Radial Velocity Semi-Amplitude

The radial velocity semi-amplitude calculates the precise gravitational wobble induced on a host star by an orbiting mass. Defined by Keplerian mechanics and conservation of momentum, this periodic velocity shift is essential for constraining the minimum mass of an exoplanet. The calculation is strictly dependent on the orbital inclination and period, demonstrating the inescapable mutual gravitational influence inherent in multi-body orbital systems.

A planet does not simply orbit its star — both bodies circle their shared center of mass, so the star traces a small loop of its own. As it swings toward us its light is blueshifted; as it recedes, redshifted. K is the top line-of-sight speed of that wobble. Jupiter tugs the Sun at about 12.5 m/s, a fast cyclist's pace, while Earth manages only 0.09 m/s.

Almost every astronomical signal weakens with distance — brightness drops with the square of it. The RV semi-amplitude K does not: it is baked into the orbit itself, so a star 10 or 1000 parsecs away wobbles at exactly the same speed. Distance only limits how many photons you can gather for the spectrum. Instruments like ESPRESSO now reach about 10 cm/s — sensing a star drift slower than a strolling human across trillions of kilometres.