Physics Question #2452

Dom Elbon, a 17 year old male from Nottingham, England asks on December 22, 2004,

Is gravity lumpy? If you were standing in a valley, then on a mountain, would your weight be less then become more, as you walked up from the valley to the mountain top, due to having a changing amount of mass under you? What if you were flying a plane over a flat area then passed a mountain? Wouldn't you be attracted to the mountain to some degree? Wouldn't this then imply that gravity has a shape, which is a function of the shape and mass of the object?

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The answer

William George Unruh answered on December 22, 2004

Yes, gravity is "lumpy"-- i.e. the gravitational field of the earth follows the distribution of matter on the earth. In fact this is used as a way of surveying for minerals--since mineral ores tend to be denser than ordinary rock, they will perturb the gravitational field around themselves. Very sensitive gravimeters are designed to allow gravity mapping by planes flying over the region. There were a special series of satellites (the Lageos satellites and more recently the Grace satellites) to map the shape of the gravitational field of the earth from space. See for example the latest map of the gravity anomalies from the Grace team.

The map can either be done in terms of the height of the equipotential surfaces (i.e. the surface that water would seek in the absence of any wind, tides, currents) or in terms of the deviations of the force of gravity on the sufrace of the "goid" (the elliptical shape the earth would have if its matter were uniformly distributed). The latter emphasizes the smaller scale variations more than does the former.

Note that in the case of the mountain, there are two effects. The dominant one is that when you climb the mountain you are further from the center of the earth than when you are in the valley. If we say that the mountain is 2000 m higher than the valley, this produces an effect of about a .03% difference in the attraction of the earth on you because you are further away from the earth's center. This is larger than the local gravitational field of the mountain itself.

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