Question

Three equal mass satellites A, B, and C are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are L_A, L_B, and L_C.  Which of the following statements is correct?

 

(A) L_A > L_B > L_C

(B) L_C > L_B > L_A 

(C) L_B > L_C > L_A 

(D) L_B > L_A > L_C 

(E) The relationship between the magnitudes is different at various instants in time

Answer 1

Correct option (a) L_A > L_B > L_C

The angular momentum of each satellite is conserved independently so we can compare the orbits at any location. Looking at the common point between orbit A and B shows that satellite A is moving faster at that point than satellite B, showing L_A > L_B. A similar analysis at the common point between B and C shows L_B > L _A.