How many astronomical units (AU) make 1 parse | vedclass

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(A) We know that $1$ parsec is defined as the distance at which an arc of length $1 AU$ subtends an angle of $1$ arcsecond $(1'')$ at the center.Using

Vedclass · Accepted Answer

$2.06 	imes 10^5 AU$

Vedclass · Answer

(A) We know that $1$ parsec is defined as the distance at which an arc of length $1 AU$ subtends an angle of $1$ arcsecond $(1'')$ at the center.Using the formula for angle: $	heta = \frac{	ext{arc}}{	ext{radius}}$Here,$	heta = 1'' = \frac{1}{3600} 	ext{ degrees} = \frac{1}{3600} 	imes \frac{\pi}{180} 	ext{ radians} \approx 4.848 	imes 10^{-6} 	ext{ radians}$.Arc length $= 1 AU$.Radius $= 1 	ext{ parsec}$.Therefore,$1 	ext{ parsec} = \frac{1 AU}{	heta} = \frac{1 AU}{4.848 	imes 10^{-6}} \approx 2.06 	imes 10^5 AU$.

How many astronomical units $(AU)$ make $1$ parsec?

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