Three equal mass satellites A, B, and C are i | vedclass

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(A) The angular momentum of a satellite in an elliptical orbit is given by $L = mvr \sin 	heta$. For a satellite of mass $m$ in an orbit with semi-ma

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$L_A > L_B > L_C$

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(A) The angular momentum of a satellite in an elliptical orbit is given by $L = mvr \sin 	heta$. For a satellite of mass $m$ in an orbit with semi-major axis $a$,the angular momentum is $L = m \sqrt{GMa(1-e^2)}$,where $M$ is the mass of the planet and $e$ is the eccentricity.Alternatively,for a circular orbit,$L = m \sqrt{GMr}$. For an elliptical orbit,the angular momentum is proportional to the square root of the semi-major axis $a$,i.e.,$L \propto \sqrt{a}$.From the figure,the semi-major axis $a_A$ of satellite $A$ is the largest,followed by the semi-major axis $a_B$ of satellite $B$,and the semi-major axis $a_C$ of satellite $C$ is the smallest.Therefore,$a_A > a_B > a_C$.Since $L \propto \sqrt{a}$,it follows that $L_A > L_B > L_C$.

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?

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