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, 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_ufloat

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 $m$.

$$g_z(\mathbf{p})=-Gm\frac{z_p-z_q}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2^2}$$

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.