Physical units and constants module

The astrophysix package also provides a Unit helper class to handle physical constants and units. In addition, a large set of physical quantities and constants are defined in this module.

Basic use cases

Unit information

You can have access to unit parameters with the name, description, coeff, dimensions, latex and physical_type properties :

>>> from astrophysix import units as U
>>> mass_unit = U.Msun
>>> mass_unit.name
Msun
>>> mass_unit.dimensions
array([1, 0, 0, 0, 0, 0, 0, 0], dtype=int32)
>>> mass_unit.coeff
1.9889e+30
>>> mass_unit.description
'Solar mass'
>>> mass_unit.latex
'\\textrm{M}_{\\odot}'
>>> mass_unit.physical_type
'mass

A summary of any Unit can be displayed using the Unit.info method :

>>> from astrophysix import units as U
>>> U.ly.info()
Unit : ly
---------
Light year

Value
-----
9460730472580800.0 m

Equivalent units
----------------
 * m            :      1.057e-16 ly
 * um           :      1.057e-22 ly
 * mm           :      1.057e-19 ly
 * cm           :      1.057e-18 ly
 * nm           :      1.057e-25 ly
 * km           :      1.057e-13 ly
 * Angstrom     :      1.057e-26 ly
 * au           :    1.58125e-05 ly
 * pc           :        3.26156 ly
 * kpc          :        3261.56 ly
 * Mpc          :    3.26156e+06 ly
 * Gpc          :    3.26156e+09 ly
 * Rsun         :    7.35153e-08 ly

Unit retrieval

The built-in units and constants defined in the astrophysix package are directly accessible as variables of the package :

>>> from astrophysix import units as U
>>> U.Msun.description
'Solar mass'
>>> U.kHz.description
'kilo-Hertz : frequency unit'

For custom units retrieval, see Custom Units

Unit operations

You can create composite units by multiplying or dividing Unit objects by float values or other Unit objects. You can also raise Unit objects to a given (integer) power :

>>> from astrophysix import units as U
>>> u = U.km/U.s
>>> print(u)
(1000 m.s^-1)

>>> joule = kg*(m/s)**2
>>> joule == U.J
True

>>> my_p = 250.0 * J * m**-3
>>> my_p.physical_type
'pressure'

Custom Units

If you want to create your own units and use them elsewhere in your code, you can create a Unit instance that will be included in the astrophysix unit registry, use Unit.create_unit method to add a new unit, and Unit.from_name to retrieve it :

>>> from astrophysix import units as U
>>> U.km_s == U.km/U.s # Soft equality => same coefficient and same dimensions
True
>>> U.km_s.identical(U.km/U.s)  # Strict equality => they do not share the same names/LaTEX formulae, descriptions
False
# Create a custom Solar mass per square kiloparsec surface density unit
>>> u = U.Unit.create_unit(name="Msun_pc2", base_unit=U.Msun/U.pc**2, descr="Solar mass per square parsec",
                           latex="\\textrm{M}_{\\odot}\\cdot\\textrm{pc}^{-2}")

>>> u.identical(U.Msun/U.pc**2)
False

>>> # Later in your Python script ...
>>> surf_dens_unit = U.Unit.from_name("Msun_pc2")
surf_dens_unit == U.Msun/U.pc**2
True
>>>surf_dens_unit.description
"Solar mass per square parsec"

Unit search

You can browse the units available in the astrophysix unit registry using the Unit.equivalent_unit_list method, the Unit.appropriate_unit method or the Unit.iterate_units iterator :

>>> # Equivalent units
>>> U.km.equivalent_unit_list()
[m : (1 m),
 um : (1e-06 m),
 mm : (0.001 m),
 cm : (0.01 m),
 nm : (1e-09 m),
 Angstrom : (1e-10 m),
 au : (1.49598e+11 m),
 pc : (3.08568e+16 m),
 kpc : (3.08568e+19 m),
 Mpc : (3.08568e+22 m),
 Gpc : (3.08568e+25 m),
 Rsun : (6.95508e+08 m),
 ly : (9.46073e+15 m)]

>>> # Most appropriate unit
>>> u = 0.3 * U.pc
>>> f, best_unit = u.appropriate_unit()
>>> print("{f:g} {bu:s}".format(f=f, bu=best_unit.name))
0.978469 ly

