choclo.point.gravity_uu#

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

Upward-upward component of the gravitational tensor due to a point source.

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

Parameters:

easting_p, northing_p, upward_pfloat

Easting, northing and upward coordinates of the observation point in meters.

easting_q, northing_q, upward_qfloat

Easting, northing and upward coordinates of the point source in meters.

massfloat

Mass of the point source in kilograms.

Returns:

g_uufloat

Upward-upward component of the gravitational tensor generated by the point source on the observation point in ${\text{s}}^{-2}$.

Notes

Returns the upward-upward component $g_{zz}(\mathbf{p})$ 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 $m$.

$$g_{zz}(\mathbf{p})=Gm[\frac{3(z_p-z_q{)}^2}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^5}-\frac{1}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^3}]$$

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.