# Newton’s Law of Gravitation

Gravitation is a natural phenomenon by which physical bodies attract each other due to their masses. This force occurs whenever masses are present and the two bodies need not to be in contact with each other. It is however the weakest of the fundamental forces of nature.

In 1687, Sir Isaac Newton concluded that this non-contact gravitational force must be as responsible for the falling of the apple from a tree as it is the cause for the rotation of the moon about the earth. Hence he published the Newton’s law of gravitation which states that:

“The mutual force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.”

This means that if there are two point masses M and m and they are separated by distance r, the magnitude of the gravitational force attracting them to each other is

|F| = GmM/r

^{2}

where G, the constant of universal gravitation, is 6.67 x 10

^{-11}N m

^{2}kg

^{-2}(will be given in data & formulae list during tests and examinations).

Note:

1. r is taken to be the centre to centre distance (i.e. centre of particle to centre of particle). Do not take r to be the radius of orbit!

2. This formula is an example of the inverse square law.

## Inquiry:

## 1) Drag mass 1 and mass 2 and observe the forces F1 (force on mass 1 due to mass 2) and F2 (force on mass 2 due to mass1 ). Click play and record what values and directions about the two forces in the below diagram?

The two forces in the diagram are action-reaction pair because each force is acting on the particle by the other particle.

2) In that case, when Earth pulls you down, why did you not pull Earth up?

You did! But the mass of Earth is relatively much bigger than my mass and

hence its acceleration is relative much smaller.

3) using the model, design an inquiry approach (hints: ask the question: is the relationship of the force on mass 1 due to mass 2, |F

_{1}| and mass 2 due to mass 1 |F

_{2}| on each other and their centre to centre distances apart r ? is the model |F| = GmM/r

^{2}valid?, plan what are the variables needed to test this model? collect the appropriate data, analyze the data, explain the data, argue with the evidences your understanding, communicate the result)