  We present a new method for computing orbits in the perturbed two-body
problem: the position and velocity vectors of the propagated object in
Cartesian coordinates are replaced by eight orbital elements, i.e., constants
of the unperturbed motion. The proposed elements are uniformly valid for any
value of the total energy. Their definition stems from the idea of applying
Sundman's time transformation in the framework of the projective decomposition
of motion, which is the starting point of the Burdet-Ferr\'andiz linearisation,
combined with the Stumpff functions. In analogy with Deprit's ideal elements,
the formulation relies on a special reference frame that evolves slowly under
the action of external perturbations. We call it the intermediate frame, hence
the name of the elements. Two of them are related to the radial motion, the
next four, given by Euler parameters, fix the orientation of the intermediate
frame. The total energy and a time element complete the state vector. All the
necessary formulae for extending the method to orbit determination and
uncertainty propagation are provided. For example, the partial derivatives of
the position and velocity with respect to the intermediate elements are
obtained explicitly together with the inverse partial derivatives. Numerical
tests are included to assess the performance of the proposed special
perturbation method when propagating the orbit of comets C/2003~T4 (LINEAR) and
C/1985~K1 (Machholz).

Classical Physics