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) `L_(a)=L_(p)`
(ii) `L_(a)=-L_(p)`
(iii) `r_(a)xxL_(a) =r_(p)xxL_(p)`
Which of the above relation(s) is/are true ?

Options

A. (i) only
B. (ii) only
C. (iii) only
D. (i) and (iii)

Answer

A

Explanation

Using the law of conservation of angular momentum.
Angular momentum of planet of p = Angular momentum of planet at a
i.e., `L_(p)=L_(a)`
But `r_(a)gtr_(p)`. So, `r_(a)xxL_(a)gtr_(p)'xxL_(p)`.