light year

Non-SI unit

Name	Symbol	Quantity		SI units
light year	ly	length	9 460 730 472 580 800 m
The light year, symbol ly, is a non-SI unit of length. The light year is not accepted for use with the SI. One light year is defined as the distance travelled by light in vacuum during a time interval of one Julian year, 365.25 days, or 31 557 600 seconds. One light year is equal to 9 460 730 472 580 800 m, or approximately 9.46 petametres.
Definition				c Δν_Cs^-1
$1 \mspace{4mu} \text{ly} \mspace{6mu} = (31 \mspace{4mu} 557 \mspace{4mu} 600)(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770) \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{ly} \mspace{6mu} = 2.900 \mspace{4mu} 973 \mspace{4mu} 963 \mspace{4mu} 449 \mspace{4mu} 52 \times10^{17} \mspace{6mu} c \mspace{4mu} {\Delta \nu _{Cs}}^{-1}$

The length in metres of one light year is calculated by multiplying the speed of light in vacuum, c, by the number of seconds in one Julian year:

$1 \mspace{4mu} \text{ly} = (299 \mspace{4mu} 792 \mspace{4mu} 458 \mspace{4mu} \text{m} \mspace{4mu} \text{s}^{-1}) \mspace{4mu} (31 \mspace{4mu} 557 \mspace{4mu} 600 \mspace{4mu} \text{s})\\ \\ 1 \mspace{4mu} \text{ly} = 9 \mspace{4mu} 460 \mspace{4mu} 730 \mspace{4mu} 472 \mspace{4mu} 580 \mspace{4mu} 800 \mspace{4mu} \text{m}$

Defining constants

The metre is defined by the equation:

$1 \mspace{4mu} \text{m} \mspace{6mu} = \dfrac{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770}{299 \mspace{4mu} 792 \mspace{4mu} 458} \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}$

Multiplying both sides of the equation by the numerical value of the speed of light in vacuum gives the definition for the distance travelled by light in one second. This distance is known as a light second.

$299 \mspace{4mu} 792 \mspace{4mu} 458 \mspace{4mu} \text{m} \mspace{6mu} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}$

The definition for the light year can then be obtained by multiplying both sides of the equation by 31 557 600, the number of seconds in a Julian year:

$1 \mspace{4mu} \text{ly} \mspace{6mu} = (31 \mspace{4mu} 557 \mspace{4mu} 600)(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770) \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{ly} \mspace{6mu} = 290 \mspace{4mu} 097 \mspace{4mu} 396 \mspace{4mu} 344 \mspace{4mu} 952 \mspace{4mu} 000 \mspace{6mu} c \mspace{4mu} {\Delta \nu _{Cs}}^{-1}$

Astronomy

The light year is used in the field of astronomy, primarily to express distances on interstellar and intergalactic scales.

Examples of distances of stars from Earth

Name	Distance in light years	Distance in SI units
Proxima Centauri	4.24 ly	40.1 Pm
Barnard’s Star	5.96 ly	56.4 Pm
Sirius	8.58 ly	81.2 Pm
Tau Ceti	11.9 ly	112.5 Pm
Altair	16.7 ly	158 Pm
Vega	25 ly	237 Pm
Arcturus	36.7 ly	347 Pm
Aldebaran	65 ly	615 Pm
Betelgeuse	548 ly	5187 Pm
Rigel	860 ly	8136 Pm
One light year is equal to approximately 9.46 petametres.

Examples of distances of galaxies from Earth

Name	Distance in millions of light years	Distance in SI units
Andromeda Galaxy (M31)	2.54 Mly	24.0 Zm
Triangulum Galaxy (M33)	2.64 Mly	25.0 Zm
Messier 83 (NGC 5236)	14.7 Mly	139 Zm
Messier 63 (M63)	29.3 Mly	277 Zm
Sombrero Galaxy (M104)	31.1 Mly	294 Zm
Cartwheel Galaxy (PGC 2248)	500 Mly	4730 Zm
One million light years is equal to approximately 9.46 zettametres.

The radius of the observable universe is approximately 440 000 zettametres, or 440 yottametres.