On an extension of the Lagrange-Laplace theory of the Moon's physical librations.
Lagrange-Laplace theory of lunar physical librations extended to include reduced estimate of mechanical ellipticity of lunar equator
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Lagrange-Laplace theory of lunar physical librations extended to include reduced estimate of mechanical ellipticity of lunar equator
Numerical solutions for librational motion of Mercury obtained by applying Runge-Kutta integration
Instability of periodic motions near collinear points of libration in plane restricted three- body problem examined with Liapunov theory
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Nonperiodic librational motions in restricted three-body problem for relatively elliptic motion of two finite masses
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Feedback control system to position satellite in vicinity of unstable collinear libration point with application to lunar communication problem
Stability analysis of long period Trojan librations treated as short period oscillations about long period reference solution
Periodic motion around triangular libration point in restricted four-body problem of earth-moon-sun system
Feedback control system to position satellite in vicinity of unstable collinear libration point applied to lunar communication problem
Due to the constant observation environment and low energy access of Sun-Earth libration point orbits, they have become extremely popular for many NASA science missions. The nonlinearity and instability of the orbits have made mission analysis more difficult as traditional approximations are no longer applicable. But the sensitivity of the orbits also provides greater flexibility in orbit design. Some typical mission trajectories are examined.
In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.
Mission analysis of libration orbit trajectories at Sun-Earth/Moon L2 typically includes predictions of lunar and Earth eclipses during the mission life-time. The NASA James Webb Space Telescope (JWST) trajectory, by design, avoids these eclipses by pruning its launch window. In an off-nominal scenario where an eclipse is predicted, a maneuver strategy is needed. In this paper, trade studies are examined for JWST that characterize the burn magnitude, location, and epochs of multiple maneuver plans to avoid an eclipse. The results enable analysts to explore the space of feasible maneuver strategies during routine operations.
The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists.
Throughout the years, different strategies have been proposed for the station-keeping around the libration point orbits. In this paper, a geometrical comparative analysis is performed between different approaches making use of the Floquet modes reference frame. Two particular station-keeping procedures are considered: the commonly used velocity constraint at the plane crossing, and the Floquet mode approach. The first method finds the Δv that ensures that the x component of the velocity vector is zero at a plane crossing, whereas the Floquet mode approach finds the Δv that cancels the unstable mode in the Floquet reference frame. It will be seen that both approaches have some basic common geometrical features, even when they are compared using high-order techniques.