How did the great Newton derived his law of gravity?

Answer 1

First to state the great Newton's law of gravity. The law of gravity states that two heavenly bodies or masses get attracted to each other with a force that is directly proportional to the product of masses and inversely proportional to the square of the distance between the two. Now let us try to analyse the same. The two bodies attract each other is a physical fact. That can be conceived easily that the force of attraction will be directly proportional to the product of the masses. There is proportion. so you have taken the product and not addition. It can be conceived that the force will decrease with the distance. There is inverse proportion. So you have to divide and not subtract. With subtraction the force will be zero at some distance, which is not logical. The golden question that remains is that how the great Newton derived that the force will decrease in proportion to the 'square' of the distance, and not 'only' distance or why the 'cube' of the distance. Here goes the very simple explanation for the same. You take a box with the size of 1*1*1 foot. Place the point source of light in the centre of the box. The light falls on all the six surfaces of the box. Then replace the box with the one with the size of 2*2*2. Here the distance got doubled. The size of one surface is 2*2. That is 4 square feet. Then replace the box with the size of 3*3*3 feet box. Here the distance got tripled. The size of one surface will be 3*3. that is 9 square feet. Then replace the box with size of 4*4*4 feet. Here the distance will get four times. The surface area of one surface will be 4*4. That is 16 square feet. You can go on increasing the size of the box. The surface area of one side will increase to the square of the distance, that increase. The force of gravity travel like the sound waves, which you can not see. So I have taken the light source. You can calculate with all the six surfaces. Great Newton used the formula of the surface area of the sphere, which is more logical. Then also you get the same results. This is how great Newton derived the formula of the law of gravity.