The purpose of this rersearch is to analyze the effective application of particular earth orbits in dynamical modeling of relative motion problem between two spacecraft. One challenge in implementing these motions is maintaining the relations as it experiences orbital perturbations (zonal harmonics J2 and J3), most notably due to the Earth’s oblateness. Certain aspects of the orbital geometry c...

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that...

We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of periodic orbits, the action is a scalar function of the slow variables and can be considered as a Hamiltonian function which generates some slow dynamics. These ...

In this paper, we study the moduli space of frozen planet orbits in Helium atom for an interpolation between instantaneous and mean interactions show that is compact.

We present variational characterizations of frozen planet orbits for the helium atom in Lagrangian and Hamiltonian picture. They are based on a Levi-Civita regularization with different time reparametrizations two electrons lead to nonlocal functionals. Within this setup, we deform problem one where interact only by their mean values use deduce existence orbits.

The science orbit for a future mission to Europa requires low eccentricity, low altitude, and high inclination. However, high inclination orbits around planetary satellites are unstable due to third-body perturbations. Without control, the orbiter impacts Europa after few weeks. To minimize control, a tour over the stable-unstable, averaged manifolds of unstable frozen orbits has been suggested...

With the upcoming launch of large constellations satellites in low-Earth orbit (LEO) region, it will become important to organize physical space occupied by different operating order minimize critical conjunctions and avoid collisions. This paper introduces definition occupancy as domain an individual satellite moves along its nominal under effects environmental perturbations throughout a given...

This paper summarizes a numerical investigation of the statistical properties of orbits evolved in "frozen," time-independent N-body realizations of smooth, time-independent density distributions corresponding to integrable potentials, allowing for 10(2.5) < or = N < or = 10(5.5). Two principal conclusions were reached: (1) In agreement with recent work by Valluri and Merritt, one finds that, i...

We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At ε = 0 the slow dynamics is frozen. We assume that the frozen system (i.e. the unperturbed fast dynamics) has families of hyperbolic periodic orbits with transversal heteroclinics. For each periodic orbit we define an action J. This action may be vi...