Category: Physics Notes PPT

Magnetic forces mediate a subset of a physical phenomenon known as magnetism. The magnetism of matter is the force exerted by magnets when they attract or repulse each other. Magnetic moments and the electric currents of basic particles give rise to a magnetic field, which acts on other magnetic and currents moments. The magnetic state of a material based on pressure, temperature, and the applied magnetic field. As these variables shift, a substance can exhibit several forms of magnetism. Magnetic properties of matter can be found in various Earth materials that act as insulators and conductors of varying degrees and shapes.

Michael Faraday is the first statistician who was discovered classifying substances according to their magnetic properties in the 19th century. The strength of a magnetic field always decreases with distance, though the required mathematical relationship between strength and distance varies. 

Magnetic dipoles have been recognized, although some theories predict the existence of magnetic monopoles.

Everyone Knows These Four Basic Facts About How Magnets Behave:

1. A magnet has two endpoints called poles, one is called a north pole or also called a north-seeking pole, and the other is called a south pole or also called a south-seeking pole.

2. The north pole of the first magnet attracts the south pole of a second magnet, while the north pole of the first magnet repels the second magnet’s pole.

3. A magnet creates a magnetic field and is an intangible sphere of magnetism all over it.

4. The north pole of a magnet is roughly towards the Earth’s north pole and vice-versa. That’s because the Earth itself involves magnetic materials and behaves like a gigantic magnet.

Source of Magnetism

Magnetism is Derived from Two Sources:

1. Electric current.

2. Spin magnetic moments of elementary particles.

The magnetic properties of matter are mainly due to the magnetic moments of their atoms orbiting electrons. The magnetic moments of the nuclei of atoms are very small than the “electrons’ magnetic” moments, so they are negligible in the condition of the magnetization of materials. 

In addition, even when the electron configuration is such that there are unpaired electrons and also non-filled subshells, it occurs frequently. In that case, the various electrons in the solid state will give the magnetic moments of that point in different, random directions so that the material will not be magnetic. Hence, the magnetic behaviour of a material is based on its structure, particularly its electron configuration, and also on the temperature. Depending on whether there is an attraction or repulsion between the north pole and south pole of a magnet, the matter is classified as being either paramagnetic or diamagnetic, respectively. 

Magnetic Properties of Matter

There are several magnetism properties of matters including Magnetization, Diamagnetism, Paramagnetism respectively.

Magnetization

In this section, we will learn about magnetization and the concept of magnetic intensity.

In electromagnetism, magnetization, also called magnetic polarization, is a vector field that contributes to the measure of the density of induced or permanent magnetic dipole moment in a given magnetic material. Magnetization is the magnetism of matter which was discovered by William Gilbert. The variation within this branch is described by direction and is either Axial or Diametric. As we know, magnetization results from magnetism, which results from the motion of electrons in the atoms or the spin of electrons in the atom or the nuclei. 

The theory of magnetization helps us in classifying the materials based on their magnetic properties. Net magnetization is the result of the response material to an external magnetic field. The magnetization of a sample material M is called the net magnetic moment for that material per unit volume. The mathematical formula of magnetization field or M-field is,

M = [frac{m_{net}}{V}]

In a magnetic field, paramagnetic materials have a weak induced magnetism, which disappears when the magnetic field is eliminated and Ferromagnetic and ferrimagnetic materials have strong magnetization. That can be magnetised to retain its magnetism in the absence of an external field, resulting in the creation of a permanent magnet.

Diamagnetism

Michael Faraday discovered diamagnetism in September 1845. This is the weak form of magnetism that is arranged in the presence of an external magnetic field. This generates a magnetic moment that is very small and in a direction opposite to that of the applied field. Diamagnetic is a magnetism of matter in which materials are opposed by a magnetic field, an applied magnetic field creates an induced magnetic field in them that is usually in the opposite direction, causing a repulsive force. In addition, paramagnetic and ferromagnetic materials are attracted by a magnetic field. 

