# 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 (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_u (float) – 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 $$m$$.

$g_z(\mathbf{p}) = - G m \frac{ z_p - z_q }{ \lVert \mathbf{p} - \mathbf{q} \rVert_2^2 }$

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.