.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_01_gilbert_magnetic_earth.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_geophysics_plot_01_gilbert_magnetic_earth.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_geophysics_plot_01_gilbert_magnetic_earth.py:


Gilbert's magnetic Earth (1600)
===============================

William Gilbert carved a sphere of lodestone, his *terrella*, and carried a
small dip needle over it. The needle lay flat at the terrella's equator, stood
vertical at its poles and dipped steadily in between, just as compass needles
did at sea. He concluded that the Earth itself is a great magnet. For an axial
dipole the dip obeys ``tan(I) = 2 tan(latitude)`` and the field at the poles is
twice that at the equator.

.. GENERATED FROM PYTHON SOURCE LINES 12-46



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_01_gilbert_magnetic_earth_001.png
   :alt: Dip needles around a terrella, tan I = 2 tan(latitude)
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_01_gilbert_magnetic_earth_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.geophysics import dipole_field, dipole_inclination, field_elements
    from earthsciencekit.units import convert

    latitude = np.linspace(-np.pi / 2, np.pi / 2, 181)
    inclination = dipole_inclination(latitude)
    field = dipole_field(latitude, 1.0, 1.0)
    intensity = field_elements(field[..., 0], 0, field[..., 1])[..., 2]
    assert np.isclose(intensity[-1] / intensity[90], 2)
    np.testing.assert_allclose(np.tan(inclination[1:-1]), 2 * np.tan(latitude[1:-1]))

    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4.5))
    circle = np.linspace(0, 2 * np.pi, 361)
    left.fill(np.cos(circle), np.sin(circle), color="0.85")
    for lat in np.radians(np.arange(-80, 81, 20)):
        north, down = dipole_field(lat, 1.0, 1.0)
        direction = north * np.array([-np.sin(lat), np.cos(lat)]) + down * np.array([-np.cos(lat), -np.sin(lat)])
        direction /= np.hypot(*direction)
        for side in (1, -1):
            centre = 1.15 * np.array([side * np.cos(lat), np.sin(lat)])
            needle = 0.1 * direction * np.array([side, 1])
            left.annotate("", centre + needle, centre - needle, arrowprops={"arrowstyle": "->", "color": "C3"})
    left.set(xlim=(-1.4, 1.4), ylim=(-1.4, 1.4), aspect="equal", title="Dip needles around a terrella")
    left.axis("off")
    right.plot(convert(latitude, "rad", "degree"), convert(inclination, "rad", "degree"), label="inclination")
    right.plot(convert(latitude, "rad", "degree"), 45 * intensity / intensity[90], "--", label="intensity (x 45 degrees)")
    right.set(xlabel="magnetic latitude [degrees]", ylabel="degrees", title="tan I = 2 tan(latitude)")
    right.legend()
    fig.tight_layout()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.196 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_01_gilbert_magnetic_earth.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/geophysics/plot_01_gilbert_magnetic_earth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_gilbert_magnetic_earth.ipynb <plot_01_gilbert_magnetic_earth.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_gilbert_magnetic_earth.py <plot_01_gilbert_magnetic_earth.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_gilbert_magnetic_earth.zip <plot_01_gilbert_magnetic_earth.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_