osculating orbit

In astronomy, an osculating orbit is an idealized elliptical orbit that a celestial body would follow if all perturbing forces were suddenly removed. This concept is useful because actual orbits are rarely perfect ellipses due to gravitational influences from other bodies.1

The osculating orbit represents the instantaneous path of a body at a specific moment in time. It's defined by the body's current position and velocity. While the true orbit deviates from this ideal ellipse over time, the osculating ellipse provides a valuable approximation for understanding and calculating celestial motion, especially when dealing with small perturbations. The term "osculating" comes from the Latin word for "kissing," referring to how the osculating ellipse "kisses" the actual path at a given point.12