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Q.

Consider a satellite orbiting the earth as shown in the figure below. Let $L_{a}$ and $L_{p}$ represent the angular momentum of the satellite about the earth when at aphelion and perihelion respectively. Consider the following relations.
(i) $\vec{L_{a}} = \vec{L_{p}}$
(ii) $\vec{L_{a}} = - \vec{L_{p}}$
(iii) $\overset{⇀}{r_{a}} \times \vec{L_{a}} = \overset{⇀}{r_{p}} \times \vec{L_{p}}$
Which of the above relations is/are true?

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a

(i) only

b

(ii) only

c

(iii) only

d

(i) and (ii)

answer is A.

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Detailed Solution

Since the angular momentum of the satellite about the earth is conserved.

$∴ \vec{L_{a}} = \vec{L_{p}}$

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Consider a satellite orbiting the earth as shown in the figure below. Let La and Lp represent the angular momentum of the satellite about the earth when at aphelion and perihelion respectively. Consider the following relations.(i) La→=Lp→(ii) La→=-Lp→(iii) ra⇀×La→=rp⇀×Lp→Which of the above relations is/are true?