Post-Newtonian equations of motion for LEO debris objects and space-based acquisition, pointing and tracking laser systems

Gambi, J. M.; Pino, Maria L. García del; Gschwindl, Jürgen; Weinmüller, Ewa

doi:10.1016/j.actaastro.2017.10.006

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…In a previous paper [1], the main post-Newtonian (p-N) corrections to the Newtonian trajectories of middle-size LEO space debris object D with respect to acquisition, pointing, and tracking (APT) laser system S, aimed at ablating D, were derived by means of a genuine p-N method for the Earth Schwarzschild field [2]. After the Earth-centered inertial (ECI) orbital coordinates of S and D are determined from appropriated p-N orbital equations, the main difficulty of this method is that the process to track D involves computations of the time-dependent coefficients of a third system of p-N equations for the relative motion of D with respect to S. These coefficients are line integrals of the Riemann tensor of space along the line of sight (LOS) segment that joins S and D (cf.…”

Section: Introductionmentioning

confidence: 92%

“…After the Earth-centered inertial (ECI) orbital coordinates of S and D are determined from appropriated p-N orbital equations, the main difficulty of this method is that the process to track D involves computations of the time-dependent coefficients of a third system of p-N equations for the relative motion of D with respect to S. These coefficients are line integrals of the Riemann tensor of space along the line of sight (LOS) segment that joins S and D (cf. [1]).…”

Section: Introductionmentioning

confidence: 99%

“…International Journal of Aerospace Engineering respect to S. In fact, this procedure is operative and ready to be used within the eclipse phases of D with respect to S, although for the time being, it does not cover all important real-life applications within the noneclipse phases, such as hypothetical APT laser system aiming at ablating space debris. In order to reach accuracies necessary for this and similar applications, the p-N corrections to the Newtonian relative motion of D with respect to S should be computed using the p-N orthodox method described in [1] for the noneclipse phases. The technical difficulty now is that these equations involve integrals (cf.…”

mentioning

confidence: 99%

“…The technical difficulty now is that these equations involve integrals (cf. [1]) whose accurate numerical approximation may be difficult. This demanding problem will be in the focus of our future work.…”

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confidence: 99%

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Numerical Approach for the Computation of Preliminary Post-Newtonian Corrections for Laser Links in Space

Gambi

Pino²,

Mosser

et al. 2019

International Journal of Aerospace Engineering

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Two systems of Earth-centered inertial Newtonian orbital equations for a spherical Earth and three systems of post-Newtonian nonlinear equations, derived from the second post-Newtonian approximation to the Earth Schwarzschild field, are used to carry out a performance analysis of a numerical procedure based on the Dormand-Prince method for initial value problems in ordinary differential equations. This procedure provides preliminary post-Newtonian corrections to the Newtonian trajectories of middle-size space objects with respect to space-based acquisition, pointing, and tracking laser systems, and it turns out to be highly efficient. In fact, we can show that running the standard adaptive ode45 MATLAB routine with the absolute and relative tolerance, TOLa = 10−16 and TOLr = 10−13, respectively, provides corrections that are final within the eclipses caused by the Earth and close to final during the noneclipse phases. These corrections should be taken into account to increase the pointing accuracy in implementing the space-to-space laser links required for ablation of designated objects or communications between space terminals.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Numerical Approach for the Computation of Preliminary Post-Newtonian Corrections for Laser Links in Space

Gambi

Pino²,

Mosser

et al. 2019

International Journal of Aerospace Engineering

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“…Unlike terrestrial networks, wavelength resources in DSCNs are expensive due to the limitation of on‐board payload and the difficulty of acquisition, pointing, and tracking (APT) 15 . In the DSCNs, satellites are connected by intersatellite laser links, and there is a collection of connection requests specifying the amount of low‐speed traffic flows to be routed from some sources to some sinks.…”

Section: Introductionmentioning

confidence: 99%