choclo.point.gravity_en

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choclo.point.gravity_en#

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

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

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

Parameters:
easting_pfloat

Easting coordinate of the observation point in meters.

northing_pfloat

Northing coordinate of the observation point in meters.

upward_pfloat

Upward coordinate of the observation point in meters.

easting_qfloat

Easting coordinate of the point source in meters.

northing_qfloat

Northing coordinate of the point source in meters.

upward_qfloat

Upward coordinate of the point source in meters.

massfloat

Mass of the point source in kilograms.

Returns:
g_enfloat

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

Notes

Returns the easting-northing component \(g_{xy}(\mathbf{p})\) 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 \(m\).

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

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.