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A satellite moves in an elliptical orbit about the earth . The minimum and maximum distance of the satellite from the centre of earth are $7000 k m$ and $8750 k m$ respectively. For this situation mark the correct statement $(s)$ [Take $M_{e} = 6 \times 10^{24} k g$ ]

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The maximum speed of the satellite during its motion is $5.64 k m / s$

The minimum speed of the satellite during its motion is $4.51 k m / s$

The length of major axis of orbit is $15750 k m$

The minimum speed of the satellite during motion is 3.84 km/s .

answer is A, B, C.

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Detailed Solution

From angular momentum conservation

$m v_{p} \times r_{p} = m v_{A} r_{A} \Rightarrow \frac{v_{p}}{v_{A}} = \frac{r_{A}}{r_{p}} = \frac{8750}{7000} = 1.25$

From energy conservation ,

$\frac{m v_{p}^{2}}{2} - \frac{G M_{e} m}{r_{p}} = \frac{m v_{A}^{2}}{2} - \frac{G M_{e} m}{r_{A}} \Rightarrow v_{A}^{2} - v_{P}^{2} = G M_{e} (\frac{1}{r_{A}} - \frac{1}{r_{p}}) \Rightarrow v_{A} = 4.51 k m / s a n d v_{p} = 5.64 k m / s$

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