Newton’s law of Universal Gravitation
Hi Guys
In this issue we will be looking at Newton’s law of Universal Gravitation. You will study this
fundamental law in grade 11.
Every one of us has been a victim of gravity when we have taken a fall of some sorts.
Gravity is the weakest of the four fundamental forces of nature. It is difficult to
believe that gravity is the weakest force since we have witnessed its strength during
the collapse of a building or the launching of a spaceship.
The English Physicist and Mathematician, Sir Isaac Newton is credited with the formulation of
the Law of Gravitation.
Newton’s law of Universal Gravitation states that the force of attraction between two masses is
directly proportional to the product of the masses and inversely proportional to the square of
the distance between their centres.
A couple of points to note:
1. The gravitational interaction is attractive.
2. Newtonian gravity follows an inverse square law, i.e.
3. The larger the masses, the greater the force.
Mathematically we can write:
.
---- (1)
where G = 6.7 x 10-11N.m2.kg-2 is a constant. Since the constant G is so small, we can understand
why the gravitational force between average size masses is negligible. In grade ten you would
have learnt to calculate the weight of an object by making use of
W = mg, where g is the acceleration due to gravity. It is important to note that the weight of an
object is also given by
If we take m1 to be the mass of the falling body and m2 the mass of the earth, then we can
write:
The mass of the falling body cancels out and we have
This is an interesting result which was first put forward by Galileo. The acceleration of an object
in free-fall is independent of the mass of the falling object.
Let us now take a deeper look at Newton’s law of gravity.
Question 1
Assume that the earth was perfectly spherical and its mass was uniformly
distributed. If you had to tunnel your way to the centre of the Earth and stood
on a bathroom scale, what would the scale reading be?
Question 2
In Newton’s law of gravity, take m1 to represent the mass of the earth and m2 the mass of the
sun. The force F calculated from formula (1) above gives the force of attraction between the
earth and the sun. If we set m2 to zero, then F is zero. Does this mean that if we remove the
sun, the earth would fly off into space almost instantaneously? Explain. Hint: gravity travels at
the speed of light.
Historical note: It is often stated that Newton hit upon the law of gravitation
while sitting under an apple tree and observing an apple fall. One wonders what
would have happened had he been sitting under a coconut tree?
A descendent of the apple tree which Newton claimed to have sat under.
Cheers and stay sharp.
Dr G