Golden Notes On Gravity

     History on gravity:

-> Galileo discovered that all objects, irrespective of their masses,fall towards the earth 🌎 with the same acceleration.

-> One of the earliest recorded model for the planetary motion proposed by Ptolemy about 2000 years ago was a "geocentric model" in which all celestial bodies revolved around the earth 🌍.

-> In 5th A.D. Aryabhatta proposed a "Heliocentric model" in which the sun was supposed to be the centre around which all the planets were revolving. The similar model in a more definitive way was proposed by Nicolas Copernicus(1473-1543)

-> It was around the same time as Galileo,Tycho Brahe(1546-1601) spent his entire life recording observations of the planets with the naked eyes.His complicated data were further analysed by his assistant ' Johannes Kepler' (1571-1640)

-> The English scientist' Henry Cavendish' determined the value of 'G' in 1798.

The calculation that he made after a long outstanding experiment was close to the present accepted value i.e., 6.67×10-11 Nm^2kg^-2.

That's why he is sometimes regarded as "The person who weighed the earth".

Some mathematical points:

1.-> If the position of the particle changes on account of force acting on it,then the change in its potential energy is equal to the amount of work done on the body by the force.The work done in moving the particle is equal to the difference of P.E. between its final and initial positions.

At height h above the surface of the earth 🌎, P.E. is given by W(h)= mgh+Wo .

So if h=0 ,then W(0)= Wo and the change in potential energy when a particle is taken from the position 1 to 2 is given by

W12= {W(h2)+Wo}-{W(h1)+Wo} = W(h2)-W(h1) .

So as you can see that Wo is just a P.E. at h=0 i.e.,at the surface of the earth which is usually ignored in the expression of gravitational potential energy of the particle due to earth's gravity and hence we write W(h)= mgh or P.E. =mgh . Remember that" only the difference of potential energy has a definite physical meaning because the potential at any point can't be absolutely determined without considering another reference point (in most cases infinity) ."

2.-> When we throw an object,its P.E. increases and its kinetic energy decreases (its velocity decreases) and when its final velocity becomes zero ,it falls back on the ground. If its final velocity never becomes zero,then it will go on forever and will escape from gravitational field of the earth and so will never return back to the earth!

The minimum initial velocity required for the escaping of object from the earth's gravitational field is known as "escape velocity" which is given as