8.5 Cosmic Engine

8.5 Cosmic Engine

Kevin Huynh

By: Kevin Huynh

Class: Saturday Physics

Time: 2:45 – 4:30 p.m.

Teacher: Ryan Phung

1. Our Sun is just one star in the galaxy and ours is just one galaxy in the

Universe

Kevin Huynh

1.1.1 Outline the historical development of models of the Universe from the time of Aristotle to the time of Newton

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Historical development of the Universe To understand the workings of the universe begins with the ancient Greeks. Then came a time of the “Dark

Ages” (4th – 13th century) not much scientific nature happened because of the powerful influence of religion. However, in the 14th century the Europeans brought back the interest and chose to be inspired by the finding of the Greeks. Unfortunately, they were found to be impressed by the ancients who had it wrong. Through time, the argument between the heliocentric and geocentric slowly came to an end as technology became more advanced through time.

Aristotle (Greek Philosopher) (330BC) Geocentric model Used logical cause-effect approach to explain

physical events, which led to the proposal of the stationary Earth surrounded by spheres revolving around at different speeds

The heavenly system consisted of a spherical Earth, fixed into the center of the universe, surrounded by 55 co-centric transparent spheres where each sphere carried a heavenly body (moons). In its simplest version, there were only 8 such spheres corresponding to the Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn.

Co-centric – share the same point i.e. the center of the circle.

Why transparent?The spheres were transparent solely on Aristotle’s reasoning that it allowed things further away to be seen

Some of the flaws caused by this model is the ability to explain the variations of brightness in accordance to the inner planets.

The inner spheres contained moons The outermost spheres contained stars Aristotle’s work remained unquestioned for nearly another 2000 years.

Aristarchus (240BC) Heliocentric model Aristarchus explains that the stars are actually motionless and that the earth rotates on its axis once daily,

which correlates to the motions observed in the sky. Annual changes were due to the Earth, with other planets, orbiting the sun. Aristarchus was only able to make this assumption when he measured the size of the sun and found it was

larger than Earth. BUT, Aristarchus’s work was not recognized by society due to strong influential views of the church.

Reasons for rejecting the heliocentric model: (mostly accounted for lack of technology)

Kevin Huynh1. There was no observable parallax of the sun and stars if the Earth was actually moving. This was because

the vast distance in space could not be seen with the naked eye and so this theory failed (ironically its correct though)

What is a parallax? It is the difference in apparent position of an object due to viewing it at different angles. A way to think about this is when we are on a trip. When we look outside the window while travelling, we

can look to the ground and it seems that it is moving relatively fast. BUT, as we look further away such as the houses (that are further away) it seems as though it is moving slowly.

With the same application, since the stars are too far away, the parallax shift is not recognisable with the human eye.

2. A moving Earth was religiously unacceptable because the strong influence of the church believed that people lived on Earth and hence must be the centre of the universe.

3. It also used a bit of common sense. If the Earth was to move, then wouldn’t everything get swept away and rushed through SPACE? No, the Earth appeared to be stationary.

Ptolemy (120AD) Geocentric model (Greek-influenced Egypt) Ptolemy’s model was based more on the “reference of frame” which suited him. In this case, since the stars

are far away, the positions in the sky relative to one another was not observable. The motion of the sun, moon and each of the other planets were

explained by a combination of perfect circular paths. The stars were located in the outermost sphere where it rotated

around the earth once a day (24 hours)- Ptolemy observed the typical retrograde motion of Mars in the

sky. It accounted for the fact that Earth was between the Sun and Mars because it was the only possible position of observe this motion.

Ptolemy then came up with some ideas.- The distance between the Earth and deferent is called the eccentric. (Earth was not exactly in the middle)- The epicycle: Planets rotated in smaller circles along the deferent. - The deferent is the path of which planets rotated around the Earth. - The equant was an imaginary mathematical point that explained the observed speed changes. It “sees”

the planet move at a uniform angular speed. It is actually not located in the center of the orbit, which causes the variations in speed.

Ptolemy’s work remained unchallenged for the next 14 centuries.

