WHY MOON IS MAGNIFIED IN HORIZON

            Not only moon every astronomical object shows magnification on horizon. In fact the objects in horizon is far than zenith, then how? Actually it explained as an optical illusion, nearer horizon we compare the object with our terrestrial objects so we realized that which become big. But i didn't satisfy with this answer, because the absence of terrestrial objects it shows its magnification , So i try to find my own answer.
                         Our atmosphere is just like Plano convex lens and also our eye has a convex lens, due to the combination of these two lens we get an natural telescope and it magnifies in order of   (fo/fe)  where "fo" is the focal length of Plano convex lens, "fe" is the focal length of eye lens. In horizon refractive index of Plano convex lens is increases which enhance the focal length and hence magnification occur. Don't be think that the increase in contrast of moon in horizon due to this lens combination, it is happens due to the long distance which scatter the majority of light rays from the moon so we get a good big moon.
       " I have no evidence to prove that this so not to believe me."  

HOW ELECTROMAGNETIC INDUCTION

         Faraday's law states that change in magnetic flux produce an induced emf on the conductor, this emf is proportional to rate of change in magnetic flux. In physics it is enough to study electromagnetic induction, but how the flux change produce an induced emf . This was solved by Lorentz force , F = q[ E + v X B] where v is the velocity of charge 'q' in magnetic field 'B', why the two forces are just added without any vector consideration, this is tells that the magnetic field or electric field doesn't mutually affects. That is magnetic field only link with other magnetic field. 

           Consider a magnetic field and a conductor which cut the flux perpendicularly( yes, of course we can't cut by parallel plane) the relative motion of conductor and hence the free electrons in conductor influenced by the magnetic force q(v X B) this force generate a potential difference called induced emf. Note that the kinetic energy of the conductor 1/2 mv^2 is converted to the electric potential energy. This is why the work done by magnetic field is zero.
     Wait, then how magnetic substance attracts nails against gravitational energy, this will explained by my next post.

SPIN AND SPINNING

                               What is the shape of electron? sphere,cube, or any other geometrical shape. It is not correct question because we cannot accept only a particle due to dual nature. Spinning motion only does particle not wave, yes of course it is spinning that gives spectral evidence so we must conclude that in atom electron behave as particle. Wait the standing wave nature explain the stability of electron so we tells that for orbit motion electron is wave but for spinning it is particle. Totally confusing to avoid this problem there is a great solution just forget this thing, that means it doesn't revolve and doesn't spinning. But we must care the experiment result for spinning. This was given by Stern Gerlac experiment but it is gives a quantised result that means spinning has only has discrete possible values this is called Spin.
            Positive or negative half spin means the spinning electron only posses two states for example assume that electron is like below shape and after quantised spin it become the second shape, but remember that electron only posses these two states or it is not a continuous rotation. You can't accommodate but it is true, so it is not a ordinary spinning something special, to resolve this confusion don't be picturised. In physics we first want reason, picturisation is second.

     So spin is a property of elementary particles like charge, it has no relation with ordinary spinning. And macroscopic objects doesn't shows this property.

SCALAR & VECTOR

Most of our physical quantities are linearly depends its variables. I not sure to explain what is mean by linear dependence, suppose we have a physical quantity R is the function of variables x, y and z if they linearly depends R can be written as,

                            R = c₁x + c₂y + c₃z  where c₁, c₃, and c₄ are constants or values. The sign “+” is not only ordinary addition also a symbol of linear operator; avoiding this confusion R can be written as the matrix form

.R = [c₁  c₂  c₃]   [x

                              y

                              z]                         

                                                                                                                                                                 In physics most of the quantities can be written as the linear combination of other physical quantities either fundamental or non fundamental quantities. But in our undergraduate levels, we deals with majority the linear combination of constants or direction or both, these are respectively called scalar and vector.

Vector is the quantity has both magnitude and direction this is we learned, but please tells like that, vector which is the quantity gives the direction, for example velocity of water gives the direction of water flows. Not, velocity of fluid is in the direction of motion. And don’t distinguish scalar and vector in the scale of magnitude and direction. They are differs in the order of writing the linear combination, scalar is zero order matrix that is no specific indication, vector is the first order matrix that is only one indices is needed. Let a_i is the vector and ‘i’ is the indices it has values, i = 1,2,3,…….etc.. Due to the single indices vector is either row only or column only matrix. A_ij  is not a vector because it has two indices ‘i’ and ‘j’.

