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(A) According to the law of conservation of angular momentum,the angular momentum of the satellite remains constant throughout its orbit.At the closes

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$1:6$

Vedclass · Answer

(A) According to the law of conservation of angular momentum,the angular momentum of the satellite remains constant throughout its orbit.At the closest point (periapsis) and farthest point (apoapsis),the velocity vector is perpendicular to the position vector.Therefore,$L = m r_{\min} V_{\max} = m r_{\max} V_{\min}$.This simplifies to $r_{\min} V_{\max} = r_{\max} V_{\min} \quad \dots(i)$.Given that the velocity at the farthest point is $6$ times less than the velocity at the closest point,we have $V_{\min} = \frac{V_{\max}}{6}$,or $\frac{V_{\min}}{V_{\max}} = \frac{1}{6}$.Substituting this into equation $(i)$,we get $\frac{r_{\min}}{r_{\max}} = \frac{V_{\min}}{V_{\max}} = \frac{1}{6}$.Thus,the ratio of the distances is $1:6$.

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