Figure 3: The equant. The planet (P) revolves around the center of the circle (C) but moves uniformly around the center of motion (M). The planet goes through each section of the circle in an equal amount of time so it would speed up as it gets farther from M.

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Copernicus (1473-1543) Heliocentric Proposed that the Sun was stationary at the centre of the universe and that everything revolved in circles By using what Ptolemy had found, he continued to use the epicycles and eccentrics to help further improve

his model. The main idea of Copernicus’s model was:

- The lack of parallax shift was due to the immense size of the universe. - Earth orbited the sun once every year and its axis every 24 hours. - The sun is the centre of the heavens and the planets moved around in circular orbits. - This model also easily explained the variations in brightness.

Tycho Brahe (1546 – 1601) Developed a precise astrolabe to help identify the position of those stars within 1/60th of a degree Proposed a compromised model consisting of the geocentric model and heliocentric model In Brahe’s model:

- The sun orbiting the stationary Earth- Other planets orbited the Sun.

Tycho Brahe was best remembered for the painstaking work in obtaining data with great accuracy. His data on Mars plays a large contribution towards future discoveries and theories.

Tycho’s student Johannes Kepler continued his work including his complete set on Mars.

Galileo (1564 – 1642) Heliocentric model Highly supported the Copernicus model Galileo developed the telescope to aid his observations. Only then he noticed:

- The phases of Venus were much similar to the moon. - The phase of the moon (full, new and crescent) is caused when it illuminates at different angles to Earth.

Thus, Galileo realized that Venus was actually orbiting the Sun. This model was consistent with Copernicus and not Ptolemy.

- Galileo viewed Jupiter only then discover there were four satellites (or moons) orbiting Jupiter. What he saw was a mini Copernican model.

- Galileo studied the surface of the moon. He observed rough features such as the mountainous tops.

Kevin Huynh- Similarly, while observing the sun he found sunspots on the surface. Moreover, these sunspots were

found to move in such a way that Galileo suggested the sun rotated once every 27days. - The traditional views of heavenly bodies were scrapped.

Johannes Kepler (1571-1630) Convinced with the rightness of the heliocentric model Study the motion of Mars and found out that planets orbit in ellipses

Kepler’s Laws:1. Law of ellipses – Each planet moves in an ellipse with the Sun at one focus.

A quantity called “e” (for eccentricity) indicates the degree of elongation of the orbit. E.g. A round path that has a value of e=0 is a circle and for e→1 has an elliptical shape.

The focus describes the circular shape in this case. In a ellipse, there are two foci’s and one in a circle (i.e. the center)

Comets and most asteroids have highly elongated orbits close to e=1 and others travel so fast that it moves in a parabolic path and won’t return.

Most planets have near-circular orbits, with ' e ' close to zero.

2. Law of area – The line drawn from the Sun to the planet sweeps out area at a constant rate Kepler explained further and realised that the sun must have been one of the foci’s and the other as

unoccupied. The planets do not move at a uniform angular rate about any point. Generally, the closer the planets are to

the Sun, the faster they are travelling. Increasing the length of the radius allows angle swept through to decrease and hence the arc length

decreases while the area remains the same.

It can be represented by the formula:

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Radius∝ 1distance travelled

3. Law of periods – The square period (T) of the planets is proportional to the cube of their average distance (Ravg) from the Sun. The law can be mathematically represented by the formula:

T2

Ravg3 =k

where :T=Period of orbit R=Average Radius¿ the planet ¿ the sunk=constant All planets revolving around the sun have the same value k. (Note: This formula works for any system of the

same object in the centre) Instead of using standard metric units such as meters and seconds we can use astronomical units.

- 1AU¿1.5×1011m(the average distance of earth to the sun)Example:Halley ’s Comet has an orbital period of 76 years. Calculate the average distance of the comet from the Sun.

T 2

R3=kR3= (762 )R=3√762¿17.9 AU

Errors in Kepler’s model: Kepler realised that forces were involved. When the planets neared the sun, it began to speed up so Kepler

suggested that there was a tangential force pushing the planets along. The closer to the Sun, the larger the magnitude of this force BUT, force is not required to keep an object in motion in space since there is negligible resistance. It was only

then that Newton was able to explain the cause.