From above discussion you ask that what is the significance of indices, this is why the mathematics and physics differ. The  scalar and vector are the mathematical concepts, but the indices gives the physical significance, here indices in vector gives the space coordinates we know that each coordinates in a coordinate system is independent so only one value is possible In each coordinate, this why the vector has only one indices.Fundamental levels we can discuss higher order (more than one indice) matrix or tensors. 

GRAVITATIONAL MOTION OF TWO BODIES

                Here I shows the advance of theoretical calculation over experimental calculation using a simple event.
All you know the experiment of Galileo, to show that all bodies of different masses will fall simultaneously without depends the mass.
          But it doesn't true the heavier mass reach at ground first. This argument cannot prove using experiment.
Consider two  bodies of mass M & m separated withe distance of 'd'. According to the Newton's gravitational law two bodies approaching to their center of mass of system.

The acceleration of mass M,                                              

             g₁ = (1/M) [G (Mm)/r²];

The acceleration of mass m,

             g₂ =- (1/m) [G (Mm)/r²];

the resultant acceleration is g = g₁-g₂ = {(1/m)+(1/M)} [G (mM)/r²]
                                         g = [G (m+M)/r²]

From the above equation you can find the gravitational acceleration depends the masses of the body.
consider two masses m, m'. If the mass of earth is M then,
                                        g = [G (m+M)/r²];
                                  g’  = [G (m’+M)/r²) 

 ^{if  m'> m then g'>g, ie. m' attain faster than m.}

^{This give that acceleration of two bodies depends their mass.} 

^{Then how we can say Galileo's experiment is true.}

                                  

DERIVATION OF STOKE’S EQUATION IN VISCOUS FLUID

I mean that the equation is,

F = 6πƞrv; where, ƞ is the coefficient of viscosity, r is the radius of sphere which flows through the fluid, v is the terminal velocity and F is the force acted on the fluid for the viscous drag.

I am sorry to convey that I couldn’t find the proper derivation of Stoke’s equation. But here I wish to say about the magical power of our mind, for past one month I searched for the derivation of Stoke’s equation, but I couldn’t find it anywhere at last I could derive it by myself. But it is not correct

fBut it helps you to find the proper derivation.

We have the Newton’s equation for viscosity,

F = ƞA (dv/dx) --------------------------- (1)

‘A’ is the area of fluid displaced and (dv/dx) velocity gradient or it is written as   “div v” here (dv/dr), since the quantities varies radial.

In this figure we can see that only half of the sphere is push the fluid, therefore A = 2πr² because, this figure 1 misunderstands you actually the fluid motion is considering from bottom to half of the sphere, but go on half to top the flow will be turbulent due to downward motion of sphere, so we cannot use Newton’s equation on the another half face.

                                                                                        

We have the equation for continuity

(dβ/dt) + V (grad β) + β (div v) = 0; OR

(dβ/dt) + v(dβ/dr) + β(dv/dr) = 0;

Where β is the density of fluid, here β is independent of time because fluid undergoes terminal velocity that is no force for  compressing the liquid. Therefore the equation be

(dv/dr) = - {v/β}(dβ/dr)

Therefore equation (1) becomes

F = -ƞ2πr²{v/β}(dβ/dr)-----------------------------------------(2)

Let ‘M’ be the mass flows out by the sphere, And using Archimedes principle, the volume displaced  is equal to the volume of sphere , So β = (3M/4πr³)

And    (dβ/dr) = -(9M/4πr⁴)

These two equations are substitute in equation (2) we get the Stoke’s equation

I.e.  F = 6πƞrv

This is my derivation, you can discuss about this derivation with me. 

GRAVITY ON STARS

         In this section I write a quiet interesting thing, that doesn't related to star formation. You know that gravity is the weakest force than other three fundamental force, but it is the great important and strong in the universe. I think gravity is the only force an important role in star formation, from the nebulae not form a single star, it forms a group of stars. But the distance between the stars are gradually increases. Why didn't they far away from each other there is only force is exist that is gravity(by strong), but gravity has attractive nature then why this happen, which force does this work.
          Actually i don't know why it is happen, because i am primitive in classical mechanics. But i think that the force behind this mystery is gravity. Yes it has a face of repulsion, don't mistaken it has not, but it is the responsible for this expansion. Are you heard about the the great "Three body problem", from its solution, it says that in three mutually gravitationally interacting body if it has total positive energy then all three masses can move away from each other, or can escape.Here there is many of bodies therefore the total energy is always positive that will cause to this expansion. Sorry i couldn't have any mathematical expression, of course i don't know the solution of three body problem the above idea is taken from "Classical Mechanics by H.Goldestein", but i believe that this is the reason. If you can solve the many body problem.