Why do we invent non-physical concepts (like e.g. point particles) to study physical phenomenons? There is nothing exist like point particles in reality then why did we invented the notion of point particles and how does it relate to real world?
 A: 
Why do we invent non physical concept to study physical phenomenons? 

People invented arithmetic ( a non physical concept) to distribute the produce of their cultivations, geometry ( a non physical concept) to study how to distribute the land they cultivated.
Then it was found that geometrical concepts fitted physical observations, stars, planets and even could give the circumference of the earth. 
Arabs continued with the invention of algebra, which helped in solving problems with arithmetic faster. The the dark ages came, and the study pf physics was stuck in descriptions by Aristotle  and Demokritos, words  words words.
Physics took off with the mathematical tools invented for the needs of studying observations, like falling apples, after the enlightenment calculus was nurtured by many people and for physics used extensively by Newton , and modeling observations by complicated mathematics took off.
Modeling is assuming simple behaviors for representations of physical observables , testing whether calculations fit the data, and whether predictions are accurately validated.
If the nonphysical concept of mathematics ( and the use of point particles) had not been invented, at best we would still be living in the technology of the middle ages, at worst, the stone age.
A: To be able to understand very physical properties and ideas, simpler theories and concepts have to be developed. 
Physics on the whole is not perfect, it is a way to model what is seen around the world. With something like a planet, understanding what happens to the mass if it is considered as a point source simplifies a lot of the mathematics and gives a very good approximation. In fact, a lot of very complicated problems cannot be solved if objects are not considered as point particles. 
Applying a force for example if the object is not considered a point source would be very difficult. The force would have to be summed over for all the particles in a system which is not feasible.  Instead if the object is simplified it is much easier to understand what is going to happen to he object when it is for instance interacting with something else. 
Also, especially in fields such as Quantum Mechanics, non-physical concepts are very important (especially at an undergraduate level) to gain very good intuition into the subject area and understand reasons for why things happen.  
A: 
then why did we invented the notion of point particles

Because that makes it simpler to work with.


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*Sometimes we say "it costs 24 \$" even though it is actually 23.99 \$.

*We also usually say that there are 365 days on a year, even though there actually are $\sim$365.24.


We are accepting a tiny error margin, when that really doesn't matter at the scale we are working at. If you are working with everyday size-scales, then you really don't have to consider the actual size of stuff like charges, atoms, electrons etc. - the modelling of them as point-like is fine, fine, fine.