Isaac Newton (1642 – 1727) Supported the heliocentric model The heliocentric model had become more acceptable but it needed an explanation to what kept the planets in

orbit. After pondering, Newton recognized the earthly force that attracted objects to fall on the ground was a force

that applied between all objects in the universe. He called it Universal gravitation.

There are two distinct steps in Newton’s argument. Newton argued, from Kepler’s law of areas, that the force must be central that is acting towards the Sun. Using Kepler’s law of Periods, he showed that the force is inversely proportional to distance squared and

force is also proportional to the masses of the objects.

F=Gm1m2r2

where :F=Gravatational force (N )G=6.67×10−11N .m2k g−2 (gravatational constant )

m1m2=massesof object (kg )r=centre¿ centredistance (m )ExampleCalculate the force due to gravity between yourself and the person next to you.

1.2.1 Assess one of the models of the Universe developed from the time of Aristotle to the time of Newton to identify limitations placed on the development of the model by the technology

available at the time

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r=0.48mm1=73kgm2=72kgG=6.67×10−11

F=(Gm1m2

r2 )¿1.52×10−6 N

An ideal answer should include: Early models were limited by technology available at the time to aid observations. Scientists were very reliant

on logic. A reference to the geocentric model in the earlier days (there was not much evidence to argue this model

especially because of observing equipment) Talks about the parallax shift – If the heliocentric model were correct, then through logic, would not the stars

(such as the sun) have appeared to be moving. Due to the lack of the observable parallax shift, the geocentric model was in favor only because of the vast distances that affect the parallax shift which cannot be observed by the naked eye.

With no sense of the astronomical distances in space, only with the technology of a large telescope could prove the long believed geocentric model.

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2. The first minutes of the Universe released energy which changed to matter, forming stars and galaxies

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2.1.1 Outline the discovery of the expansion of the Universe by Hubble, following its earlier prediction by Friedmann

2.1.1 Outline the discovery of the expansion of the Universe by Hubble, following its earlier prediction by Friedmann

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Albert Einstein In 1905, Albert Einstein proposed the Special Theory of Relativity, which stated that the speed of light is a

constant in the whole universe. This resulted in the relationship of:

E=mc2

Where :E=Energym=massc=constant (speed of light) This equation indicated that energy and mass are simply interchangeable The General Theory of Relativity is a mathematical theory that predicted the universe is not static and is

either expanding or contracting. It introduced time as the 4th dimension of what was called space-time. However, Einstein disagreed with his own prediction and attempted to solve the problem himself by

modifying his equation. He introduced a cosmological constant Λ as a static universe as he believed it to be. This was later shown incorrect as observations made by Hubble confirmed an expanding universe.

Alexander Friedmann In 1922, a Russian mathematician proposed that the universe was expanding. This was proposed solely on

Einstein’s equation after ignoring the cosmological constant. Friedmann also realized the fate of the universe depended on the amount of matter present in the universe.1. The Big “CRUNCH” theory:

- If the density of the material is great enough then gravity will eventually stop the expansion of the universe and draw it back in again.

2. The open universe:- When the density of material is insufficient to slow the expansion of the universe and will continue to

expand3. Flat Universe:

- When matter is at a critical level; in this case the expansion continues to expand at a decreasing rate until time reaches infinity and the universe would have stopped.

Edwin Hubble (1889 – 1953) While studying the nebulae Hubble noticed a pulsating star in the Andromeda nebula. By calculating its

distance, he found that Andromeda was actually 800 000 light years away which was far beyond most distant stars known

Rather than being a gaseous object in our galaxy, Hubble was able to show that this was another galaxy.The Doppler Effect:

- Definition: The change in frequency of a wave for an observer moving relative to the source- If the source of the object is stationary, there is no change in pitch. Once moving, the waves at the front

of the source are compressed. This decreases wavelength causing a higher pitch. - Behind the source, the wave is stretched thus wavelength is increased. Hence a lower pitch is produced.

With the same application, we can apply this to EM waves and instead of using pitch, we can use the spectral colours to identify its wavelength.

