A new class of orbits, called rock-around orbits, which are compatible to an assigned target orbit, is presented. These orbits allow the design of systems whose purpose is to explore and/or observe the space around an assigned target orbit. The proposed orbit design guarantees that, within a given repetition time, the whole space around the target orbit is observed under a prescribed maximum observation distance constraint. Potential applications can be civilian, to design orbits for mapping and monitoring systems, as well as military, to design orbits for space-based surveillance systems. This study shows how to design rock-around orbits for circular and elliptical target orbits, how to evaluate the observation efficiency, and how to estimate the orbit maintenance costs. Copyright 2010 by Daniele Mortari.