When placed inside the strong diamagnetic and electromagnetic materials are attracted toward regions where the magnetic field is weak.  In ferromagnetic and paramagnetic material, the weak diamagnetic force is controlled by the attractive force of magnetic dipoles in the material. 

Diamagnetism was first discovered by Michael Faraday in the year of 1845. In addition, when Anton Brugmans observed in 1778 that bismuth was opposed by magnetic fields. A simple rule of thumb is used in chemistry to determine whether a particle or atom or iron is paramagnetic or diamagnetic materials. In diamagnetic material, all electrons in the atom are paired, and the substance made from this atom. A paramagnetic material has an unpaired electron.

Paramagnetism

Paramagnetism has an unpaired electron in the material, so most atoms are incompletely filled with atomic orbitals. Hence this atom is called paramagnetism. Paramagnetism is a form of magnetism whereby several materials are weakly attracted by a strong magnetic field. In addition, paramagnetism creates a magnetic field in the direction of the applied magnetic field. Paramagnetism was discovered by the British scientist Michael Faraday in 1845. The materials that are arranged in paramagnetism are called paramagnetic. Therefore, true paramagnets are arranged in magnetic susceptibility conforming to the Curie-Weiss laws and exhibit paramagnetism over a wide temperature range. 

This type of magnetization depends on Curie’s law. According to Curie’s law, paramagnetic materials, magnetic susceptibility χ are inversely proportional to their temperature. It is represented as;

M = χH = C/T x H

Where,

M = magnetization,

χ = magnetic susceptibility,

C = material-specific Curie constant,

T = absolute (Kelvin) temperature,

H = auxiliary magnetic field.

Here are some examples of paramagnetic materials, aluminium, oxygen, titanium, and iron oxide (FeO). In addition, a simple rule of thumb is used in chemistry to determine whether a particle or atom or molecule is paramagnetic or di
amagnetic. This rule depends on the paired or unpaired electron.

Consider an ideal system having n particles occupying a volume V, whose total energy is E. Here, the value of E is constant because no energy is being added or taken away from the system. So the total energy of the system is equivalent to the sum of total energies of the individual particles.

Since the system has multiple states, if we consider an ith state of the system, then, the probability at this state will be:

[P_{i} alpha E^{-frac{epsilon i}{kT}}]

Where εi is the energy of a system in ith state.

k  = Boltzmann constant (= [1.38 times 10^{-23} JK^{-1}])

T =Temperature

Now,

[P_{i} = frac{1}{z} E^{-frac{epsilon i}{kT}}]

Here z is the partition function, which is the sum of the energies of all the states in the system.

Maxwell Boltzmann Distribution Derivation

The molecules inside the system travel at varying speeds so two persons named James Maxwell and Ludwig Boltzmann came up with a theory to demonstrate how the speeds of the molecule are distributed for an ideal gas which is Maxwell-Boltzmann distribution theory.

Consider a system having n particles occupying a volume V, whose total energy is E.

So, [E = sum_{i=0}^{infty} n_{i} epsilon_{i}]

Where n is the number of particles having energy εi.

The number of particles N is also constant, i.e.,

[N = sum_{i=0}^{infty} n_{i}]

The number of microstates for the energy levels of molecules of a system can be expressed as:

[W = frac{N}{n_{0}! n_{1}! n_{2}}!] …. (1)

Stirling’s equation of eq(1) is,

ln N!. ≅ N ln N – N + 1/2 ln(2πN)…(2)

And, for large N it is:

N!. ≅ N ln N – N

Thus, in W it can be expressed as:

ln W ≅ N ln [N – sum_{i} n_{i} ln n_{i} – (N – sum_{i} n_{i})]

The term inside the parentheses is zero because, [N = sum_{i=0}^{infty} n_{i}] is a constant value.

