Distances And Their Units In Astrophysics

Rishabh Nakra

Admin and Founder of ‘The Secrets Of The Universe’ and former intern at Indian Institute of Astrophysics, Bangalore, I am a science student pursuing a Master’s in Physics from India. I love to study and write about Stellar Astrophysics, Relativity & Quantum Mechanics.

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 to 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. 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.

All the articles of Basics of Astrophysics 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 the 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 kilo-parsecs and mega-parsecs.

Astronomical Unit (AU)

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

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 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 the gravitational constant G and the 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.

Also watch: 10 unsolved mysteries of the universe

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.

Importance of Light Year

It is important to know that if something is “light-x’ away, it means the distance that light traveled in x units. The nearest star is about 4.2 light years away. This means that the light from that star takes 4.2 years to reach us. Similarly, the Sun is 500 light seconds away. This implies that light from the Sun, the moment it escapes its surface, takes 500 seconds to reach the Earth. We see the Sun as it was 500 seconds ago. Hence astronomy is actually the study of the history of the cosmos. No one knows what is currently going on in the universe.

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.

In Astronomy, one of the oldest methods 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 the 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.

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.

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. If you have any questions, please feel free to contact me.

All the articles of Basics of Astrophysics series