
Arrange the following lengths in descending order of their magnitudes: Light year, parsec, and Astronomical unit.
Answer
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Hint:We know the distance traveled by light in one year is called light-year(ly). It is used to measure large distances. A parsec is a distance at which one astronomical unit subtends an angle of one second of arc, and the Astronomical unit measures the distance between the earth and the sun. A light-year is also related to astronomy and parsec. For the arrangement of these lengths in descending order, we calculate the values of each.
Complete step by step answer:
We know that one light-year is equal to the distance that light travels in a year.
Here c is the speed of light in a vacuum, which is equal to and 1 ly means one light year. Hence on simplifying the above relation, we get,
.
The relation between light-year (ly) and astronomical unit (A.U)
…… (I) and,
…… (II)
Here 1 A.U. means 1 astronomical unit.
On dividing equations(I) and (II), we get:
The relation between the light-year (ly) and parsec
Again …… (III)
And …… (IV)
On dividing equations (III) and (IV), we get
Suppose we saw the actual value of light year, parsec, A.U. (Astronomical unit). In that case, we will observe that parsec has greater value than a light-year, and a light year is greater than the Astronomical unit.
Therefore arrange in descending order of their magnitudes parsec>light year>astronomical unit.
Note:The lengths of a light-year, parsec, and astronomical unit are the same and scientifically proven throughout the universe. When we calculate the large distances and very small distances, we use non-S.I units of lengths for such measurements.
Complete step by step answer:
We know that one light-year is equal to the distance that light travels in a year.
Here c is the speed of light in a vacuum, which is equal to
The relation between light-year (ly) and astronomical unit (A.U)
Here 1 A.U. means 1 astronomical unit.
On dividing equations(I) and (II), we get:
The relation between the light-year (ly) and parsec
Again
And
On dividing equations (III) and (IV), we get
Suppose we saw the actual value of light year, parsec, A.U. (Astronomical unit). In that case, we will observe that parsec has greater value than a light-year, and a light year is greater than the Astronomical unit.
Therefore arrange in descending order of their magnitudes parsec>light year>astronomical unit.
Note:The lengths of a light-year, parsec, and astronomical unit are the same and scientifically proven throughout the universe. When we calculate the large distances and very small distances, we use non-S.I units of lengths for such measurements.
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