# geoana.gravity.PointMass.gravitational_potential#

PointMass.gravitational_potential(xyz)#

Gravitational potential due to a point mass. See Blakely, 1996 equation 3.4.

$U(P) = \gamma \frac{m}{r}$
Parameters
xyz(…, 3) numpy.ndarray

Observation locations in units m.

Returns
(…, ) numpy.ndarray

Gravitational potential at observation locations xyz in units $$\frac{m^2}{s^2}$$.

Examples

Here, we define a point mass with mass=1kg and plot the gravitational potential as a function of distance.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from geoana.gravity import PointMass


Define the point mass.

>>> location = np.r_[0., 0., 0.]
>>> mass = 1.0
>>> simulation = PointMass(
>>>     mass=mass, location=location
>>> )


Now we create a set of gridded locations, take the distances and compute the gravitational potential.

>>> X, Y = np.meshgrid(np.linspace(-1, 1, 20), np.linspace(-1, 1, 20))
>>> Z = np.zeros_like(X) + 0.25
>>> xyz = np.stack((X, Y, Z), axis=-1)
>>> r = np.linalg.norm(xyz, axis=-1)
>>> u = simulation.gravitational_potential(xyz)


Finally, we plot the gravitational potential as a function of distance.

>>> plt.plot(r, u)
>>> plt.xlabel('Distance from point mass')
>>> plt.ylabel('Gravitational potential')
>>> plt.title('Gravitational Potential as a function of distance from point mass')
>>> plt.show()