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The red shift: Hubble discovered the red

shift in 1929. He had access to the most powerful optical telescope of all time – The Mount Wilson 100-inch Hooker

Telescope. The expansion of the universe became apparent because each star and galaxy possessed a degree of red shift

in them. This produced the first evidence to support Friedmann’s model of an expanding universe. The movement speed of galaxies is determined by the amount of red shift. Hubble observed galaxies that are

far more distant and found them to be more red-shifted. This led to Hubble’s law where galaxies are receding at an increasing rate.

Spectral lines A spectroscope is used to examine light from a source such as a light bulb that produces a continuous

spectrum of colours (similar to stars) Spectral lines are produced by the wavelengths that have been absorbed by the atmosphere. When observing far away objects we see that the spectral lines have shifted towards the red end of the

spectrum. Thus, it is evident that the stretching of space causes the cosmological red shift. NOTE! – This does not mean the galaxy or star is actually red or blue (if blue shifted)

The Hubble Constant Describes the rate at which distant galaxies are moving away Hubble discovered the recessional velocity (v) of a galaxy is proportional to its distance (d) from us. i.e. a

galaxy twice as far away will be receding twice the speed. This is an agreement to Einstein’s Theory of General Relativity which predicts that the expansion will look the

same from any point in space. The mathematical relationship can be written as:

v=H 0d

Where :v=velocity at whichgalaxy ismoving away (km . s−1 )H 0=Hubbl e

' s constant (67.8km . s−1 . MPC−1 ) (this constant changes over time)

d=distance¿ galaxy (megaparasecs)

2.1.2 Describe the transformation of radiation into matter, which followed the ‘Big Bang’. + 2.1.4. Outline how the accretion of galaxies and stars occurred…….

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In 1930, physicists had agreed on the idea of the universe not being static – it is constantly expanding. They concluded that the universe must have started out as something much smaller.

In 1948, George Gamow proposed the first theory about the origins of the universe.

The big bang theorySingularity

The universe began with a single tiny point of energy. It had extremely high temperatures, density and pressure. Space, matter and time did not exist.

The universe exploded and expanded from that single point, releasing immense amounts of energy that cooled. It was then possible that some of the energy turned into matter.

Recombination Initially some energy was transformed

into the very basic fundamental particles. These are the electrons and quarks (in general). Quarks – the building blocks of protons and neutrons.

Three quarks is required to create a proton or neutron. This process carried out is known as recombination.

It would take the next few hundred thousand years until the universe cooled sufficiently for electrons, protons and neutrons to form.

The first atoms created would have been hydrogen.

Radiation released Over the next half a million years, the

universe went into a pause mode. No complex nuclei were formed and all matter existed as individual particles.

As the universe reached to 4000kelvin, it was now ideal for protons and electrons to form the first atoms. Question? If the whole universe was one temperature, then how come galaxies and stars formed at some

spots and not others? Tiny variations in the cosmic background radiation shows the different densities to cause gravitational pull on matter.

The large amount of radiation released during the process still exist today. It is known as the Cosmic background Radiation. (discovered in 1964)

Accretion As the universe was expanding and cooling, particles lost kinetic energy and began to attract other nearby

materials and gain mass. This formed regions of high mass and density. This process is called accretion. Due to accretion, matter in the universe formed discrete gas clouds known as protogalaxies. The

continuation of this process will lead up to a galaxies and stars being formed. To this day, our universe continues to expand (14 billion years later) at a rate according to Hubble’s constant.

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Stars -A huge mass of gas held together by its own gravity with a very high core temperature which initiates nuclear fusion reactions.

Stars form from local condensation of gases and dust (or protogalaxy). A disturbance in these gas particles can cause a lager mass of gas to form and attract further surrounding gases.

The gases condense progressively which at the same time gravitational potential energy is being converted into heat. High enough temperatures were able to induce reactions in the gas clouds.

Nuclear fission: The splitting of a large nucleus into a smaller nuclei.

Nuclear fusion: The combining of two (or more) small nucleus to form a larger nucleus which releases a large amount of energy.

H+1+H+1→H e0+Energy The gas clouds have an uneven weight-

density distribution throughout space allowing it to clump to attain mass via gravity.