Thus, ln W ≅ [N ln N – sum_{i} n_{i} ln  n_{i}] ..(3)

Taking differential of eq(3):

[d(ln W) = -sum_{i} (1 + ln n_{i})dn_{i} = – sum ln n_{i} d n_{i}] …(4)

Since dni = dN = 0

Now using the Lagrange multipliers here, it is known that:

[dE = 0   = sum_{i} n_{i} epsilon_{i}] , and

[dN = 0 = sum_{i} dn_{i}] …(5)

Adding (4) to (3), for any constant α and β, following should be true:

[d(ln W) = – sum_{i} ln n_{i} d n_{i} – alpha sum_{i} d n_{i} – beta sum_{i}d n_{i}]

At maximum, W = 0

0 = – Σ (α + βεi + ln ni )dni 

Or, 0 = (α + βεi + ln ni )

ln ni  = – α – βεi 

Removing the logarithmic, we get:

[n_{i} =e^{-alpha} e^{-beta epsilon i}]

Evaluating N using the distribution law here:

[e^{alpha} = frac{N}{e^{-beta epsilon i}}] and z, the partition function = [sum_{i} e^{-beta epsilon i}]

Therefore, ni  = N/Q e-βεi

Applying zeroth law of thermodynamics, we get

β = 1/kT

Maxwell Boltzmann Distribution Equation Derivation

Maxwell distribution of velocities states that the gaseous molecules inside the system travel at different velocities.

Fraction F(v) = [4 pi N(frac{m}{2 pi k T})^{3/2} v^{2} e^{-mv^{2/2kT}}]

The Maxwell distribution of velocities can be derived from Boltzmann’s equation:

[f (E) = Ae^{-kT}]

This equation tells us the probability that a molecule will be found with energy E that decreases exponentially with energy; i.e., any molecule is highly unlikely to capture much more than its average part of the total energy available to all the molecules.

()

If Maxwell-Boltzmann distribution is applied in one dimension of velocity for a molecule in an ideal gas is vz.

Where the factor F = dN/dV

This F states that if we consider a small rectangular inside the above graph, then the probability of the gas molecules traveling at velocity can be found.

Where Fraction F(v) = [4 pi N(frac{m}{2 pi k T})^{3/2} v^{2} e^{-mv^{2/2kT}}]

Maxwell Boltzmann Equation Derivation

The probability of finding a molecule at some velocity is one. Then, by using the definite integral form here from minus-infinity to plus-infinity as:

[int_{-infty}^{infty} e^{-x^{2}} dx = sqrt{pi}] and substituting [x = sqrt{frac{m}{2kTv_{z}}}]

[A sqrt{frac{m}{2kT} v_{z}} int_{-infty}^{infty} e^{-frac{m}{2 pi k T}} dx = sqrt{pi}]

[F(v_{z}) =sqrt{frac{m}{2kT}} v^{2} e^{-mvz^{2/2kT}}]     [sqrt{frac{m}{2kT}}  dv_{z} = 1]

It gives [A = sqrt{frac{m}{2kT}}]

This normalizes the function to:  [F(v_{z}) =sqrt{frac{m}{2kT}} v^{2} e^{-mvz^{2/2kT}}]

In terms of three dimensions, it becomes:

[F(v) =4 pi (frac{m}{2kT})^{3/2} v^{2} e^{-mvz^{2/2kT}}]

Maxwell Boltzmann Derivation

Consider the fraction of molecules in a three-dimensional box having the translation energy ε, then, as a function, it will be:

ε  = h² / 8m [nx2 + ny2+ nz2]/[Lx2 + Ly2 + Lz2]

ni2   = nx2 + ny2+ nz2  ,and

 εi  = n²h²/8mL²

The length of each side of the box is equal.

So, we would consider the density of translational states as a sphere in space.

