Neue Formeln und Hilfstafeln zur Ephemeridenrechnung

Stumpff, Karl

doi:10.1002/asna.19472750703

Cited by 23 publications

(4 citation statements)

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“…The best method to handle the reference is to use the universal variables introduced by Stumpff (1947) and developed further by Herrick (1965), since they allow the reference to be projected ahead easily in rectangular coordinates. The most efficient notation and formulation, in our opinion, are those by Goodyear (1965) and Pitkin (1966).…”

Section: Encke Equations and Close Encountersmentioning

confidence: 99%

Implicit single-sequence methods for integrating orbits

Everhart

1974

Celestial Mechanics

236

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Abstract. The solutions of .~ = F(x, t), and also .~ --F (x, t), are developed in truncated series in time t whose coefficients are found empirically. The series ending in the t n term yields a position at a final prechosen time that is accurate through 9th order in the sequence size. This is achieved by using Gauss-Radau and Gauss-Lobatto spacings for the several substeps within each sequence. This timeseries method is the same in principle as implicit Runge-Kutta methods, and the present algorithm generates coefficients for families of implicit Runge-Kutta forms, including some not described previously. In some orders these methods are unconditionally stable (A-stable). In the time-series formulation the implicit system converges rapidly. For integrating a test orbit the method is found to be about twice as fast as high-order explicit Runge-Kutta-Nystr6m-Fehlberg methods at the same accuracies. Both the Cowell and the Encke equations are solved for the test orbit, the latter being 3 5 faster. It is shown that the Encke equations are particularly well-adapted to treating close encounters when used with a single-sequence integrator (such as this one) provided that the reference orbit is re-initialized at the start of each sequence. This use of Encke equations is compared with the use of regularized Cowell equations.

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Section: Encke Equations and Close Encountersmentioning

confidence: 99%

Implicit single-sequence methods for integrating orbits

Everhart

1974

Celestial Mechanics

236

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“…1 Introduction Stumpff (1947Stumpff ( , 1962 devised a method to represent the solution of the twobody problem at any time t from the position (r 0 ) and velocity (ṙ 0 ) at some reference epoch t 0 (see also Stumpff, 1959, vol. 1, chap.…”

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confidence: 99%

Uniform formulation for orbit computation: the intermediate elements

Baù

Roa

2020

Celest Mech Dyn Astr

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We present a new method for computing orbits in the perturbed twobody problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e. constants of the unperturbed motion. The proposed elements are uniformly valid for any value of the total energy. Their definition stems from the idea of applying Sundman's time transformation in the framework of the projective decomposition of motion, which is the starting point of the Burdet-Ferrándiz linearisation, combined with Stumpff's functions. In analogy with Deprit's ideal elements, the formulation relies on a special reference frame that evolves slowly under the action of external perturbations. We call it the intermediate frame, hence the name of the elements. Two of them are related to the radial motion, and the next four, given by Euler parameters, fix the orientation of the intermediate frame. The total energy and a time element complete the state vector. All the necessary formulae for extending the method to orbit determination and uncertainty propagation are provided. For example, the partial derivatives of the position and velocity with respect to the intermediate elements are obtained explicitly together with the inverse partial derivatives. Numerical tests are included to assess the performance of the proposed special perturbation method when propagating the orbit of comets C/2003 T4 (LINEAR) and C/1985 K1 (Machholz).

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“…Ferrándiz en 1987 [41] introdujo una nueva familia de transformaciones biparamétrica en las se incluyen otras anomalías. Más recientemente, Floría en 1995 [42] conecta la anomalía intermedia con las llamadas funciones universales introducidas por Stumpf [117], así llamadas por ser independientes del tipo de órbita (elíptica, parabólica o hiperbólica). Fukushima [46] introdujo la anomalía antifocal para el estudio del movimiento en el caso de bajas excentricidades.…”

Section: Anomalías Generalizadasunclassified

Estudio de transformaciones temporales para la mejora de algoritmos numéricos y semianalíticos en el movimiento orbital

Gómez¹

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Neue Formeln und Hilfstafeln zur Ephemeridenrechnung

Cited by 23 publications

References 1 publication

Implicit single-sequence methods for integrating orbits

Implicit single-sequence methods for integrating orbits

Uniform formulation for orbit computation: the intermediate elements

Estudio de transformaciones temporales para la mejora de algoritmos numéricos y semianalíticos en el movimiento orbital

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