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 $m$.

$$g_{xz}(\mathbf{p})=Gm\left[\frac{3(x_p-x_q)(z_p-z_q)}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^5}\right]$$

where $\Vert \cdot {\Vert }_2$ refer to the $L_2$ norm (the Euclidean distance between $\mathbf{p}$ and $\mathbf{q}$) and $G$ is the Universal Gravitational Constant.