So the total volume of the sphere is:

[epsilon = frac{4 pi}{8} int_{0}^{n} n^{2} dn]

and  dε = π/2 n² dn

Also n²h²/8mL² = ½ mu², and

dn  = 2mV1/3/hdu

So,  π/2 n² dn = dNi/N = dε/Q [e^{-beta epsilon i}] 

Substituting in for thermal wavelength, we
get:

[frac{1}{N} frac{du}{dN} = 4 pi u^{2} (m/2 pi k T)^{3/2} e^{-mu^{2/2kT}}]

This is the Maxwell-Boltzmann distribution.

We know that we have many elementary particles available in nature. Elementary particles are those particles that can not be created by other particles. All the elementary particles are classified into two types, Fermions and Bosons. Fermions are the odd half integral spin particle with antisymmetric wavefunctions. Whereas the bosons are the integral spin particles with symmetric wavefunctions. All the elementary particles are classified according to their spin, charge and characteristic behaviours. And they are mainly classified as leptons, mesons and baryons.

Mesons are one of the elementary particles classified under baryons and these are considered to be the heaviest particles and the mesons do not include protons in their decay product. In this article, we will go through a detailed explanation of mesons, meson meaning and what is a meson.

Meson Meaning

Now, let us understand the meaning of Meson. Basically, a meson is a hadronic particle, which means it is having considerable mass. We can define a meson as a fundamental particle that will never decay into a proton or any particles that could subsequently decay into a proton. That means we can say that the mesons will always have comparatively less mass than the protons. Thus, a meson possesses an intermediate mass between the electron and the proton.

The mesons are the fundamental particles or the elementary particles carrying unit charge and possessing mass intermediate between the mass of the electron (m_e) and the mass of the proton (m_p).The name meson was proposed by famous nuclear physicist Yukawa in 1935.  The mesons are the hadronic subatomic particles composed of a combination of quark and an antiquark. 

What is a Meson?

But, what is a meson? Meson is a fundamental particle categorized under the hadrons. Mesons are the hadronic particles made up of a quark and an antiquark, specifically a meson its own antiparticle. Mesons are the interaction agents between nucleons (protons and electrons). The rest mass of the mesons lies between 250-100mₑ .

The most common type of mesons are the pions (pi mesons), kaons (K mesons) and the eta meson (η-meson).These are also the only types of meson that are long-lived enough to be seen directly by their tracks in a detector.

Pions or The Pi Meson

• The pi meson is the lightest type of meson. And they are commonly called the pions.

• Pi mesons are composed of up quarks or down quarks and their antiquark counterparts. 

• Pions are of charge +1, -1, and 0 are denoted π⁺(+e charge), π^–(-e charge), and π⁰(neutral charge), respectively. 

• The π0 (mass 135 MeV) is composed of either an up or anti up quark pair or a down/anti down quark pair the π+ is an up/anti down pair, and the π– is a down/anti up pair (both have a mass of 140 MeV). All have zero spins.

• Pi mesons or the pions were predicted theoretically by Hideki Yukawa in the year 1935, and discovered in cosmic ray experiments on the Pic du Midi by researchers from the Bristol University, England, headed by Cecil Powell, in 1947. They are produced copiously in high-energy particle collisions.

Kaons or K Mesons

• A kaon or k meson is a meson that contains one ordinary quark, either an up quark or a down quark and one strange quark. 

• The K mesons were first discovered in 1947. The k mesons are abbreviated as kaon or the k meson came into use in about 1958. 

• The k mesons or Kaons come in two varieties: positively charged(K⁺) and neutral (K⁰)and their antiparticles K^– and [bar{K^{0}}] .

• They are spin 0 particles, the weight of kaons is about half as much as nucleons, and decay by means of weak interactions. 

• The charge parity violation was first observed in the k mesons.

Meson Octet

We know that there are a total of eight mesons available in nature and these are arranged in an octet for easier understanding and determination of the charge, strangeness and the spin and it is known as the meson octet structure. Such that along the x-axis we will have isospin of the particles and along the y-axis strangeness. The meson octet is as shown in the below figure. 

