By Jaan Kalda (TalTech).
Two satellites orbit Earth on the same plane along elliptic paths of eccentricities e_1 and e_2 respectively. The angle between their major axes is \alpha. The rate at which a line segment connecting a satellite and the Earth’s centre sweeps out an area is L_1 and L_2 respectively. What is the maximal relative velocity of the satellites? Provide also a simplified answer for \alpha=90\degree and L_1=L_2. The ratio of the orbital periods of the satellites is an irrational number. Earth’s mass is denoted by M, and the gravitational constant by G.