Newtons Law of Gravitation
المؤلف:
Professor John W. Norbury
المصدر:
ELEMENTARY MECHANICS & THERMODYNAMICS
الجزء والصفحة:
p 158
29-12-2016
2936
Newton's Law of Gravitation
We already know about Newton's three laws of motion, the second of which is 
. These three laws describe motion in general. They never refer to a specific force. Newton however did also study in detail a specific force, namely gravity. He conjectured that the gravitational force between two bodies of mass m1 and m2 whose centers are separated by a distance of r has a magnitude of
The minus sign tells us that the force points inwards. The value of G was determined later in 1798 by Cavendish. It's value measured today is
G = 6.67 × 10-11Nm2 kg-2
However, it is interesting that today the gravitational constant is the least accurately known of all the fundamental constants. For instance, its most accurately known value is actually G = (6:67259±0.00085)×10-11 Nm2kg-2 whereas for example the charge of the electron is (1:60217733 ± 0.00000049) × 10-19 Coulomb or the speed of light is 299 792 458 m sec-1 which are known much more accurately than G. Another example is the strength of the electrical force, called the fine structure constant, α-1 = 137:0359895 ± 0.0000061.
Note: Now the vector form of Newton's Law is
where 
is a unit vector point from one mass out to the other. The gravitational force is an inward force and that's why the minus sign appears.
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