Question

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. [AMU 2012]
(i) L_a = L_p
(ii) L_a = $-$ L_p
(iii) r_ax L_a = r_p x L_p
Which of the above relation{s) is/are true?

Easy

Solution

Using the law of conservation of angular momentum,
Angular momentum of planet at p
= Angular momentum of planet at a
i.e., L_a = L_p
But $r_{a} > r_{p} . So, r_{a} \times L_{a} > r_{p} \times L_{p}$

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