Newton's Gravity Continued...

http://vaibhavkhamgaonkar.blogspot.com/2011/05/newtons-gravity.html
                                            (link to previous post)

As in the previous post we have found out the Newtons most famous equation i.e. Law of Gravitation which is given by

F = G*(m1 * M2)/r^2
where G is the gravitational constant = 6.67 * 10 ^-11
m1 & M2 are the masses of an object experiencing gravitational force.
r is the distance between two object.


Now lets see what does it mean, it simply tells that if a objects having mass (m1 & M2) which are separated by certain distance (r) then according to Newton, they will experience some kind of attraction (they will experience force of attraction) which depends on products of there Masses & the Square of Distance between them. This is often called as Inverse square law.


Now with this we can find the force of attraction between two object. But wait if it is true that two object separated by certain distance they will experience a force then why we not experiencing that force since we are pretty close to various objects around us.
let me clarify you, in day today life we used to pass through various objects but we haven't experience that kind of attraction.
Why ?
Well if you look at the Equation carefully, there is a term called Gravitational constant "G" & whose value is very very small. now if u thing that u should experience the same kind of force then the only thing is to overcome that value is the mass but  you don't have enough mass to overcome thus we aren't experience this force. This phenomenon occurs only for the the objects whose mass is very very high (like Planets, Stars, Galaxies etc)

Now just tell me that if you are having two objects of different masses lets say 1 is of 1Kg & other is of 10 kg. they both are falling from 100 stories building. so which one will fall first on the ground if they are start falling at same time...?

If u say that they will going to fall at same time then u are corrects....
let me tell u how :-

what is the force:-
F = m * a ----------------------- (m= mass , a = Acceleration)


According to Galileo's model

F = - m * g ------------------------------ ( - because object is accelerating downward)

equating 1 & 2
 m * a = = - m * g

thus  a = -g --------------------------------i.e acceleration will be equal to gravitational force pulling the object down word with 10 m/s^2

Now lets consider an object of mass (m) who is falling towards earth having mass (M).
Now according to newtons gravitational law
the force of attraction between two objects (m &M ) are given by

F = (m * M) * G / r^2

& also we know that object of mass 'm' is moving & is being attracted towards 'M' by certain force & that can be given by

F= m * a

therefore on comparing these  2 equations we have
m * a = (m * M) * G / r^2
Which finally gives

a =  (M * G) / r^2 ---------------------------------------------( Note down here the mass of small object falling to earth is not appearing)

Acceleration of small object is independent of its mass. i.e if there are no. of objects falling towards earth then their acceleration will not depend on their individual masses but it depends on the the other object on which they are falling.
Thus we can say that every object falling on ground will take same time provided they are dropped at same time.

Newton's Gravity

Everybody knows who is the father of gravity. He is none other than Sir Isaac Newton. He accidentally invented the gravity. As you all know by just seeing apple falling on the ground. He called this force as Gravity. It is the force that attracts every object towards the center.(Gravitation is a natural phenomenon by which physical bodies attract with a force proportional to their mass).

 At the time of Newton, Everybody knows that planets orbits around the Sun but the question was how does the planets moves, what held them around the orbit ?

The most famous theory comes from the french Philosopher(Henri Decart), he thought a universe as a giant machine like a clock & even the orbit of planets can be explained by simple mechanical interaction of the part of the machine. But Newton had trouble accepting this concept.

With the falling Apple from the tree he realized that what held the planets in the orbit is not a physical mechanism as suggested by (Decart) but an invisible force he called "Gravity" & he was convinced that force pulling apple down the earth & the motion of the moon around the earth is one & the same thing.

The Italian Scientist (Galileo) has already proved that motion of an all object falling down word picks up the same speed regardless the Mass of an object & finding a average speed (of an object) is an straight forward process.
e.g:- If you want to find the average speed of falling apple, all you have to divide the distance traveled by apple & time taken by apple to fall down.
 i.e.
              Avg Speed = 60 ft / 2 sec
                                = 30 ft per sec

 
 But the Newton was not satisfied with this.
=> What would be the speed of an apple which is constantly accelerating at every point along the way?
=> What would be the apple velocity at half way point?
                                     
To find out this, you have to measure avg speed for smaller & smaller period of time. shorter the internal closer you get to knowing the apple speed at that moment. But to find the precise speed at a single instance you have to reduce time interval close to zero as you can [ Newton invented a way to make time interval infinitesimally small ]
 with this technique it was possible to calculate quantities that are constantly changing like speed of an apple at any particular moment or our planet position changes over time. With this technique Newton invented a new branch of Mathematics called Calculus ( It is the quantitative understanding of how the things changed ).

At those days scientist thought that Sunlight (white light) was pure & colors are produced by physically modifying the white light which they believe passing it through Prism did.
 But newton did something different he send a light beam through a prism & he produces spectrum of colors & then he moved one more step further he then send red ray of light  to 2nd prism he found instead of having new color it remains Red. Newton concluded that White light is not pure but it is the combination of all the colors of rainbow.
Galileo has spent years studying motion on earth & he determined that projectile always follows a curved path called a parabola. But he believed motion of celestial object like moon was very different.
 Newton disagreed to this & he thought same law must be govern on earth & on the Heaven.
 He then made his 3 laws of motion.

 1) An object in motion will remain in motion forever unless acted by an external force
 2) An object's rate of acceleration is proportional to force exerted on it
 3) Every action there is equal & opposite reaction

These laws makes scientist to make accurate prediction about how object moves & they are still used today to send Rockets into Space & to explore other  world. But explaining the orbital motion of planet requires other ingredient. 
To show how gravity works on earth & heaven newton decided a thought experiments.
 lets imagine cannon ball is going to fire from top of an mountain.
--> From the first law if the cannon ball is fired then it would travel in a straight line forever but gravity pulls the ball down word.
 --> If the speed is low then cannon ball hits the earth down the mountain
 -->Higher the speed, farther  away the ball lands
 -->But if the speed is high enough then the cannon ball would travel all the way around the earth & settle down in the orbit.
 Newton then thought the moons orbit around the earth & cannon ball motion on earth are govern by same law of gravity.
 now if the gravity govern the motion on moon on earth then why not Jupiter or other planet & their moon;Why not the Entire solar System?

 In other words this invisible force (Gravity) operated every where in the Universe.
Newton called this "Universal Law of Gravitation" & it is given by single mathematical expression

F = G*(m1 * M2)/r^2
where G is the gravitational constant = 6.67 * 10 ^ -11
m1 & M2 are the masses of an object experiencing gravitational force.
r is the distance between two object



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