.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_02_newton_oblate_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_02_newton_oblate_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_02_newton_oblate_earth.py:


Newton's oblate Earth (1687)
============================

Newton argued that a rotating, fluid Earth must bulge at the equator. Treating
it as homogeneous, he balanced the weight of two water-filled canals, one to
the pole and one to the equator, and found a flattening of 1/230. The modern
value is 1/298: the Earth's mass is concentrated toward its centre, which makes
it less flattened than a uniform fluid. Jupiter, spinning in under ten hours,
shows the same effect more strongly.

.. GENERATED FROM PYTHON SOURCE LINES 12-38



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_02_newton_oblate_earth_001.png
   :alt: Rotation flattens a fluid planet
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_02_newton_oblate_earth_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import OMEGA_EARTH
    from earthsciencekit.geophysics import centrifugal_ratio, homogeneous_flattening
    from earthsciencekit.units import convert

    earth = homogeneous_flattening(centrifugal_ratio(OMEGA_EARTH, 6378137.0, 9.7803267715))
    assert 225 < 1 / earth < 235
    day = np.linspace(6, 48, 200)
    flattening = homogeneous_flattening(centrifugal_ratio(2 * np.pi / convert(day / 24, "day", "s"), 6378137.0, 9.7803267715))
    jupiter_ratio = centrifugal_ratio(2 * np.pi / convert(9.925 / 24, "day", "s"), 7.1492e7, 24.79)
    jupiter = homogeneous_flattening(jupiter_ratio)
    assert jupiter > 0.0649

    fig, ax = plt.subplots()
    ax.loglog(day, flattening, label="homogeneous Earth, 5 m / 4")
    ax.plot(convert(2 * np.pi / OMEGA_EARTH, "s", "day") * 24, earth, "o", label=f"Newton: 1/{1 / earth:.0f}")
    ax.plot(23.934, 1 / 298.257, "s", label="observed Earth: 1/298")
    ax.plot(9.925, jupiter, "^", label=f"homogeneous Jupiter: {jupiter:.3f}")
    ax.plot(9.925, 0.0649, "v", label="observed Jupiter: 0.065")
    ax.set(xlabel="length of day [hours]", ylabel="flattening (a - c) / a", title="Rotation flattens a fluid planet")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.166 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_02_newton_oblate_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_02_newton_oblate_earth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_newton_oblate_earth.ipynb <plot_02_newton_oblate_earth.ipynb>`

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

      :download:`Download Python source code: plot_02_newton_oblate_earth.py <plot_02_newton_oblate_earth.py>`

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

      :download:`Download zipped: plot_02_newton_oblate_earth.zip <plot_02_newton_oblate_earth.zip>`


.. only:: html

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

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