The core contracts under gravity while the heat created produces an outward pressure that works against gravity, BUT only slightly.

Eventually, the core gets hotter, building outward pressure and eventually immobilizing the collapse of the star. The star’s core is now stable.

This process takes about 1 million years.

2.1.3 Identify that Einstein described the equivalent of energy and mass

2.2.1 Identify data sources and gather secondary information to describe the probable origins of the universe

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In 1905, Einstein showed in the special theory of relativity that E = mc2, so establishing the equivalence of mass and energy.

It meant that energy could be formed from mass and mass can be produced from energy. Einstein’s Special theory of relativity was not consistent with Newton’s Law of universal Gravitation hence

produced the General theory of relativity. This theory included factors of gravity The theory explained:

- The planets are actually moving forward but in orbits is due to the ability of large masses (such as our sun) to warp space-time.

- The theory predicts that even light rays can be affected by warped space-time and should curl around stars. This is called gravitational lensing

- Predicts that time runs slower near an object as large as a planet.

Evidence that shown the Universe was expanding would help support the Big Bang Theory. Freidmann’s modification to Einstein’s cosmological constant allowed him to deduce that Universe was

actually not static hence the origins of the universe would have started from a single point. Hubble’s calculations of the red-shift supported the expanding universe. By measuring the degreeof red-shift,

Hubble was able to determine the rate at which galaxies were moving away. His law stated ‘The further away a galaxy is, the greater its speed away from us.’ Much like a balloon, the universe would have started from a point in space and expanded to cause this movement of galaxies and stars.

The cosmic background radiation provided further evidence in the expanding universe. The big bang theory suggested that after the initial explosion, the temperature would have kept dropping as the Universe expanded. The cosmic background radiation depicted small temperature variations which in turn also shows different densities in space. This was vital for the birth of planets, stars, galaxies etc. because if the universe was uniform, gravity could not take place. Hence the big bang would have shown some signs of radiation i.e. the cosmic background radiation.

The amount helium in the Universe also provides evidence of the Big bang theory. We know that stars are converting hydrogen in helium, but young stars also have a lot of helium in them. The production of helium as soon as protons and neutrons were formed is predicted by the big bang theory. This explains why 25% of the universe in helium.

3. Stars have a limited life span and may explode to form supernovas

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3.1.1 Define the relationship between the temperature of a body and the dominant wavelength of the radiation emitted from that body

3.1.2 Identify that the surface temperature of a star is related to its colour

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Temperature and colour

We note that stars have different colours To find the conncection between temperature and and dominant wavelength we use a black body

Black body

An ideal black body is absorbs all the energy it receives and re-emit all the energy.

EM waves produced is entirely dependent on the temperature The intensity Vs wavelength graph of the EM wave is plotted at

different temperatures. As temperature increased intensity is increased. However, the dominant wavelength would shift towards shorter

wavelengths as temperature was increased.

Wien’s law

λ pT=2.9×10−3

Where :λ p=dominant wavelength(m)T=Temperature (k )

2.9×10−3=Wien' sconstant

Just like the above, the amount of energy being radiated from a

star is related to the wavelength of the EMR’s it’s emitting. For light, shorter wavelength’s correspond to colours such as blue and violet while longer wavelengths

correspond to reds and orange.

Cooler stars at 3000K emit far more red and yellow light.

3.1.3 Describe a Hertzsprung- Russell diagram as the graph of a star’s luminosity against its colour or surface temperature.

3.1.4 Identify energy sources characteristics of each star group, including Main sequence, red giants and white dwarfs.

Kevin Huynh Stars with 5800K, including our sun, emit most green and yellow light. We only view yellow because we see

that the blue light has been scattered over the atmosphere and so when blue is eliminated from green we get yellow.

Temperatures of 10000K > produce blue and more violet colours.

The Hertzsprung diagram is a graph of a star’s luminosity against its surface colour and surface temperature. 1911: Ejnar Hertzsprung plotted the luminosity versus surface temperature of all strars for which the data

were known. 1913: American Astronomer Henry Russell also came to the same conclusion independently. The H-R diagram is important as it allows astronomers to classify stars and further understand its evolution.

