Single lunation N-observation orbits

Initial orbit determination by least squares of N observations is essentially a linear problem if the coordinates x ₀ and x ₁ at two standard epochs are used as elements. The orbit of a main belt object is approximated within the observational errors by a third degree polynomial during a month. A 4-observation orbit is useful for the initial linking between two nights. Parallax is treated rigorously and future simultaneous space and Earth based observations determine the critical distance directly. The N-observation method is a great simplification of the classical 3-observation orbit followed by a differential correction by N observations.