>>> # Unit iterator
>>> for u in Unit.iterate_units(phys_type="time"):
        print(u.name)
s
min
hour
day
sid_day
year
kyr
Myr
Gyr

Unit conversion

Unit conversion can be done with the Unit.express method :

>>> from astrophysix import units as U
>>> # Basic unit conversion
>>> l = 100.0 * U.kpc
>>> t = 320.0 U. Myr
>>> v = l/t
>>> print("v = {c:g} km/s".format(c=v.express(U.km_s)))
v = 305.56 km/s

Built-in quantities and constants

Base units

Name

Description

A

Ampere : electric intensity base unit

K

Kelvin : base temperature unit

cd

Candela: base luminous intensity unit

kg

Kilogram : base mass unit

m

Meter : base length unit

mol

mole: amount of a chemical substance base unit

none

Unscaled dimensionless unit

rad

radian: angular measurement (ratio lengh / radius of an arc)

s

Second : base time unit

Constants and common units

Name

Value

Decomposition in base units

Description

Angstrom

1e-10

m

Angstrom: 10**-10 m

C

1

s.A

Coulomb

F

1

kg^-1.m^-2.s^4.A^2

Farad

G

6.67428e-11

kg^-1.m^3.s^-2

Graviational constant

GHz

1e+09

s^-1

giga-Hertz : frequency unit

Gauss

0.0001

kg.s^-2.A^-1

Gauss

Gpc

3.08568e+25

m

Gigaparsec

Gyr

3.15576e+16

s

Gigayear : trillion years

H

2.26855e-18

s^-1

Hubble’s constant

H_cc

2.18421e-21

kg.m^-3

Atoms per cubic centimeter

Henry

1

kg.m^2.s^-2.A^-2

Henry

Hz

1

s^-1

Hertz : frequency unit

J

1

kg.m^2.s^-2

Joule : (SI) energy unit

Jy

1e-26

kg.s^-2

Jansky

Lsun

3.846e+26

kg.m^2.s^-3

Solar luminosity

MHz

1e+06

s^-1

mega-Hertz : frequency unit

Mearth

5.9722e+24

kg

Earth mass

Mpc

3.08568e+22

m

Megaparsec

Msun

1.9889e+30

kg

Solar mass

Myr

3.15576e+13

s

Megayear : million years

N

1

kg.m.s^-2

Newton : (SI) force unit

Ohm

1

kg.m^2.s^-3.A^-2

Ohm

Pa

1

kg.m^-1.s^-2

Pascal: (SI) pressure unit

Rsun

6.95508e+08

m

Solar radius

S

1

kg^-1.m^-2.s^3.A^2

Siemens

T

1

kg.s^-2.A^-1

Tesla

V

1

kg.m^2.s^-3.A^-1

Volt

W

1

kg.m^2.s^-3

Watt

a_r

7.56577e-16

kg.m^-1.s^-2.K^-4

Radiation constant

arcmin

0.000290888

rad

arc minute: 1/60 of a hour angle

arcsec

4.84814e-06

rad

arc second: 1/60 of an arcminute

atm

101325

kg.m^-1.s^-2

atm: atmospheric pressure (101 3525 Pa)

