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choclo.point.gravity_eu

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choclo.point.gravity_eu#

choclo.point.gravity_eu(easting_p, northing_p, upward_p, easting_q, northing_q, upward_q, mass)[source]#

Easting-upward component of the gravitational tensor due to point source

Returns the easting-upward component of the gravitational tensor produced by a single point source on a single computation point

Parameters:

  • easting_p (float) – Easting coordinate of the observation point in meters.

  • northing_p (float) – Northing coordinate of the observation point in meters.

  • upward_p (float) – Upward coordinate of the observation point in meters.

  • easting_q (float) – Easting coordinate of the point source in meters.

  • northing_q (float) – Northing coordinate of the point source in meters.

  • upward_q (float) – Upward coordinate of the point source in meters.

  • mass (float) – Mass of the point source in kilograms.

Returns:

g_eu (float) – Easting-upward component of the gravitational tensor generated by the point source on the observation point in \(\text{s}^{-2}\).

Notes

Returns the easting-upward component \(g_{xz}(\mathbf{p})\) of the gravitational tensor \(\mathbf{T}\) on the observation point \(\mathbf{p} = (x_p, y_p, z_p)\) generated by a single point source located in \(\mathbf{q} = (x_q, y_q, z_q)\) and mass \(m\).

\[g_{xz}(\mathbf{p}) = G m \left[ \frac{ 3 (x_p - x_q) (z_p - z_q) }{ \lVert \mathbf{p} - \mathbf{q} \rVert_2^5 } \right]\]

where \(\lVert \cdot \rVert_2\) refer to the \(L_2\) norm (the Euclidean distance between \(\mathbf{p}\) and \(\mathbf{q}\)) and \(G\) is the Universal Gravitational Constant.

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