Did You Know?

• Some scientists say that the electron is not an elementary particle (also known as the fundamental particle) and is actually made up of two smaller particles. 

• Particles made up of the composition of quarks are called hadrons. A bunch of gluons bound together is called a glueball. A tachyon is a hypothetical particle that travels faster than the speed of light. 

• Quarks and gluons are said to have a coloured charge as well as an electric charge. A proton is made from a composition of blue up quark, a red up quark, and a green down quark

Modern Physics is a branch of physics that deals with the fundamental nature of the universe with post-Newtonian concepts. In the early twentieth century, some experimental results could not be matched with the predictions of classical physics, which describes physical phenomena at an ordinary scale. Modern physics gradually took birth from these theories. The two pillars of modern physics are quantum theory and the theory of relativity. Quantum theory explains the physical phenomena at a short scale whereas the theory of relativity describes large-scale physics and gravity. The results of classical theory can be approximated from both theories.

Father of Physics

Physics is the study of all-natural phenomena from both theoretical and experimental view points. The developments of the subject have been made by numerous scientists. Considering the most important contributions, the title “Father of Physics” is given to three scientists at different times. 

Galileo Galilei is called the Father of Observational Physics for his contributions to Astrophysics. 

Sir Issac Newton gave the laws of motion and gravitation. Classical physics is based on his theory, which works fine on an ordinary scale. He also gave the theory of calculus in mathematics. For their remarkable contributions, Newton is known as the Father of Physics.

Albert Einstein is considered the Father of Modern Physics. He gave the special theory of relativity and the general theory of relativity. These theories govern the behaviour of objects at high speeds (close to the speed of light) and gravity. He was awarded the Nobel prize for the explanation of the photoelectric effect. 

The Advent of Quantum Theory

Classical physics failed to explain the experimental results of black body radiation, photoelectric effect, and the phenomena of interference of electrons, the stability of an atom. Classical physics considers waves and particles as different notions. In 1900, Max Planck hypothesized that light consists of packets or quanta of energy, called photons. Each photon has energy

E = hv

Here, v is the frequency of light and h is Planck’s constant. 

Although it contradicts the classical theory that considers light as an electromagnetic wave, the black body radiation phenomenon could be described by this hypothesis. Later in 1905, Einstein successfully explained the photoelectric effect, considering light as a swarm of photons (quanta of energy). 

On the other hand, the interference of electrons and the stability of an atom could only be described if electrons were considered as waves. De Broglie hypothesized that every particle behaves as a wave, having wavelength:

[lambda] = [frac{h}{p}]

Here, p is its momentum. Everyday objects have very short wavelengths, such that classical theory works at an ordinary scale but the wavelengths of subatomic particles like electrons are comparable with their dimensions. 

To describe physics at small scales (e.g. atomic scale), quantum theory was found to be necessary. In this theory, energy, angular momentum, and other quantities of a bound system are quantized. Many physicists including Bohr, Heisenberg, Schrödinger, Pauli, and Dirac formulated the theory from a mathematical point of view. In the late twentieth century, Quantum Field Theory emerged through the works of scientists like Jordan, Hawking, Weinberg, Feynman.

Origin of the Theory of Relativity

Einstein realized that space and time are not different concepts. Any observation depends on a frame of reference, so that space and time are relative. Newtonian physics considers time as a constant that does not depend on the observer. The classical theory failed to explain Mercury’s precision and time difference of satellites. The theory of relativity could explain these phenomena. Einstein introduced the idea of “spacetime”. A massive object can wrap the fabric of spacetime and gravity is its consequence. Einstein also realized that mass and energy are equivalent concepts. The equivalent energy E corresponding to a mass m is,

()

Here, c denotes the speed of light in a vacuum. 

