Universal Law of Gravitation
Have you heard of the story about Sir Isaac Newton and a falling apple which was pulled toward earth by the force of gravity? An apparently unimportant event led to Newton’s formation of a fundamental law of nature (Law of universal gravitation or Law of Gravitation) which involves gravitational forces. We’ll discuss on this law now and also derive the equation of the Gravitational force.
As said by this law of universal gravitation every object in this universe is attracting every other object towards it. This force of gravitational attraction between any two objects in the universe is inversely proportional to the square of the distance between the objects. This force is again directly proportional to the product of the masses of these two objects involved.
Derivation of Gravitational Force formula from the Law of Gravitation
Say FG is the force of gravitational attraction between any two objects,
m1 is the mass of one object,
m2 is the mass of a second object,
d is the distance between the centers of the two objects. (Objects are assumed to be spherical.)
Now as said in the Law of Gravitation:
FG ∞ m1.m2
FG ∞ 1/d2
So, FG ∞ m1.m2/ d2
FG = (G.m1.m2)/ d2
G is a constant which is discussed in the next section.
This equation gives us the expression of the gravitational force.
Universal Gravitational Constant or Gravitational constant
In the equation above, G is a constant, called Universal Gravitational Constant or Gravitational constant.
Its value is 6.67408 × 10-11 m3 kg-1 s-2
Law of Gravitation-Notes
With the law of universal gravitation, it is important to notice that two equal but opposite forces are present between any 2 objects. Earth pulls on the Moon and the Moon pulls on Earth with a force of equal magnitude.
On the Earth’s surface, Earth pulls down on a 1 kg mass with a force of magnitude 9.8 N, and the 1 kg mass pulls upward on Earth with a force of magnitude 9.8 N. (Ref: Newton’s third law of motion.)