The application of Newtonís Law of Gravity in the above example is a little more complicated than it might seem for the following reasons:

  • Mass m on the Earthís surface is attracted to every particle within the Earth. Therefore, the attractive force W between object m and the Earth (i.e., mís weight) is a vector sum of all of the m/particle forces.

In the above example, object m and M1 (a random particle within the Earthís sphere) have a mutual attraction F. However, only the vector component of F. (i.e. f) directed toward the Earthís center contributes to the weight of object m. The summation of all these vector forces between mM1, mM2, ...... will compute the accurate weight of m. This is a calculus problem for a mathematician.

  • Another condition which complicates the calculation of mís weight is the fact that the earth is not a homogeneous sphere. The Earthís interior consists of the crust, asthenosphere, transition zone, lower mantle, outer and inner core, all consisting of materials of different densities.

  • Also, the Earth is not a perfect sphere. It is flattened at the poles and therefore, the force of gravity is greater (i.e. an objectís weight is greater) at the poles.

If object m could descend into the Earth toward the Earthís center, its weight would decrease until it became weightless at the Earthís center. As the object descended from the Earthís surface, the Earthís mass above the object would exert an attractive force tending to pull the object toward the surface. The more powerful Earth centered force would offset the surface directed force until the object reached the Earthís center.

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