Black Body Radiation

Black-body radiation is the thermal electromagnetic radiation released by a black body when it is in thermodynamic equilibrium with its surroundings (an idealised opaque, non-reflective body). It has a defined spectrum of wavelengths that are inversely linked to intensity and are only dependent on the body’s temperature, which is considered to be uniform and constant for the sake of calculations and theory.

Many everyday items spontaneously release thermal radiation that can be approximated as black-body radiation. Internally, a fully insulated container in thermal equilibrium includes black-body radiation, which it will release through a hole in its wall if the opening is small enough to not influence the equilibrium.

Solid State Physics

Quantum mechanics, crystallography, electromagnetism, and metallurgy are all used in solid-state physics to explore rigid matter or solids. It is the most important subdiscipline in condensed matter physics. Solid-state physics investigates how solid materials’ large-scale characteristics are derived from their atomic-scale properties. Solid-state physics is thus the theoretical foundation of materials science. It also has direct uses, such as in transistor and semiconductor technologies.

The majority of solid-state physics is centred on crystals as a generic theory. This is mostly because the periodicity of atoms in a crystal — its distinguishing feature — makes mathematical modelling easier. Similarly, crystalline materials frequently possess electrical, magnetic, optical, or mechanical characteristics that can be used in engineering applications.

Atomic Theory

The scientific hypothesis that matter is made up of tiny bits called atoms is known as atomic theory. The origins of atomic theory may be traced back to an ancient intellectual tradition known as atomism. According to this theory, if you cut a lump of stuff into smaller and smaller bits, you would ultimately reach a point where the parts can no longer be sliced into smaller pieces. These hypothesised fundamental elements of substance were given the name ‘atomos’ by ancient Greek philosophers, which meant “uncut.”

John Dalton

John Dalton researched and expanded on this previous work, defending a new idea later known as the law of multiple proportions: if the same two elements can be combined to form several different compounds, the ratios of the two elements’ masses in their various compounds will be represented by small whole numbers. This was a prevalent pattern noted by Dalton and other scientists at the time in chemical processes.

Avogadro

Amedeo Avogadro addressed the weakness in Dalton’s theory in principle in 1811. Equal volumes of any two gases, under equal temperature and pressure, contain equal numbers of molecules, according to Avogadro (in other words, the mass of a gas’s particles has no bearing on the volume it occupies). By observing the volumes at which gases interacted, Avogadro’s law allowed him to derive the diatomic nature of many gases. For example, when two litres
of hydrogen react with one litre of oxygen to make two litres of water vapour (at constant pressure and temperature), a single oxygen molecule splits in half to produce two water particles. As a result, Avogadro was able to provide more precise estimations of the atomic mass of oxygen and other elements, as well as distinguish between molecules and atoms.

Brownian Motion

Robert Brown, a British botanist, noticed that dust particles inside pollen grains floating in water jiggled around for no apparent cause in 1827. Albert Einstein proposed in 1905 that the Brownian motion was created by water molecules constantly pushing the grains around, and he constructed a hypothetical mathematical model to explain it. In 1908, French physicist Jean Perrin confirmed this model experimentally, offering more support for particle theory (and by extension atomic theory).

Concepts of Modern Physics

The key concepts of quantum theory are,

• Wave-Particle Duality: Light behaves as both wave and particle. Light consists of photons or quanta of energy. Particles have a wave nature. Particles are delocalized in space

• Uncertainty Principle: It is not possible to measure the precise position and momentum of a particle simultaneously.

• Measurement Problem: Performing a measurement or observing a system changes its state.

The Concepts of Relativity are:

• No massive object can have a speed greater than that of light. The laws of physics always remain invariant for all observers.

• Mass causes curvature in spacetime.

• When an object approaches the speed of light, its length reduces (length contraction). A moving clock slows down (time dilation).

• The sequence of events or the cause-effect structure (causality) remains preserved.

