semiasse

Semiasse is a term used in geometry and astronomy to denote the distance from the center of a conic section to its edge along a principal axis. The word is common in Italian, where semiasse refers to a semi-axis; in English the analogous terms are semi-axis or semi-major axis (for ellipses).

For an ellipse with semiaxes a and b (a ≥ b), the equation is x^2/a^2 + y^2/b^2 = 1. The major axis length is 2a and the minor axis length is 2b. The eccentricity e = sqrt(1 - (b^2/a^2)). A circle is a special ellipse with a = b, so both semiaxes equal the radius. For a hyperbola x^2/a^2 - y^2/b^2 = 1, the parameter a is the semiaxis along the x-direction and b along the y-direction; the concept of semiaxis generalizes to conic sections.

In astronomy, the semimajor axis of an orbit around a body is a fundamental parameter that largely determines the orbit’s size and energy; the orbital period is related to a by Kepler’s third law. For example, Earth’s orbital semimajor axis is about 1 astronomical unit, roughly 149.6 million kilometers.

Etymology and usage: semiasse derives from Latin semi- meaning “half” and axis meaning axis. In Italian mathematical literature it is commonly used to describe the axis lengths of ellipses and hyperbolas; in English texts the terms semi-axis or semi-major axis are used to express the same concept.

---