  A novel approach is developed for analytic orbit propagation based on
asymptotic expansion with respect to a small perturbative acceleration. The
method improves upon existing first order asymptotic expansions by leveraging
on linear systems and averaging theories. The solution starts with the
linearization of Gauss planetary equations with respect to both the small
perturbation and the six orbital elements. Then, an approximate solution is
obtained in terms of secular and short period components. The method is tested
on a low-thrust maneuver scenario consisting of a Keplerian orbit perturbed by
a constant tangential acceleration, for which a solution can be obtained in
terms of elliptic integrals. Results show that the positional propagation error
is about one order of magnitude smaller with respect to state-of-the-art
methods. The position accuracy for a LEO orbit, apart from pathological cases,
is typically in the range of tens of meters for a dimensionless tangential
acceleration of 1e-5 after 5 orbital periods propagation.
