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choclo.point.gravity_u

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choclo.point.gravity_u#

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

Upward component of the gravitational acceleration due to a point source

Returns the upward component of the gravitational acceleration 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_u (float) – Upward component of the gravitational acceleration generated by the point source on the observation point in \(\text{m}/\text{s}^2\).

Notes

Returns the upward component \(g_z(\mathbf{p})\) of the gravitational acceleration \(\mathbf{g}\) 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 \(m\).

\[g_z(\mathbf{p}) = - G m \frac{ z_p - z_q }{ \lVert \mathbf{p} - \mathbf{q} \rVert_2^2 }\]

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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