A satelete is in an all optical orbit around planet P. It is observed that the velocity of the satelite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances b/w the satelite and the planet at closest and farthest point is :-
 
Option: 1 3:4
Option: 2 1:6
Option: 3 1:2  
Option: 4 1:3

Answers (1)

As the angular momentum remains conserved. So,

L_{Nearest} = L_{Farthest}

m \times v_n \times r_n = m \times v_f \times r_f

Also,

V_{f}=\frac{V_{n}}{6}

As,

V_{n} \times r_{n}={V}_{f} \times{r}_{f}

V_{n} \times r_{n}=\frac{V_n}{6} \times{r}_{f}

So,

\frac{r_n}{r_f} = \frac{1}{6}

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