadro’s number
R | 8.31446262 | J / (K mol) | Gas constant
Ryd | 10973731.6 | 1 / (m) | Rydberg constant
a0 | 5.29177211e-11 | m | Bohr radius
alpha | 0.00729735257 |  | Fine-structure constant
atm | 101325 | Pa | Standard atmosphere
b_wien | 0.00289777196 | m K | Wien wavelength displacement law constant
c | 299792458 | m / (s) | Speed of light in vacuum
e | 1.60217663e-19 | C | Electron charge
eps0 | 8.85418781e-12 | F/m | Vacuum electric permittivity
g0 | 9.80665 | m / s2 | Standard acceleration of gravity
h | 6.62607015e-34 | J s | Planck constant
hbar | 1.05457182e-34 | J s | Reduced Planck constant
k_B | 1.380649e-23 | J / (K) | Boltzmann constant
m_e | 9.1093837e-31 | kg | Electron mass
m_n | 1.6749275e-27 | kg | Neutron mass
m_p | 1.67262192e-27 | kg | Proton mass
mu0 | 1.25663706e-06 | N/A2 | Vacuum magnetic permeability
muB | 9.27401008e-24 | J/T | Bohr magneton
sigma_T | 6.65245873e-29 | m2 | Thomson scattering cross-section
sigma_sb | 5.67037442e-08 | W / (K4 m2) | Stefan-Boltzmann constant
u | 1.66053907e-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 | 5.97216787e+24 | kg | Earth mass
M_jup | 1.8981246e+27 | kg | Jupiter mass
M_sun | 1.98840987e+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

#### Classes

`Constant`(abbrev, name, value, unit, uncertainty) | A physical or astronomical constant.
`EMConstant`(abbrev, name, value, unit, ...[, ...]) | An electromagnetic constant.

#### Class Inheritance Diagram