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Tesseroids 1.0: User Manual and API Documentation |
About Coordinate SystemsThe two coordinate systems involved in the computations are the Global and Local coordinate systems. The Global system has origin on the center of the Earth and Z axis aligned with the Earth's mean rotation axis. The X and Y axis are contained on the equatorial parallel with X intercepting the mean Greenwich meridian and Y completing a right-handed system. The Local system has origin on the computation point. It's z is oriented along the radial direction and points away from the center of the Earth. The x and y axis are contained on a plane normal to the z axis and x points North and y East. The tesseroids are defined using the Global Coordinate system with spherical coordinates, while the gravitational fields are calculated on the Local Coordinate system of the computation point. WARNING: The ![]() Figure1: View of a tesseroid, the integration point Q, the global coordinate system, the computation P and it's local coordinate system. Gravitational Fields of a TesseroidThe gravitational attraction of a tesseroid can be calculated using the formula (Grombein et al., 2010):
The gravity gradients can be calculated using the general formula (Grombein et al., 2010):
where
Numerical IntegrationThe above integrals are solved using the Gauss-Legendre Quadrature rule (Asgharzadeh et al., 2007):
where References
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