Star Fuel

3.2.1 Gather secondary sources to relate brightness of an object to its luminosity and distance. 3.2.2. Solve problems to apply the inverse square law of intensity of light to relate the

brightness of a star to its luminosity.

Kevin HuynhMain Sequence Are generally fuelled by the nuclear fusion of hydrogen into helium.

It relies on the “proton-proton” chain which involves no catylyst. When the hydrogen depletes, the star progressively produces less

energy until not being able to hold up itself.Red Giant In the situation of limited supply of hydrogen, the star begin to

resort for “triple alpha reaction”, which is basically the combining of two helium nuclei’s.

Produces alpha radiation.White Dwarf Have no nuclear reactions occurring.

They are collapsed. Radiate heat into space and cool to become black dwarfs.

Brightness: The amount of energy received per square meter per second. (Watts) Luminosity: Energy radiated by an object per second. (J/sec/m2 or W/m2)

Brightness= luminosity4 π r2

(r=distance ) Brightness is related luminosity by the inverse square law.

E.g. 1The sun 1.5×10−1m away from Earth was observed to have a luminosity of 3.9×1026W .

a. What is the perceived brightness as viewed by an observer on Earth?

B= l

4 π r2¿ 3.9×1026

4 π (1.5×1011 )2¿1379.34 W

m2

b. What is the perceived beightness as viewed by a satellite which is three times further away from the sun than that of the earth.

1379.34×19=153.26 W

m2

4. The sun is a typical star, emitting electromagnetic radiation and

particles that influence the Earth

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4.1.1 Identify that energy may be released from the nuclei of atoms.

4.1.2 Describe the nature of emissions from the nuclei of atoms as radiation of alpha, beta particles and gamma rays.

4.1.3 Identify the nature of emissions reaching the Earth from the Sun.

4.1.4 Describe the particulate nature of the solar wind

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Stars fuse together to form a larger nuclei and release energy. However, not all large nuclei formed are stable.

These unstable nuclei release particles and energy until they become stable. These unstable larger nuclei are said to be radioactive. These main types of radioactive particles are:

- Alpha- Beta - And Gamma

Ionising power Penetration Magnetic field Electric fieldAlpha High Very low Up, when

magnetic field is into the page

Attracted to negative

Beta Low Low Down, when magnetic field is into the page

Attracted to positive

Gamma Very Low Very high No effect No effect

The nature of each particle:

- Alpha: Helium nucleus consisting of two protons. - Beta: Fast moving electrons- Gamma: Uncharged high energy and freaqency electromagnetic radiation.

The sun emits large amounts of EMR, as well as streams of trillions high energy ioni8sed particles, known as the solar wind each second.

These emission come from the corona or specifically corona holes.

The pressure difference between the corona and vaccum causes an outflow of material from the corona. The low-density, hot plasma of the corona streams out reaching other planets.

They contain mostly helium and other ions. The wind is able to induce a magnetic field. As it passes through Earth, the Earth’s magnetic field traps it and forms doughnut shaped regions. Known as

the Van Allen Belts.

4.1.5 Outline the cyclic nature of sunspot activity and its impact on Earth through solar wind 4.1.6 Describe sunspots as representing regions of strong magnetic activity and low

temperature

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Sunspot: Cooler regions on the sun’s surface that appears black. They possess very strong magnetic field. The sun goes through an 11 year cycle of high and low levels of sunspot activity. There is also a periodic variation in solar wind activity every 27 days (period of the suns rotation) There are about 100 sunspots during its peak cycle.

Effect and cause: At the peak of the sunspot cycle, solar flares are produced Solar flare: a sudden explosion of hot material that bursts thousands of kilometres from the Sun’s surface. They can last for a few minutes to hours. They emit large amounts of radiation (UV, X-ray, visible) Solar flares can cause a major disrupt in satellite communication and electrical components. This is because

the fluctuation of the magnetic field of the earth, caused by the solar flare, affects radio communication and power grids.

Solar flare actually intensifies the solar wind.

8.5 Cosmic Engine

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