Orbital period

The Alpha Centauri star system is located about 4.37 light years away from the solar system in the Orion Arm of the Milky Way. It consists of 3 stars : Alpha Centauri A, Alpha Centauri B and Proxima Centauri, which is possibly gravitationally bound to the other two. Furthermore, Proxima Centauri is orbited by an exoplanet referred to as Proxima Centauri b. The orbital period of the planet can be calculated.

Alpha Centauri A and B with Proxima Centauri circled in red

In celestial mechanics, the orbital period T of a smaller body around a larger one can be calculated by :

Where a refers to the length of the orbit's semi major axis in metres and the Greek letter μ is the standard gravitational parameter, which is the product of the gravitational constant and the mass of the more massive body, which in this case is the star Proxima Centauri.

Artist's depiction of Proxima Centauri b orbiting its parent star

Semi-major axis

The major axis of an ellipse is the length of it's longest diameter, which runs from the foci and the widest ends of the ellipse. The semi-major axis is half that value, as shown below.

Semi-major and semi-minor axis of an ellipse

The semi-major axis of Proxima Centauri b is 0.0485 AU and it has a mass of 2.46 * 10^29 kg. Therefore, the values can be plugged in :

The value for T, orbital period turns out to be approximately 956479.4 seconds or about 11 days.