# Location dependence of the acceleration due to gravity – What does acceleration depend on?

May 23, 2022

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In fact, one cannot assume that the earth is an ideal sphere with a uniform mass distribution. Due to the rotation of the earth around an axis that goes through the north and south poles, the earth – which is not a rigid body but is almost liquid inside – would flatten out into an ellipsoid.< /p>

However, more detailed investigation has revealed that the earth also deviates from the ellipsoidal shape and has a rather irregular shape, which is called a geoid. Some scientists disrespectfully say that the earth is shaped like a potato.

The distances between points on the earth’s surface and the center of the earth differ not insignificantly in the case of the geoid, so that for this reason alone it is to be expected that the gravitational accelerations on the geoid’s surface will be different. In addition, the globe is not a homogeneous body. There are areas of land and water, mountains and deposits of ores, etc., so that the mass distribution is quite inhomogeneous, which in turn causes locally different gravitational acceleration on the surface.

the Grace Duo (NASA)

In 2002, two identical Grace satellites were launched into orbit for the precise measurement of local gravitational acceleration. The distance between the two satellites was about $$220\,\rm{km}$$. The measurement of the earth’s gravitational field is achieved by the satellites constantly determining their own position with the help of a GPS system and two star sensors with high accuracy and also determining their mutual distance with the help of microwaves to within fractions of a millimeter. If, for example, the first satellite flies through a zone of increased attraction, it will be accelerated slightly more, thus increasing the distance to the following satellite.

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Conclusion: The local differences in the gravitational acceleration cause a disturbance in the satellite orbits.

You can see the evaluation of the data obtained in the adjacent figure. It shows the deviation of the local gravitational acceleration from a standard value. This deviation is given in milligal ($$1\,{\rm{mGal}}} = {10^{-5}}\,\frac{{\rm{m}}}}{{{{\rm{s} }^{\rm{2}}}}}$$) specified.

You get an impression of the precision of the measurements if you consider the following information for the gravitational accelerations at the equator and at the pole:${g_{{\rm{Pol}}}} = 983221 \,{\rm{mGal}}$${g_{{\rm{Equ}}}} = 978049\,{\rm{mGal}}}$Due to the local deviations of the gravitational acceleration, one can possibly Make forecasts on oil or ore deposits.

From the values ​​obtained for the local gravitational acceleration, one can deduce the height deviation of the geoid from the ideal ellipsoid. The following images and animations, which come from the Geoforschungszentrum Potsdam (GFP), give you an impression of the irregularities of the earth’s surface.

The two views of the globe clearly show the deviation from the ideal ellipsoidal shape. The soil looks like a potato.

The color of the surface shows the respective deviation of the surface height from that of the ellipsoid in meters.

Red colored areas are above, green to blue colored areas are below the ellipsoid surface.

You can go to http://www-app2.gfz-potsdam.de/sec13/animated-potato-d-cms.html You can also view an animated representation of the earth’s elevation profile (e.g. click on “Northern view”).

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