The maximum and minimum distances of a comet | vedclass

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(A) According to the law of conservation of angular momentum,the angular momentum of the comet remains constant throughout its orbit.$L = mvr \sin(	h

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) According to the law of conservation of angular momentum,the angular momentum of the comet remains constant throughout its orbit.$L = mvr \sin(	heta) = 	ext{constant}$.At the points of perihelion (nearest) and aphelion (farthest),the velocity vector is perpendicular to the radius vector,so $	heta = 90^{\circ}$.Thus,$m v_{	ext{near}} r_{	ext{near}} = m v_{	ext{far}} r_{	ext{far}}$.Given:$r_{	ext{near}} = 1.6 	imes 10^{12} \, m$$r_{	ext{far}} = 8 	imes 10^{12} \, m$$v_{	ext{near}} = 60 \, m/s$Substituting these values into the equation:$60 	imes 1.6 	imes 10^{12} = v_{	ext{far}} 	imes 8 	imes 10^{12}$$v_{	ext{far}} = \frac{60 	imes 1.6}{8} = \frac{96}{8} = 12 \, m/s$.

The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

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