The maximum and minimum distances of a comet | vedclass

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(C) According to the law of conservation of angular momentum,the angular momentum of the comet remains constant at all points in its orbit.Let $r_1$ a

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$3.0$

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(C) According to the law of conservation of angular momentum,the angular momentum of the comet remains constant at all points in its orbit.Let $r_1$ and $v_1$ be the distance and speed at the nearest point (perihelion),and $r_2$ and $v_2$ be the distance and speed at the farthest point (aphelion).Given:$r_1 = 8.0 	imes 10^{10} \ m$$v_1 = 6 	imes 10^{4} \ m/s$$r_2 = 1.6 	imes 10^{12} \ m$Using the conservation of angular momentum:$m v_1 r_1 = m v_2 r_2$$v_2 = \frac{v_1 r_1}{r_2}$Substituting the values:$v_2 = \frac{(6 	imes 10^{4}) 	imes (8.0 	imes 10^{10})}{1.6 	imes 10^{12}}$$v_2 = \frac{48 	imes 10^{14}}{1.6 	imes 10^{12}}$$v_2 = 30 	imes 10^{2} \ m/s = 3 	imes 10^{3} \ m/s$Thus,the speed at the farthest point is $3 	imes 10^{3} \ m/s$.

The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \ m$ and $8.0 \times 10^{10} \ m$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4} \ m/s$,the speed at the farthest point is ......... $\times 10^{3} \ m/s$.

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