The Concept Of Astronomical Unit, Light Year And Parsec.

This is the fourth article in Basics of Astrophysics series and we are now ready to explore the cosmos in detail from here on. Every branch of science has its own order of work field. The convenient units of length vary according the system that a scientist is studying. For example, a material scientist mostly deals in microns (10^-6 m), an atomic physicist deals in Angstrom (10^-10 m), a nuclear physicist deals in Fermi (10^-15 m) and so on. No doubt, there is an SI unit of length (meter), yet it cannot be used conveniently in every branch of physics. It will be absurd to state the atomic diameters in meters or kilometers. So, according to the system, we have to choose our own units. So what about Astronomy? Are there any special units? Yes! Let us understand the concept of light year, parsec and astronomical unit.

Here are for all the previous posts of the series.

The Order of Distances And Units

Unlike the quantum systems, the universe is big. Very big. So big that even kilometers fall short. So astronomers developed a new system of units of length. We will discuss three major units that you will come across in most of the astronomy books. They are: Light Year, Parsec and Astronomical Unit (AU). The usage of the units depends on the range of distance. To describe the distance to planets in solar system, we generally use AU. Distance to nearby stars is generally expressed in light years and parsecs while the distance to galaxies is expressed in kiloparsec and megaparsec.

Astronomical Unit (AU)

The Astronomical Unit is the average distance between Sun and the Earth. Its exact value is 149,597,870,700 metres or about 150 million kilometres (93 million miles).

Astronomical Unit
1 AU

We know that the orbit of Earth (or any other planet) around the Sun is not a circle. It is an ellipse. So the distance of the Earth from the Sun keeps on changing over the course of year. The AU was originally defined as the length of the semi-major axis of the elliptical orbit of Earth. But, in 1976, this definition was revised by International Astronomical Union (IAU) for a greater precision. Now, the AU is the the distance from the center of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days (one Gaussian year). More accurately, it is the distance at which the heliocentric gravitational constant (the product GM) is equal to (0.017 202 093 95)² AU³/d². Here
M is the mass of the Sun.

Importance of AU:

It should be kept in mind that the value of gravitational constant G and mass of Sun M are not known to a great precision. The value of their product, though, is known precisely. Calculations in celestial mechanics are performed mainly using AU and solar masses. This approach makes all results dependent on the gravitational constant. These constants are not changed to SI units to avoid introduction of any uncertainty.

Light Year (ly)

The product of a Julian year (365.25 days) and the speed of light (299,792,458 m/s) is formally defined as a light year. Since it is a product of time and speed, it is the distance that light travels in one Julian year. The numeric value of this distance is 9.46 trillion Km or 63,241.077 AU. Light year is the parent unit from which other units such as light seconds, light minutes and light hours can be derived. If something is "light-x' away, it means the distance that light traveled in x units.

Importance of light year:

Light year is extensively used in astronomy. One great benefit of using light year as the unit of distance is that it tells how far back in time we are looking. Suppose a star is 4 light years away. This means that light took 4 years to travel from that star to Earth. So when we make an observation, we are looking at the star that was 4 years back. Similarly, Sun is 500 light seconds away. So if Sun blacks out now, its light will be there for another 500 seconds.

Parsec (pc)

The value of one parsec is 3.26 light years. You must be wondering, if there is such a less difference between ly and pc, what is the need of another unit? Let us see.

The concept of Parsec from Astronomical unit
Concept of Parsec

In Astronomy, one of the oldest method to find the distance to a star is the parallax method. In this method, the difference in angle between two measurements of the position of the star in the sky is recorded. The first observation is made from Earth on one side and the second one six months later when the Earth is on the opposite side of Sun. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the distant vertex.

So the parallax is half the angular distance that the star appears to move across the sky. Equivalently, it is the subtended angle, from that star's perspective, of the semi-major axis of the Earth's orbit. It can be easily seen that the star (D), the Sun (S) and the Earth (E) form a right angled triangle.

Definition of Parsec

So we know the angle SDE and the length SE (1 AU). From this information, using trigonometry, we can find the distance SD and hence ED. Now if the angle subtended is 1 arc second, then the distance to the star is 1 parsec. So we are now in a position to define 1 parsec: The distance at which 1 AU subtends an angle of 1 arc second.

Importance of parsec

The parsec method is the most fundamental calibration step of distance determination in astrophysics. Ground based telescopes have a limit of parallax measurement of 0.01 arc seconds and thus stars beyond 100 parsec cannot be measured accurately. This is because the Earth's atmosphere limits the sharpness of a star's image. However space telescopes are not limited by this effect. Parsecs, kiloparsecs and megaparsecs are used to state the distances to deep sky objects.

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Author's Message

I hope the fourth article of Basics of Astrophysics series has given idea about distance measurement in astronomy: Astronomical unit, Light Year and Parsec. This is a fundamental lesson in astronomy. In the coming articles, we will be using these units in our text regularly. So it was important to share an article on these fundamental concepts. Hope you're enjoying this series. I was asked which book to follow for Astrophysics. I recommend you buy "Basics of Astrophysics" by Baiydanaath Basu (click on the Amazon link below to buy). It is very nice book with basic concepts written in a simple language. You'll relish reading it.

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