orbital elements
If you want to tell a friend exactly which orbit a comet is on, a single number will not do. You have to say how big the orbit is, how stretched it is, how it is tilted, which way it points, and where the object is along it right now. Orbital elements are the small set of numbers — usually six — that pin down an orbit completely, the way an address pins down a house.
The six classical (Keplerian) elements split into three jobs. Two fix the shape: the semi-major axis a (the orbit's overall size) and the eccentricity e (how far from circular it is). Three fix the orientation of the ellipse in space: the inclination i (how tilted the orbit plane is relative to a reference plane such as the ecliptic), the longitude of the ascending node (which way the tilt points), and the argument of periapsis (which way the long axis of the ellipse points within its plane). The sixth, the true anomaly or epoch, says where the body is on the orbit at a chosen moment. Together they replace the position and velocity at one instant with six quantities that, for a pure two-body orbit, stay constant.
Orbital elements are the working language of celestial mechanics: every satellite, asteroid, and exoplanet is catalogued by them, and a spacecraft navigator changes an orbit by deliberately changing one element at a time. Their power is also their limit — they are exactly constant only for the idealized two-body case; real perturbations from other bodies and non-spherical planets make them drift slowly, which is itself how we detect and study those perturbations.
When a new asteroid is spotted, observers measure its position on a few nights, fit the six orbital elements, and can then predict where it will be years from now — or warn whether its a and e bring it dangerously near Earth.
Six numbers turn a handful of sightings into a future ephemeris.
Several conventions and alternative element sets exist (mean anomaly versus true anomaly, different reference planes), so two catalogues can describe the same orbit with differently named or differently zeroed numbers — always check the reference frame and epoch.