au

1.49598e+11

m

Astronomical unit

bar

100000

kg.m^-1.s^-2

Bar

barn

1e-28

m^2

barn: surface unit used in HEP

barye

0.1

kg.m^-1.s^-2

Barye: (CGS) pressure unit

c

2.99792e+08

m.s^-1

Speed of light in vacuum

cm

0.01

m

Centimeter

cm3

1e-06

m^3

Cubic centimeter

day

86400

s

Day

deg

0.0174533

rad

degree: angular measurement corresponding to 1/360 of a full rotation

dyne

1e-05

kg.m.s^-2

dyne : (CGS) force unit

e

1.60218e-19

s.A

e : elementary electric charge carried by a proton

eV

1.60218e-19

kg.m^2.s^-2

electron-Volt

erg

1e-07

kg.m^2.s^-2

erg : (CGS) energy unit

g

0.001

kg

Gram

g_cc

1000

kg.m^-3

Gram per cubic centimeter

h

6.62607e-34

kg.m^2.s^-1

Planck Constant

hPa

100

kg.m^-1.s^-2

Hectopascal

hbar

1.05457e-34

kg.m^2.s^-1

Reduced Planck constant

hour

3600

s

Hour

hourangle

0.261799

rad

hour angle: angular measurement with 24 in a full circle

kB

1.38065e-23

kg.m^2.s^-2.K^-1

Boltzmann constant

kHz

1000

s^-1

kilo-Hertz : frequency unit

kPa

1000

kg.m^-1.s^-2

Kilopascal

km

1000

m

Kilometer

km_s

1000

m.s^-1

kilometers per second

kpc

3.08568e+19

m

Kiloparsec

kpc3

2.938e+49

m^3

Cubic kiloparsec

kyr

3.15576e+10

s

kyr : millenium

lm

1

rad^2.cd

Lumen

lx

1

m^-2.rad^2.cd

Lux

ly

9.46073e+15

m

Light year

m3

1

m^3

Cubic meter

mGauss

1e-07

kg.s^-2.A^-1

Milligauss

mH

1.66e-27

kg

Hydrogen atomic mass

m_s

1

m.s^-1

Meters per second

min

60

s

Minute

mm

0.001

m

Millimeter

nm

1e-09

m

Nanometer

pc

3.08568e+16

m

Parsec

pc3

2.938e+49

m^3

Cubic parsec

percent

0.01

One hundredth of unity

rhoc

9.2039e-27

kg.m^-3

Friedmann’s universe critical density

sid_day

86164.1

s

Sidereal day : Earth full rotation time

sigmaSB

5.6704e-08

kg.s^-3.K^-4

Stefan-Boltzmann constant

sr

1

rad^2

Steradian: solid angle (SI) unit

t

1000

kg

Metric ton

uGauss

1e-10

kg.s^-2.A^-1

Microgauss

um

1e-06

m

Micron

year

3.15576e+07

s

Year

Physical quantities

Quantity

Decomposition in base units

acceleration

m.s^-2

amount of substance

mol

angle

rad

angular acceleration

s^-2.rad

angular momentum

kg.m^2.s^-1

angular velocity

s^-1.rad

area

m^2

dimensionless

dynamic viscosity

kg.m^-1.s^-1

electric capacitance

kg^-1.m^-2.s^4.A^2

electric charge

s.A

electric charge density

m^-3.s.A

electric conductance

kg^-1.m^-2.s^3.A^2

electric conductivity

kg^-1.m^-3.s^3.A^2

electric current

A

electric current density

m^-2.A

electric dipole moment

m.s.A

electric field strength

kg.m.s^-3.A^-1

electric flux density

m^-2.s.A

electric potential

kg.m^2.s^-3.A^-1

electric resistance

kg.m^2.s^-3.A^-2

electric resistivity

kg.m^3.s^-3.A^-2

energy

kg.m^2.s^-2

energy flux density

kg.s^-3

entropy

kg.m^2.s^-2.K^-1

force

kg.m.s^-2

frequency

s^-1

inductance

kg.m^2.s^-2.A^-2

kinematic viscosity

m^2.s^-1

length

m

linear density

kg.m^-1

luminance

m^-2.cd

luminous emittence

m^-2.rad^2.cd

luminous flux

rad^2.cd

luminous intensity

cd

magnetic field strength

m^-1.A

magnetic flux

kg.m^2.s^-2.A^-1

magnetic flux density

kg.s^-2.A^-1

magnetic permeability

kg.m.s^-2.A^-2

mass

kg

molar volume

m^-3.mol

moment of inertia

kg.m^2

momentum/impulse

kg.m.s^-1

permittivity

kg^-1.m^-3.s^4.A^2

power

kg.m^2.s^-3

pressure

kg.m^-1.s^-2

radiant intensity

kg.m^2.s^-3.rad^-2

solid angle

rad^2

specific energy

m^2.s^-2

specific volume

kg^-1.m^3

spectral flux density

kg.s^-2

surface density

kg.m^-2

temperature

K

thermal conductivity

kg.m.s^-3.K^-1

time

s

velocity

m.s^-1

volume

m^3

volume density

kg.m^-3

wavenumber

m^-1