.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_05_cavendish_weighs_the_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_05_cavendish_weighs_the_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_05_cavendish_weighs_the_earth.py:


Cavendish weighs the Earth (1798)
=================================

Henry Cavendish hung a 1.8 m rod carrying two small lead balls from a fine
wire and brought two 158 kg balls close to them. The rod twisted by about a
milliradian, and timing its slow free swing calibrated the wire. Together these
give the gravitational constant, and with surface gravity the mean density of
the Earth: Cavendish found 5.48 times that of water, about twice the density of
surface rock, so the interior must be much denser.

.. GENERATED FROM PYTHON SOURCE LINES 12-42



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_05_cavendish_weighs_the_earth_001.png
   :alt: Torsion balance, Weighing the Earth
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_05_cavendish_weighs_the_earth_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import EARTH_RADIUS, G
    from earthsciencekit.geophysics import earth_mean_density, torsion_balance_gravitational_constant

    arm, separation, large, period = 1.86, 0.225, 158.0, 420.0
    deflection = 1.0e-3
    measured = torsion_balance_gravitational_constant(arm, separation, deflection, large, period)
    density = earth_mean_density(9.81, EARTH_RADIUS, measured)
    assert np.isclose(measured, G, rtol=0.01)
    assert 5400 < density < 5600 and density / 2700 > 2

    twist = np.linspace(0.5e-3, 1.5e-3, 50)
    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    left.plot(twist * 1e3, torsion_balance_gravitational_constant(arm, separation, twist, large, period))
    left.axhline(G, color="0.5", ls="--", label="CODATA G")
    left.plot(deflection * 1e3, measured, "o")
    left.set(xlabel="rod deflection [mrad]", ylabel="G [m^3/(kg s^2)]", title="Torsion balance")
    left.legend()
    constants = np.linspace(5e-11, 9e-11, 50)
    right.plot(constants, earth_mean_density(9.81, EARTH_RADIUS, constants))
    right.axhline(2700, color="0.5", ls=":", label="granite")
    right.plot(measured, density, "o", label=f"{density:.0f} kg/m^3")
    right.set(xlabel="G [m^3/(kg s^2)]", ylabel="mean density [kg/m^3]", title="Weighing the Earth")
    right.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.209 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_05_cavendish_weighs_the_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_05_cavendish_weighs_the_earth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_cavendish_weighs_the_earth.ipynb <plot_05_cavendish_weighs_the_earth.ipynb>`

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

      :download:`Download Python source code: plot_05_cavendish_weighs_the_earth.py <plot_05_cavendish_weighs_the_earth.py>`

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

      :download:`Download zipped: plot_05_cavendish_weighs_the_earth.zip <plot_05_cavendish_weighs_the_earth.zip>`


.. only:: html

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

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