minimum mass

A calculated minimum mass (often labeled m sin i) can sometimes be determined for an extra-solar planet (or other companion, e.g., brown dwarf or binary companion) when the actual mass cannot be. Often the reported mass for a new discovery is this minimum mass. A quantity labeled m sin i represents the mass of the planet times the sine of the orbital inclination from the observer's perspective (called i, with 0° meaning the orbit is observed "from above", i.e., the orbital plane is perpendicular to the line of sight, and 90° meaning the orbit is viewed edge-on). This minimum mass matches the actual mass (m) if the inclination is 90° (when sin i = 1). Otherwise, sin i is less than one and this minimal mass is less than the companion's actual mass (m).

A minimum mass is often all that is cited because the orbital inclination is generally not revealed by observation, and constitutes a missing factor in calculating the companion's mass. This is the case if the star's mass has been determined (e.g., stellar mass determination), and the RV method has revealed the companion. RV observations yield the radial velocity and the orbital period. Knowing the orbital speed as well would be enough information to complete the derivation of the mass, and also knowing the orbital inclination would reveal the speed. The orbital speed is always, at minimum, the magnitude of the measured relative radial velocity of the host and companion.