  We relate the known Oberth effect and the nonrelativistic analogue of the
Penrose process. When a particle decays to two fragments, we derive the
conditions on the angles under which debris can come out for such a process to
occur. We also consider the decay and the Oberth effect in the relativistic
case, when a particle moves in the background of the Schwarzschild black hole.
This models the process when a rocket ejects fuel. Different scenarios are
analyzed depending on what data are fixed. The efficiency of the process is
found, in particular, near the horizon and for a photon rocket (when the
ejected particle is massless). We prove directly that the most efficient
process occurs when fuel is ejected along the rocket trajectory. When this
occurs on the horizon, the efficiency reaches 100% for a photon rocket. We
compare in two ways how a rocket can reverse its direction of motion to a black
hole near the event horizon by restoring the initial energy-to-mass ratio: (i)
by a single ejection or (ii) in the two-step process when it stops and moves
back afterwards. For a nonphotonic rocket, in case (ii) a larger mass can be
taken out from the vicinity of a horizon. For a photonic one, there is no
difference between (i) and (ii) in this respect. We also consider briefly the
scenario when a rocket hangs over a black hole due to continuous ejection of
fuel. Then, the fuel mass decays exponentially with the proper time.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena;Space Physics