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Concept
Minimum mass
Summary
In astronomy, minimum mass is the lower-bound calculated mass of observed objects such as planets, stars and binary systems, nebulae, and black holes.
Minimum mass is a widely cited statistic for extrasolar planets detected by the radial velocity method or Doppler spectroscopy, and is determined using the binary mass function. This method reveals planets by measuring changes in the movement of stars in the line-of-sight, so the real orbital inclinations and true masses of the planets are generally unknown. This is a result of sin i degeneracy.
If inclination i can be determined, the true mass can be obtained from the calculated minimum mass using the following relationship:
Methods of detecting exoplanets
Most stars will not have their planets lined up and orientated so that they eclipse over the center of the star and give the viewer on earth a perfect transit. It is for this reason that when we often are only able to extrapolate a minimum mass when viewing a star's wobble because we do not know the inclination and therefore only be able to calculate the part pulling the star on the plane of celestial sphere.
For orbiting bodies in extrasolar planetary systems, an inclination of 0° or 180° corresponds to a face-on orbit (which cannot be observed by radial velocity), whereas an inclination of 90° corresponds to an edge-on orbit (for which the true mass equals the minimum mass).
Planets with orbits highly inclined to the line of sight from Earth produce smaller visible wobbles, and are thus more difficult to detect. One of the advantages of the radial velocity method is that eccentricity of the planet's orbit can be measured directly. One of the main disadvantages of the radial-velocity method is that it can only estimate a planet's minimum mass (). This is called Sin i degeneracy. The posterior distribution of the inclination angle i depends on the true mass distribution of the planets.
However, when there are multiple planets in the system that orbit relatively close to each other and have sufficient mass, orbital stability analysis allows one to constrain the maximum mass of these planets.
Official source
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