Semieje

Semieje is a term used in geometry and astronomy to refer to the semi-axis of an ellipse, with the most common usage being the semi-major axis. It is the half-length of the ellipse’s major axis and, together with the semi-minor axis, defines the ellipse’s size and shape. In many cases, the semieje mayor is simply called the semieje, while the semieje menor is the other semi-axis.

In mathematical terms, an ellipse centered at the origin has the standard equation x^2/a^2 + y^2/b^2 = 1, where a is the semi-major axis and b is the semi-minor axis. The eccentricity e is defined by e = sqrt(1 - b^2/a^2), and the distance from the center to each focus is c = ae. The foci are located at (±c, 0), and the sum of the distances from any point on the ellipse to the two foci is constant and equal to 2a. When a = b, the ellipse becomes a circle.

In astronomy and orbital mechanics, the semi-major axis a serves as a size parameter for orbits and corresponds to the average distance of the orbiting body from the focus. For example, Earth’s orbital semimajor axis is about 1 astronomical unit (AU). Kepler’s third law relates the orbital period P to a via P^2 ∝ a^3 for planets around the Sun. The specific orbital energy of a bound orbit is ε = -μ/(2a), where μ is the standard gravitational parameter.