Two probes are launched from an orbital station moving at a speed of u in
a circular orbit around the planet. The initial velocity of the probes relative
\sqrt
to the planet is v ( 2u > v > u). One probe moves in the direction of the
planet’s radius; the initial velocity of the other probe is perpendicular to its
radius. Find the ratio of the maximum possible distances from the probes to
the center of the planet.