A set of mean elements can still be defined for such an orbit, after abstracting the perturbational variations with time.

The reason is that a perturbational analysis requires the provision of risk sensitivity numbers for each factor, and in some cases these may simply not be available.

To arrive at a true longitude from a mean mean longitude, the perturbational terms must be applied as well as the equation of the center.

Nonetheless there were places where gravitational "knotting" and other minor perturbational drifts brought the asteroids clumping closer together than usual, sometimes only ten or twenty or fifty kilometers apart.

Not only do the perturbation theory series diverge, but each perturbational term also in some sense is infinite, and a special renormalization of the interaction constant is required to give the result the physical sense.

The Laplace plane is a result of perturbational effects, which were discovered by Laplace while he was investigating the orbits of Jupiter's principal moons (the Galilean satellites of Jupiter).

Beside the effects of perturbational changes in the Earth's orbital eccentricity, as found by Laplace and corrected by Adams, there are two tidal effects (a combination first suggested by Emmanuel Liais).

It was said that he was an expert on meteors and comets yet to be discovered (in the next millennium), this ability mathematically to project future trajectories owing to his favorite pastime: the perturbational analysis of celestial bodies.

Pierre-Simon Laplace produced in 1786 a theoretical analysis giving a basis on which the Moon's mean motion should accelerate in response to perturbational changes in the eccentricity of the orbit of the Earth around the Sun.

The star with the second greatest perturbational effect in the past or future 10 million years was Algol, a triple star system that passed no closer than 9.8 light years, 7.3 million years ago, but with a considerably larger total mass of 5.8 solar masses.

Conveniently, the perturbational approach may be extended to new asset types without requiring any new pricing code or types of data, and it also works for benchmark sectors as well as individual securities, which is useful if benchmark data is only available at sector level.

E.g. one can have some nearly degenerate determinants for the multi-configurational self-consistent field method to account for static correlation and/or some truncated CI method for the biggest part of dynamical correlation and/or on top some perturbational ansatz for small perturbing (unimportant) determinants.