choclo.point.gravity_nn#

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

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

Returns the northing-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_nnfloat

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

Notes

Returns the northing-northing component $g_{yy}(\mathbf{p})$ 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 $m$.

$$g_{yy}(\mathbf{p})=Gm[\frac{3(y_p-y_q{)}^2}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^5}-\frac{1}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^3}]$$

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.