Question

What is the difference between a radian, an arc-second and a parsec?

Answer 1

In order to solve this question, we should know that basic measurements of an angle subtends in two dimensional plane is measured in degrees and a complete circle makes an angle of ${360^o}$ which we call total angle in two dimensional plane, here we will discuss each terms one by one and will see how these quantities are different from one another.

Complete answer:
The major differences between a radian, an arc-second and a parsec are given in below table:

A Radian	An Arc-Second	A Parsec
Radian represents the measurement of angle in a two dimensional plane.	Arc-Second is also used to measure the angle in a two dimensional plane.	Parsec represents the measurement of distance.
It’s the angle made by radii of a circle subtending a circular arc of distance ‘s’ and circle having radius of ‘r’ then angle in radians is written as $\theta = \dfrac{s}{r}$	It’s an angle which is counted for $\dfrac{1}{{3600}}th$ part of one degree. or we can also say that arc second is $\dfrac{1}{{60}}th$ of a minute of an arc.	It’s defined as the distance at which the mean radius of our earth makes an angle of one arc-second. and It’s an astronomical unit of distance.
The relation between radian measurements and degree measurements is related as ${1^o} = \dfrac{\pi }{{{{180}^o}}}$	An arc-second is represented as $x''$ where x represents the numerical value of an arc-second.	Approximately, one parsec value is close to $1par\sec = 3.086 \times {10^{16}}m$

Note: It should be remembered that the terms may look very similar to each other like arc-second, parsec and looks like they represent units of time but arc-second is a measurement of an angle whereas parsec is a measurement of distance used in astronomy.