This paper introduces a new concept compressor in which piston orbits in the cylinder having an annular space formed between two concentric circular walls. In this configuration, two gas pockets are formed with $180^{circ}$ phase difference: one between the wrap of the orbiting piston and the inner cylinder wall and the other between the piston wrap and the outer cylinder wall. This alternating feature of gas compression and discharge processes yields several advantages such as low torque variation and low gas pulsation. Computer simulation program has been developed to evaluate the compressor performance. The volumetric, adiabatic, and mechanical efficiencies of the orbiter compressor are calculated to be $85.6\%,;97.2\%,;and;95.2\%$, respectively, when it is used as an air compressor.