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Those unable to write their own SPICE-based program may try using WebGeocalc, a browser interface to a SPICE-based geometry engine running on the NAIF server. Using WebGeocalc is much easier than writing your own program, but it still requires considerable knowledge about SPICE data and solar system geometry, and it doesn't offer the full range ...
Pole figure and diffraction figure. Consider the diffraction pattern obtained with a single crystal, on a plane that is perpendicular to the beam, e.g. X-ray diffraction with the Laue method, or electron diffraction in a transmission electron microscope. The diffraction figure shows spots. The position of the spots is determined by the Bragg's ...
Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system.
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
The five equilibrium points of the circular problem are known as the Lagrangian points. See figure below: Restricted three-body problem. In the restricted three-body problem math model figure above (after Moulton), the Lagrangian points L 4 and L 5 are where the Trojan planetoids resided (see Lagrangian point); m 1 is the Sun and m 2 is Jupiter.
In 4D space, the Hopf angles {ξ 1, η, ξ 2} parameterize the 3-sphere. For fixed η they describe a torus parameterized by ξ 1 and ξ 2, with η = π / 4 being the special case of the Clifford torus in the xy - and uz-planes. These tori are not the usual tori found in 3D-space. While they are still 2D surfaces, they are embedded in ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.