Note
Click here to download the full example code
Overview¶
The main functionality of Boule is contained in the Ellipsoid
class.
It defines a Reference Ellipsoid:
an oblate ellipsoid that approximates the shape of the Earth (or other
planetary body).
Ellipsoids are generally specified by 4 parameters:
The semi-major axis (\(a\)): the equatorial radius.
The flattening (\(f = (a - b)/a\)): the ratio between the equatorial and polar radii.
The geocentric gravitational constant (\(GM\)): the multiplication of the total mass of the ellipsoid and the gravitational constant.
The angular velocity (\(\omega\)): spin rate of the ellipsoid which defines the centrifugal potential.
With these parameters, Boule can calculate gravity, coordinate conversions, and other derived physical and geometric properties of the ellipsoid.
The library¶
All functions and classes in Boule are available in the base namespace of the
boule package. This means that you can access all of them with a single
import:
# Boule is usually imported as bl
import boule as bl
Ellipsoids¶
Boule comes with built-in ellipsoids that can be accessed
as global variables in the boule module:
Out:
Ellipsoid(name='WGS84', semimajor_axis=6378137, flattening=0.0033528106647474805, geocentric_grav_const=398600441800000.0, angular_velocity=7.292115e-05, long_name='World Geodetic System 1984', reference='Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical Geodesy (2nd, corr. ed. 2006 edition ed.). Wien\u202f; New York: Springer.')
Ellipsoid(name='MARS', semimajor_axis=3395428, flattening=0.005227617843759314, geocentric_grav_const=42828372000000.0, angular_velocity=7.0882181e-05, long_name='Mars Ellipsoid', reference='Ardalan, A. A., Karimi, R., & Grafarend, E. W. (2009). A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars. Earth, Moon, and Planets, 106(1), 1. doi:10.1007/s11038-009-9342-7')
As seen above, Ellipsoid instances can be printed to record
their defining attributes. Additionally, ellipsoids define a name (short and
long version) and reference for the origin of the numbers used:
print(bl.MARS.name)
print(bl.MARS.reference)
Out:
MARS
Ardalan, A. A., Karimi, R., & Grafarend, E. W. (2009). A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars. Earth, Moon, and Planets, 106(1), 1. doi:10.1007/s11038-009-9342-7
Other derived properties of ellipsoids are calculated on demand when accessed:
Out:
0.10211712735480878
3.731907392736793
3.7087546578837722
You can also define your own ellipsoid. For example, this would be a definition of an ellipsoid with 1000 m semimajor axis, flattening equal to 0.5 and dummy values for \(GM\) and \(\omega\):
ellipsoid = bl.Ellipsoid(
name="Ellipsoid",
long_name="Ellipsoid with 0.5 flattening",
flattening=0.5,
semimajor_axis=1000,
geocentric_grav_const=1,
angular_velocity=1,
)
print(ellipsoid)
print(ellipsoid.semiminor_axis)
print(ellipsoid.first_eccentricity)
Out:
Ellipsoid(name='Ellipsoid', semimajor_axis=1000, flattening=0.5, geocentric_grav_const=1, angular_velocity=1, long_name='Ellipsoid with 0.5 flattening', reference=None)
500.0
0.8660254037844386
If the ellipsoid has zero flattening (a sphere), you must use the
boule.Sphere class instead. For example, this would be the definition of
a sphere with 1000 m radius and dummy values for \(GM\) and \(\omega\):
Out:
Sphere(name='Sphere', radius=1000, geocentric_grav_const=1, angular_velocity=1, long_name='Ellipsoid with 0 flattening', reference=None)
Computations¶
Ellipsoids can be used for computations generally encountered in geodetic and geophysical applications:
See the respective tutorials and reference documentation for more information.
Total running time of the script: ( 0 minutes 0.004 seconds)