Physics Cup – TalTech 2024 – Problem 4

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.

Please submit the solution of this problem via e-mail to First intermediate results will be published on 3rd February, 13:00 GMT. After the publication of the first hint, the base score is reduced to 0.9 pts. For full regulations, see the “Participate” tab.