An astronaut in the vicinity of an orbiting spacecraft must navigate himself by means of impulsive velocity changes Δv, imparted by hands or feet or by small rockets. The motion relative to the spacecraft produced by such an impulse is noticeably nonlinear; if ejected from the spacecraft with a typical Δv of magnitude 2 m/sec in the orbital plane of the spacecraft, the astronaut suffers a net transverse deflection of 22.5 cm after 10 sec. Celestial mechanics can give only a numerical solution, which is of little practical help to the astronaut. In this paper we present approximate closed‐form solutions valid for low speeds (≲100 m/sec) and short elapsed times (≲0.1 orbital period), for a Skylab‐like Earth orbit of semimajor axis 6800 km.