A planet revolves around the Sun in an ellipt | vedclass

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(C) According to the law of conservation of angular momentum,the angular momentum of the planet remains constant throughout its orbit.At the closest p

Vedclass · Accepted Answer

$\frac{d_1 v_1}{d_2}$

Vedclass · Answer

(C) According to the law of conservation of angular momentum,the angular momentum of the planet remains constant throughout its orbit.At the closest point (perihelion),the velocity vector is perpendicular to the position vector,so the angular momentum is $L_1 = m v_1 d_1$.At the farthest point (aphelion),the velocity vector is also perpendicular to the position vector,so the angular momentum is $L_2 = m v_2 d_2$.Since $L_1 = L_2$,we have $m v_1 d_1 = m v_2 d_2$.By simplifying this equation,we get $v_1 d_1 = v_2 d_2$.Therefore,the velocity at the farthest point is $v_2 = \frac{d_1 v_1}{d_2}$.

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

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