Newton's Law of Universal Gravitation
Godfrey Kneller's 1689 portrait of Isaac Newton (aged 46)
Newton explains, "Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects."
Newton eventually published his still famous law of universal gravitation in his Principia Mathematica as follows:
F = Gm1m2/r2
where:
F = gravitational force between two objects
m1 = mass of first object
m2 = mass of second object
r = distance between the objects
G = universal constant of gravitation
Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the true force has to be found by integrating the forces between the various points.
The above form is a simplified version. It is more properly expressed as vector equation. (All quantities in bold represent vector quantities in what follows.) The form below is vectorially complete:
F12 = (Gm1m2(r2-r1))/(|r2-r1|3)
where:
F12 is the force on m1 by m2
m1 and m2 are the masses
r1 and r2 are the position vectors of their respective masses
G is the gravitational constant
For the force on mass two, simply multiply F12 by -1.
The primary difference between the two formulations is that the second form uses the difference in position to construct a vector that points from one mass to the other, and then divides that vector by its length to prevent it from changing the magnitude of the force.
It's important to understand that while Newton was able to formulate his law of gravity in his monumental work, he was not comfortable with it because he never, in his words, "assigned the cause of this power." In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity. Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science.
He lamented the fact that 'philosophers have hitherto attempted the search of nature in vain' for the source of the gravitational force, as he was convinced 'by many reasons' that there were 'causes hitherto unknown' that were fundamental to all the 'phenomena of nature.' These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer is yet to be found. While it is true that Einstein's hypotheses (see below) are successful in explaining the effects of gravitational forces more precisely than Newton's in certain cases, he too never 'assigned the cause of this power,' in his theories. It is said that in Einstein's equations, 'matter tells space how to curve, and space tells matter how to move,' but this new idea, completely foreign to the world of Newton, does not enable Einstein to assign the 'cause of this power' to curve space anymore than the Law of Universal Gravitation enabled Newton to assign its cause. In his own words:
I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain.
If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fullfiled as well.
This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.
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