• Gravitational and inertial masses are equivalent.

Did You Know?

• Gravity can bend light. It causes gravitational lensing, which is the phenomenon of bending of light near a massive object.

• Time slows down near a massive object. 

• Gravitational attraction is the consequence of the bending of spacetime.

• An accelerating mass can create ripples in spacetime, which is referred to as gravitational waves. In 1915, gravitational waves were detected.

• Classical physics can be retrieved from modern physics by taking appropriate limits.

• Interference of electrons, photoelectric effect, hydrogen spectrum, blackbody radiation are verifications of quantum physics.

• Anomalies in the orbits of planets, time gaps in satellites, gravitational waves match the predictions of relativity.

• There are four fundamental forces in nature namely gravitational force, electromagnetic force, strong and weak forces. The last three forces are described by the Standard model.

• Scientists are trying to incorporate quantum theory and the theory of relativity through the conception of a more general theory, often referred to as the “theory of everything”.

Conclusion

Modern physics deals with the fundamental nature of the universe with post-Newtonian concepts. Two pillars of modern physics are quantum theory and the theory of relativity. The title “Father of Physics” is given to three scientists at different times for their contributions to Astrophysics.

Motion of Celestial Bodies

The motion of celestial bodies such as the moon, the earth, other planets have been a subject of significant interest for a long time.

A famous Indian astronomer and mathematician, Aryabhata did the in-depth study of these motions.

After that, he proposed a theory of the elliptical path of planets where he stated that all the planets remain stable, and as they come closer to the sun because of attraction, their speed increases proportionately.

He also gave a conclusion in his book Aryabhatiya that the earth revolves around its axis and moves in a circular orbit about the sun and that the moon moves in a circular orbit around the earth.

Movement of Celestial Bodies

A thousand years after Aryabhata, the brilliant combination of Tycho Brahe and Johannes Kepler studied planetary motion in significant detail.

Kepler formulated his important findings in his three laws of planetary motion. They are:

1. First Law: It states that all planets make an elliptical locus with the sun at a focus.

2. Second Law: The radius vector, r from the sun to the planet traces equal area in equal intervals of time.

3. Third Law: This law is also called the law of ellipses. This states that the square of the time period, T of the revolution of a planet is proportional to the cube power of the semi-major axis,r of the ellipse.

T ∝ r³

In the year 1665, an English mathematician, physicist, astronomer, and theologian named Isaac Newton studied the motion of the moon about the earth.

He stated that the laws of nature are the same for earthly and heavenly bodies.

This means all the objects in the universe fall freely under the influence of gravity such that the force acts towards the center of the earth.

The acceleration of a body falling near the earth’s surface = 9.8 ms^-2.

He formulated an equation to showcase the force between the earth and the body, i.e.,

     F =GmM/r²..(1)

G = Universal gravitational constant whose value = 6.673 x 10-11Nm²/kg²

m =  mass of the smaller body, and

M = Mass of a larger body, separated by the square of the distance ‘r.’

Newton further generalized the law by saying that not only the earth but all material bodies in the universe attract each other according to equation (1) with the same value of G.

Motion of Celestial Bodies in the Solar System

All planets orbit in a counterclockwise direction. The inner planets orbit swiftly than the outer planets.

They all move in a path that obeys the laws of motion and the force that controls their motion is the gravity.

The earth is the third planet away from the sun, which takes 365 days to complete one orbit.

Motion of Celestial Bodies in Space  

All the heavenly bodies like planets and satellites move in an elliptical orbit due to the attractive force of gravity, their centrifugal motion is balanced by the gravitational attraction.

The elliptical orbit is the elongated or skewed circle.

Instead of having a single center like a circle, ellipses have two centers called foci.

f1  and f2 (in Fig.1 (a)).

[Fig 1 & Fig 2- Image to be added Soon]

For planets in space, the center of the sun is always at the focus as shown in Fig.2.

