# 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_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_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 $$m$$.

$g_{zz}(\mathbf{p}) = G m \left[ \frac{ 3 (z_p - z_q)^2 }{ \lVert \mathbf{p} - \mathbf{q} \rVert_2^5 } - \frac{ 1 }{ \lVert \mathbf{p} - \mathbf{q} \rVert_2^3 } \right]$

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.