Question

State the relation between 1AU, 1 Parsec and 1 Light year. DON'T COPY FROM ANYWHERE.​

Answer 1

Solution :

☀ To Find :-

✏ Relation between astronomical unit(AU), light year(ly) and parsec.

☀ Calculation :-

• 1 AU = 1.5 × 10$^{11}$m
• 1 ly = 9.46 × 10$^{15}$m
• 1 parsec = 3.08 × 10$^{16}$m

$\implies\sf\:\dfrac{1\:ly}{1\:AU}=\dfrac{9.46\times 10^{15}}{1.5\times 10^{11}}=6.3\times 10^4\\ \\ \therefore\bf\:1\:ly=6.3\times 10^4\: AU\\ \\ \implies\sf\:\dfrac{1\:parsec}{1\:ly}=\dfrac{3.08\times 10^{16}}{9.46\times 10^{15}}=3.26\\ \\ \therefore\bf\: 1\:parsec = 3.26\:ly\\ \\ \bigstar\:\boxed{\sf{\pink{\large{1\:parsec>1\:ly>1\:AU}}}}$

Answer 2

Hello Dear.

Here is the answer---

←→→→→→→→→→

Astronomic unit(A.U.) : One A.U. is equal to the Mean distance between the Earth and the Sun.

        1 A.U. = 1.496 × 10¹¹ m.

   ⇒  1 m = (10⁻¹¹/1.496) A.U.      --------------------eq(i)

Parsec : One Parsec is the distance from the semi major axis of the orbits of the earth subtends an angle of one second of arc at the centre of the sun. 

One Parsec is 3.26 times the light year.

      1 Parsec = 3.26 Light Year.

                     = 3.26 × 9.46 × 10¹⁵ m.

                     = 30.8396 × 10¹⁵ m.

  ⇒  1 m = (10⁻¹⁵/30.8396)  -----------------------eq(ii)

From eq(i) and eq(ii),

     (10⁻¹¹/1.496) A.U. = (10⁻¹⁵/30.8396) Parsec.

         ⇒     1 Parsec = (30.8396/1.496) × 10⁴ A.U.

         ⇒     1 Parsec = 20.6147 × 10⁴ A.U.

         ⇒     1 Parsec ≈  2.06 × 10⁴ A.U.

Thus, the Relation between the Parsec and the A.U.(Astronomical Unit) is Proved above.

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Hope it helps.

HAVE A MARVELOUS DAY.