Adaptive scheme for Accurate orbit propagation

Two extensions of the fast and accurate special perturbation method recently developed by Peláez et al. are presented for respectively elliptic and hyperbolic motion. A comparison with Peláez?s method and with the very efficient Stiefel- Scheifele?s method, for the problems of oblate Earth plus Moon and continuous radial thrust, shows that the new formulations can appreciably improve the accuracy of Peláez?s method and have a better performance of Stiefel-Scheifele?s method. Future work will be to include the two new formulations and the original one due to Peláez into an adaptive scheme for highly accurate orbit propagatio

Orbit determination with the two-body integrals. III

We present the results of our investigation on the use of the two-body integrals to compute preliminary orbits by linking too short arcs of observations of celestial bodies. This work introduces a significant improvement with respect to the previous papers on the same subject: citet{gdm10,gfd11}. Here we find a univariate polynomial equation of degree 9 in the radial distance $ho$ of the orbit at the mean epoch of one of the two arcs. This is obtained by a combination of the algebraic integrals of the two-body problem. Moreover, the elimination step, which in (Gronchi et al. 2010, 2011) was done by resultant theory coupled with the discrete Fourier transform, is here obtained by elementary calculations. We also show some numerical tests to illustrate the performance of the new algorithm

Non-singular orbital elements for special perturbations in the two-body problem

Seven spatial elements and a time element are proposed as the state variables of a new special perturbation method for the two-body problem. The new elements hold for zero eccentricity and inclination and for negative values of the total energy. They are developed by combining a spatial transformation into projective coordinates (as in the Burdet–Ferrándiz regularization) with a time transformation in which the exponent of the orbital radius is equal to one instead of two (as commonly done in the literature). By following this approach, we discover a new linearization of the two-body problem, from which the orbital elements can be generated by the variation of parameters method. The geometrical significance of the spatial quantities is revealed by a new intermediate frame which differs from a local vertical local horizontal frame by one rotation in the instantaneous orbital plane. Four elements parametrize the attitude in space of this frame, which in turn defines the orientation of the orbital plane and fixes the departure direction for the longitude of the propagated body. The remaining three elements determine the motion along the radial unit vector and the orbital longitude. The performance of the method, tested using a series of benchmark orbit propagation scenarios, is extremely good when compared to several regularized formulations, some of which have been modified and improved here for the first time

Keplerian integrals, elimination theory and identification of very short arcs in a large database of optical observations

Modern asteroid surveys produce an increasingly large number of observations, which are grouped into very short arcs (VSAs) each containing a few observations of the same object in one single night. To decide whether two VSAs collected in different nights correspond to the same observed object we can attempt to compute an orbit with the observations of both arcs: this is called the linkage problem. Since the number of linkages to be attempted is very large, we need efficient methods of orbit determination. Using the first integrals of Kepler’s motion we can write algebraic equations for the linkage problem, which can be put in polynomial form. In Gronchi et al. (Celest Mech Dyn Astron 123(2):105–122, 2015) these equations are reduced to a polynomial equation of degree 9: the unknown is the topocentric distance of the observed body at the mean epoch of one VSA. Here we derive the same equations in a more concise way, and show that the degree 9 is optimal in a sense that will be specified in Sect. 3.3. We also introduce a procedure to join three VSAs: from the conservation of angular momentum we obtain a polynomial equation of degree 8 in the topocentric distance at the mean epoch of the second VSA. For both identification methods, with two and three VSAs, we discuss how to discard solutions. Finally, we present some numerical tests showing that the new methods give satisfactory results and can be used also when the time separation between the VSAs is large. The low polynomial degree of the new methods makes them well suited to deal with the very large number of asteroid observations collected by the modern surveys

Preliminary orbits with line-of-sight correction for LEO satellites observed with radar

In Fusco et al (2011 Inventiones Math. 185 283–332) several periodic orbits of the Newtonian N-body problem have been found as minimizers of the Lagrangian action in suitable sets of T-periodic loops, for a given T  >  0. Each of them share the symmetry of one Platonic polyhedron. In this paper we first present an algorithm to enumerate all the orbits that can be found following the proof in Fusco et al (2011 Inventiones Math. 185 283–332). Then we describe a procedure aimed to compute them and study their stability. Our computations suggest that all these periodic orbits are unstable. For some cases we produce a computer-assisted proof of their instability using multiple precision interval arithmetic

A Variational Method for the Propagation of Spacecraft Relative Motion.

A new formulation of the spacecraft relative motion for a generic orbit is presented based on the orbital propagation method proposed by Peláez et al. in 2006 [1]. Two models have been developed. In the first model the method is applied to each spacecraft using a time synchronization of the system dynamical states. In the second model we employ a local orbital reference frame with a linearization of gravitational terms, apply the method to the formation center of mass and propagate the relative dynamics with respect to the center of mass reference orbit. The models are compared in terms of computational speed for the case of a bounded triangular formatio

Multi-walled Carbon Nanotubes, NM-400, NM-401, NM-402, NM-403: Characterisation and Physico-Chemical Properties

In 2011 the JRC launched a Repository for Representative Test Materials that supports both EU and international research projects, and especially the OECD Working Party on Manufactured Nanomaterials' (WPMN) exploratory testing programme "Testing a Representative set of Manufactured Nanomaterials" for the development and collection of data on characterisation, toxicological and ecotoxicological properties, as well as risk assessment and safety evaluation of nanomaterials. The JRC Repository responds to a need for availability of nanomaterial from a single production batch to enhance the comparability of results between different research laboratories and projects. The present report presents the physico-chemical characterisation of the multi-walled carbon nanotubes (MWCNT) from the JRC Repository: NM-400, NM-401, NM-402 and NM-403. NM-400 was selected as principal material for the OECD WPMN testing programme. They are produced by catalytic chemical vapour deposition. Each of these NMs originates from one respective batch of commercially manufactured MWCNT. They are nanostructured, i.e. they consist of more than one graphene layer stacked on each other and rolled together as concentric tubes. The MWCNT NMs may be used as a representative material in the measurement and testing with regard to hazard identification, risk and exposure assessment studies. The results are based on studies by several European laboratories participating to the NANOGENOTOX Joint Action.JRC.I.4-Nanobioscience