  We consider the problem of relativistic projectiles in a uniform
gravitational force field. For the first time, we have found the curve that
joins the points of maximum height of all trajectories followed by a projectile
in the ultra-relativistic limit. The parametric equations of this curve produce
an onion-like curve; in fact, it is one of the loops of a lemniscate-type
curve. We also verify that the curve is an ellipse in the nonrelativistic
approximation. These two limiting results are obtained by following two
slightly distinct approaches. In addition, we calculate the nonrelativistic and
ultra-relativistic approximations of the trajectory equation and parametric
equations of the trajectory as functions of time. All limiting cases in the
article are studied in detail. The content of the article is appropriate for
advanced undergraduate students.
