Question

The radius of an arc having length $1$ astronomical unit $\left( {AU} \right)$ which subtends an angle of $2\,s$ is?
(A) $1.63\,$light year
(B) $3.26$ light year
(C) $1$ parsec
(D) $1.2$ light year

Answer 1

For the most space objects, we use the light years to describe the distance between the two objects. By using the radius of arc in space formula, the radius of an arc having length $1$ astronomical unit $\left( {AU} \right)$ which subtends an angle of $2\,s$ is determined.

Formula Used:
Radius of arc, $d = \dfrac{{1\,AU}}{t}$
Where, $t$ is the time, $AU$ is the astronomical unit which is equal to Parsec

Complete step-by-step solution :Parsec is a unit of distance used in astronomy, equal to about $3.26$ light years.
Radius of arc,
$d = \dfrac{{1\,AU}}{t}\,..................\left( 1 \right)$
Here $1\,AU$ is equal to the Parsec, and one Parsec is equal to the $3.26$ light years. So, $1\,AU$ is equal to the $3.26$ light years.
Now substituting the astronomical unit value and the time value in the equation (1), then,
$d = \dfrac{{3.26}}{2}$
On dividing the above equation is written as,
$d = 1.63$
Thus, the radius of the arc is $1.63$ light years.
Hence, the option (A) is the correct answer.

Note:- Students must know about the light year, and how the light year is related to the distance. Generally, the speed of light in space is $3 \times {10^8}\,m{s^{ - 1}}$that means it travels about $300000\,km$ per second. So, the calculation is done to find the total distance travelled by light in one year. For one year the light can travel about $9.4608 \times {10^{12}}\,km$ (Approximately ten trillion kilometres).
The distance between the two objects in space is very large, So, that we cannot express it in normal value. Because the value is very large in number. Hence, the new term or unit is introduced here to express the distance between two objects. By the help of the new unit, the distance between the two objects is expressed in simple form. So, the distance between the two objects is expressed in light years. A light year is defined as the total distance travelled by the light in one year.