Orbital

Orbital is an adjective relating to an orbit and a noun used in physics and astronomy to describe a path or region associated with a gravitating or quantum system. In astronomy, an orbit is the trajectory of a celestial body around another under gravity. In quantum mechanics and chemistry, an atomic orbital is a region around a nucleus where there is a high probability of finding an electron.

The motion in an orbit is described by orbital elements such as the semi-major axis (a), eccentricity (e), inclination (i), the longitude of the ascending node (Ω), the argument of periapsis (ω), and the true anomaly (ν). Kepler's laws govern the motion, with the orbital period related to the size of the orbit by P^2 proportional to a^3. Orbits can be circular (e=0), elliptical (0<e<1), parabolic (e=1), or hyperbolic (e>1). Celestial orbits range from low Earth orbit to geostationary orbit, and from highly inclined polars to resonant configurations. Transfers between orbits often use energy-efficient trajectories such as the Hohmann transfer.

Atomic orbitals arise as solutions to the quantum mechanical description of electrons in atoms. They are labeled by quantum numbers n (principal), l (angular momentum), m_l (magnetic), and m_s (spin). Orbitals have characteristic shapes: s is spherical, p is dumbbell-shaped, d and f are more complex. Each orbital can hold up to two electrons with opposite spins, in accordance with the Pauli exclusion principle. The arrangement of electrons among orbitals determines an atom's chemical properties and behavior in spectroscopy.

The term derives from Latin orbis, meaning circle or ring, reflecting the geometric idea of a path around a body.