So the larger is the distance between the two foci, the more elongated the ellipse is.

The amount of elongation of the orbit is given by the eccentricity of the orbit.

A planet like the earth has a low eccentricity where both the foci lie within the sun itself. So, we can say that Earth’s orbit is almost circular.

[Fig 2-Image to be added Soon]

Motion of Celestial Objects in Space

Let’s understand the planetary motion by understanding Kepler’s laws.

Where Kepler’s first law states that planets revolve around the sun in elliptical shape with the center of the sun being at one focus as you can in Fig.1 (b). This law is also called the Law of ellipses.

The second law states that an unreal line drawn from the center of a star to the center of a planet traces equal areas in equal time intervals.

This law is also called the law of equal areas.

Third law: It states that the ratio of the squares of the periods of revolution of any two planets is equivalent to the cubes of their mean distances from the sun.

[Image to be added Soon]

This is the law of Harmony’s for each point on an ellipse, the sum of the distances from each focus is a constant equal to the time the major-axis length.

In most planetary systems, the eccentricity is low enough that we can approximate the average distance between the star and the planet which is the major axial length of the orbit.

The neutrino can be defined as an elementary subatomic particle with no charge and 1/2 unit spin. These fermions then react because of weak interaction and gravity. The rest mass of a Neutrino is almost negligible hence considered to be zero. The rest mass of a neutrino is comparatively very small than the elementary particles. Wolfgang Pauli discovered Neutrino in 1930, and the name was popularized in Science by the Italian Physicist Enrico Fermi. In Italians, The Neutrinos means “the little neutral ones” are electrically neutral particles, and their size is smaller than that of Neutrons. 

Properties and Types of Neutrino

Some of the most prominent properties of Neutrino are:

• These Neutrinos belong to the family of leptons, this particle family has weak interactive forces. 

• The Neutrino is of three basic kinds depending upon the charged lepton that they are associated with. These charged leptons are the electron, the muon, and the tau respectively. These associated electrons are named electron-neutrino, muon-neutrino, and tau-neutrino. 

• A neutrino also has an antimatter component that is known as an antineutrino. The Neutrino and antineutrino together comprise a hot area of research in modern physics with many scientists and experts working in this field.

• Neutrinos are not affected by the electromagnetic forces and hence, do not cause the ionization of matter. 

• These Neutrinos react with matter only through extremely weak interactive forces.

• They are also capable of passing through an enormous number of atoms without causing any reaction and hence these are the most penetrating subatomic particles.

• The Neutrinos can also change a nucleus into another and this process is used in a radiochemical neutrino detector.

Neutrinos are found in various types in space. These types are:

As mentioned earlier, neutrinos are of three types or flavours and each of them has its respective properties. The first discovered neutrino is the electron-neutrino. Electron-neutrino has no electric charge and mass. It was discovered by Wolfgang Pauli to satisfy the energy loss in the process of radioactive beta decay. This particle is emitted along with a positron in positive beta decay. For negative beta decay, an electron with its antimatter particle that is an antineutrino is emitted.

Post the discovery of the second charge lepton, the muon, eventual identification of the second type of neutrino, the muon-neutrino started. Based on the results of a particle-accelerator experiment, high energy muon-neutrinos were discovered in 1962. They were produced from the decay of pi-meson. Though usually unreactive like other neutrinos, sometimes muon-neutrino reacts with protons and neutrons to produce muons.

In 2000, physicists experimentally showed the first evidence of the existence of the tau-neutrino. It was after the discovery of the tau leptons.

There are many active research areas involving neutrinos. Neutrino properties, testing predictions of their behaviour, and masses and rates of CP violation which is still unpredicted from the current theories. These subatomic particles are indispensable for the validation of the law of conservation of energy. They are related to radioactivity and play a very important role in nuclear physics. Knowledge of neutrinos and their properties enable physicists to understand the dynamics of several nuclear reactions.