# Constants (`astropy.constants`

)¶

## Introduction¶

`astropy.constants`

contains a number of physical constants useful in
Astronomy. Constants are `Quantity`

objects with
additional metadata describing their provenance and uncertainties.

## Getting Started¶

To use the constants in International System of Units (SI 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 of the constants you need, you can do:

```
>>> from astropy import constants as const
```

and then subsequently use, for example, `const.G`

. Constants are fully-fledged
`Quantity`

objects, so you can conveniently 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 2018
>>> print(const.c.to('km/s'))
299792.458 km / s
>>> print(const.c.to('pc/yr'))
0.306601393788 pc / yr
```

You can then use them in conjunction with unit and other nonconstant
`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 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
```

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
```

The astronomical and physical constants are combined into modules with
names like `astropyconst13`

, `astropyconst20`

, and `astropyconst40`

for different versions.
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 `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 and the
IAU 2012 astronomical constants:

```
>>> from astropy import physical_constants, astronomical_constants
>>> physical_constants.set('codata2010') # doctest: +SKIP
<ScienceState physical_constants: 'codata2010'>
>>> physical_constants.get() # doctest: +SKIP
'codata2010'
>>> astronomical_constants.set('iau2012') # doctest: +SKIP
<ScienceState astronomical_constants: 'iau2012'>
>>> astronomical_constants.get() # doctest: +SKIP
'iau2012'
```

Then all other packages that import `astropy.constants`

will self-consistently
initialize with that prior version 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') # doctest: +SKIP
<ScienceState physical_constants: 'codata2010'>
>>> physical_constants.get() # doctest: +SKIP
'codata2010'
>>> astronomical_constants.set('astropyconst13') # doctest: +SKIP
<ScienceState astronomical_constants: 'iau2012'>
>>> astronomical_constants.get() # doctest: +SKIP
'iau2012'
```

If either `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
```

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 = 6.62607015e-34
Uncertainty = 0.0
Unit = J s
Reference = CODATA 2018
```

The context manager may be used at any time in a Python session, but it
uses the prior version only for `astropy.constants`

, and not for any
other subpackage such as `astropy.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 | 6.6743e-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 |

#### 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. |