A computational study is presented of the properties of a guardring-type circular planar Langmuir probe, commonly flush-mounted in the skin of a satellite. This geometry results in a three-dimensional potential distribution which cannot be treated analytically, even in axially symmetric problems. Given arbitrary particle velocity distributions at infinity, the current-voltage characteristics of the external aperture grid potentials) may be determined by detailed particle trajectory calculations. The electric field and charge density distributions in the vicinity of the probe are defined at the nodes of a grid. The charge density in the Poisson equation is evaluated by summing trajectory contributions. The collected currents are similarly evaluated. The Poisson field is computed self-consistently by an iterative technique. Two kinds of particle velocity distribution are considered, e.g., a streaming Maxwellian at infinity, and photoelectric (or secondary) emission at the satellite surface. An infinite-satellite model is assumed for the Poisson case (Debye length = 1 cm). For the Laplace case (Debye length infinite), the effects of finite satellite dimensions, of Mach streaming at an angle, and of photoelectrons are investigated.