Angular momenta of satellites

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According to me momenta of every satellite should be same .
At point 1 $L_B = L_C$
and at point 2 $L_C = L_A$

If B and C had the same angular momentum $(L_B=L_C)$ then at point 1 we would have $m_Bv_Br_B=m_Cv_Cr_C$.
We are told that $m_B=m_C$. Since B and C are at the same position then $r_B=r_C$. Therefore we must also have $v_B=v_C$.
However, if this were the case then B and C would follow the same orbit at point 1. Instead they follow different orbits. So we must have $v_B \gt v_C$. It cannot be true that $L_B=L_C$.