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Newton's law of gravitation is sometimes expressed by the equation - F = Gm1m2/d(squared) where F represents the force between two masses m1 and m2, d is the distance between centers of mass, and G is a constant. Is this a correct formulation of Newton's law of gravitation?
Question
#24026. Asked by Impress me. (Nov 07 02 1:25 AM)
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Impress me
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No...Consider a carpenter's square with a point C an inch up and inside from where the two lines of the L intersect, and a point A a half inch further in from C. Now place a small spherical body at C. The distance between the center of mass of these two bodies, the sphere and the carpenter's square is zero! According to the statement of Newton's law of gravitation given in the question the attractive force between the two bodies would become infinite, which is clearly not the case. Indeed one may conclude that if the small sphere is placed at A the attractive force may tend to increase the distance between the center of the mass. Thus in terms of the statement of the law given in question the force becomes repulsive rather than attractive!
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greencavalier
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Although the distance from the centrre of gravity is zero, the gravitational attraction is now coming from all around the little sphere, so it cannot be treated as if it is at the centre of gravity of the t-square.
It is intersting that your weight is at a maximum at the earth's surface. If you go up in the air, or down a mine, you will weigh less. (But your mass will stay the same - sorry!)
See this website:
 http://www.sciencenet.org.uk/database/Physics/0207/p01562d.html
for a better explanation than I can manage.
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Impress me
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Newton was well aware of the problem of determining the distance used in the formula for gravitational force. In his formulation the inverse-square law applies to mass particles rather than extended bodies, and the distance d is the distance between two mass particles. It is only in the special case of spheres whose densities are dependent only on the distance from their centers that d refers to the distance between their centers of mass, i.e., their geometrical centers.
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