# 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):
...
```

## 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)

R

8.31446262

J / (K mol)

Gas constant

Ryd

10973731.6

1 / (m)

Rydberg constant

a0

5.29177211e-11

m

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

R_jup

71492000

m

R_sun

695700000

m

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.