# Dimensions of Light Year

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## What is a Light-year?

A light-year is a unit to measure distance. It is defined as the distance that a beam of light can travel in one year. One light-year is equal to 6 trillion miles or 9.5 trillion kilometers or 63,241 astronomical units. No object in the universe travels faster than the light. Light moves in space at a speed of 300 million meters per second. Astronomers use the light-year to measure enormous distances in space, like how far the stars, planets, and galaxies are. For example, after the Sun, the next closest star to Earth is 4.3 light-years away.

Light travels large distances very quickly in space. For example, it takes 8.53 minutes to travel from the Sun to the Earth. There is a unit even larger than a light year, called a parsec. It is about 3.26 light-years. Parsec has made it easier for astronomers to measure even larger distances. Now when we know what a light-year is, let us find the dimension of the light-year. However, before starting with our findings, we need to understand the significance of dimensions.

### Significance of Dimensions

Understanding dimensions helps us in studying the nature of physical quantities mathematically. The fundamental concept of dimensions is that we can add or subtract only those quantities which have the same dimensions. Also, two physical quantities can be equal only if they have the same dimensions.

## Dimension of a Light-Year

Through our readings above, we conferred that light-year is how quickly light can travel in space. This means we are talking about the distance that light covers between two astronomical objects. As we know that the dimension of length or distance is [M0L1T0]. Similarly, the dimension of a light-year is [M0L1T0].

Now, if we look at the value of one light year in terms of Kms, miles, and Astronomical units, these are all units of distances, and also these all have dimensions of length. So, whatever units we take, the dimension of the light-year remains the same. Let us take a look at the values of the light-year in different systems of units.

## Conversions

 System of Units Value In Metric Units 9.4607 x 1015 m9.4607 Pm Imperial and S.I. Units 5.8786 x 1012 mi Astronomical Units 63,241 au 0.3066 pc

As we know that light-year is a distance travelled by astronomical objects. In the macrocosm measurements, i.e., measuring very large distances, we have two more units for the same.

### Some Important Macrocosm Units

Let us discuss some important practical units to measure astronomical distances.

1. Astronomical Unit

It is the average distance of the center of the Sun from the center of the Earth.

The value of one astronomical unit or 1 A.U  is 1.496 x 1011m~ 1.5 x 1011m.

2. Parsec

It is another unit of measurement of very large distances in space. Here, parsec represents Parallactic seconds. Parsec is the distance at which an arc 1 AU subtends an angle of 10.

We know that 1 AU = 1.496 x 1011m

And,   Ө =  1 sec or $\frac{1}{60}$s = $\frac{1}{60 × 60}$degrees.

So, 1 sec =  $\frac{1}{60 × 60}$ × $\frac{π}{180}$radian

We know that r = $\frac{l}{Ө}$

where, l = 1 AU and 1 sec = $\frac{1}{60 × 60}$ × $\frac{π}{180}$

So, 1 parsec = $\frac{1AU}{1sec}$ = $\frac{1.496 × 10^{11}}{\frac{1}{60 × 60} × \frac{π}{180}}$

On solving, we get,

1 parsec = 3.1 x 1016 m

### Relationship Between ly, AU, and parsec

Let us derive the relation between these three units.

1. The relation between ly and AU

We know that 1 ly =  9.4607 x 1015 m

1 AU = 1.5 x 1011m

Now, $\frac{1ly}{1AU}$= 9.4607 x 1015 m / 1.5 x 1011m On solving, we get,

 1 ly = (6.3 x 104 m) AU

2.The relationship between parsec and ly:

We know that 1 parsec = 3.1 x 1016 m and

ly = 9.4607 x 1015 m

Now, 1parsec / 1ly = 3.1 x 1016m / 9.4607 x 1015 m

On solving, we get,

 1 parsec = 3.26 ly

This is how we can derive the relationship between various astronomical units.

Q1: Calculate the number of Astronomical Units in one meter.

Ans: We know that 1 AU = 1.5 x 1011m

Or, 1.5 x 1011m = 1 AU

So,  1 m = 1/1.5 x 1011 AU

On solving, we get,

1 AU = 6.67 x 10-12m.

Q2: Calculate the number of Light-years in one meter.

Ans: We know that 1 ly = 9.4607 x 1015 m

So, 1 m = 1/9.4607 x 1015ly

On solving, we get,

1 ly = 1.057 x 10-16ly

Q3: Derive the value for one Light-year.

Ans: We know that the speed of light = 3 x 108ms-1

Length of Earth year = 365 days, and

365 days = 365 x 24 hours = 365 x 24 x 60 minutes = 365 x 24 x 60 x 60 seconds

On solving, we get the length of Earth year = 3.15 x 107 s.

∴ Distance = Speed x time = 3 x 108ms-1 x 3.15 x 107 s

So, 1 light-year = 9.45 x 1015m.

Q4: Define Light-year in days.

Ans: According to the International Astronomical Units, a light-year is a distance that light travels in a vacuum in one Julain year, i.e., 365.25 days.