Extension of the Naval Space Command satellite theory PPT2 to include a general tesseral M-daily model

Precise Analytical Computation of Frozen-Eccentricity, Low Earth Orbits in a Tesseral Potential

“…The period of terms depending on Ω − is close to one day and may be comparable to the orbital period in thecase of high-altitude orbits. On the contrary, for LEO orbits their period is one order of magnitude higher than the orbital period and the inclusion of higher-order -daily terms in the disturbing potential is occasionally recommended [34,36]. Terms with − 2 + = 0 and ̸ = 0 are sometimes classified as medium-period terms.…”

“…The standard elimination of the parallax [33] simplifies the original Hamiltonian by reducing the parallactic terms to the form −2 , and by removing short-period terms related to the argument of the latitude. In the case of LEO orbits, a side effect of the standard elimination of the parallax is the removal of longitude-dependent terms, except for those related to the so-called -dailies [34]. After this initial simplification, short-period terms depending on the mean anomaly are removed from the Hamiltonian via Delaunay normalization [35].…”

Numerical Validation of the Delaunay Normalization and the Krylov‐Bogoliubov‐Mitropolsky Method

“…Most of the analytical theories in the artificial satellite problem start by removing the short-period terms [1][2][3][4]. In fact, the most frequently used AOPPs, SGP4 (simplified general perturbations 4) [5,6] and PPT2 (position and partials as functions of time 2) [7,8], are developed from the Brouwer-Lyddane theory. However, other analytical theories, like AOP [9], simplify the problem by means of a Lie transform known as the elimination of the parallax [10].…”