HELIOSEISMOLOGY : SOUND OF SUN

Listen to the sound of sun( shifted in audible range)- click here 

Source - nasa.gov

"The Sun is playing a secret melody, hidden inside itself, that produces a widespread throbbing motion of its surface. The sounds are coursing through the Sun's interior, causing the entire globe, or parts of it, to move in and out, slowly and rhythmically like the regular rise and fall of tides in a bay of a beating heart." - Kenneth R. Lang

Study of stars is a tedious task because you have only a beam of light to decode everything. What what if I say that we are learning about the stars , or I should say the whole universe by listening to the

 'Star - Song ' !
Welcome to the world of Asteroseismology .
Astro - Relating to space and
Seismology -Oscillations in stars
It is a scientific word for the studying Stars by listening to it's heartbeat .
In this blog we are going to talk about Helioseismology . That is , the study of sun by listening to the surface oscillations 

Why sun 🌞? 

Because it is the only closest star to us . We can easily get more information from Sun than what we can get from very distant stars - our lives depend on it.
We are building a model for sun first and then we will extend it to other stars - Logical Approach .

Before starting with Helioseismology , let's me share some important information about interior of Sun:

Sun is not as peaceful as it looks . Home of complex magnetic field, source of solar flares and solar winds💥, (capable of disrupting communication, and generating auroras here on earth ) this hot ball of plasma is 27 million Fahrenheit🌡in the core and 10,000 Fahrenheit on the surface. It's a dense body , with density around 100 g / cm^3 ( the density of rock is about 5 g / cm^3) .

Moving out of the core , we have radiative zone - which can be thought about as inserting an individual in a room jam-packed with people . The person moved in will transfer his energy to the other person , and that person to others in room . This chain of energy transfer will continue taking place among people in the room , but no one is going to move very much . Similarly , in radiative zone , we have energy moving throughout the zone , with very little movement of actual material.

Then we have Convective Zone - Where the bulk motion of material takes place . The hot material rises up , cools and sinks back. It generates magnetic field.
Hydrogen is being stably burnt in the core since the past 4.6 billion years and the process will continue till coming 5 billion years , after which the star will start burning Helium to Carbon . We know all of this about Sun but , for far away distance , if we take two stars , one that has ignited Helium and one that has not , they can look exactly same on the surface - same temp , luminosity , colour , etc . That is very annoying for astronomers , for they might predict the phenomenon but it won't be visible in these observations .

This shows that we aren't fully aware of all the information we need to describe a star
Let's look at how do we know the internal structure of earth ?

 We came to know about it by studying earthquakes or seismology .When an earthquake hits an area that earthquake injects some energy that is measured using seismographs placed at specific locations to detect them . Earthquake waves use different paths and reach the detector traveling through different layers of planet . Once we know about the time and path , we can decode the interior structure of Earth. We use the similar procedure for Sun , but we don't place seismographs on Sun ( we cannot of course) ,and we don't need too . The observation of surface of sun is enough .

Stars are the musical instruments 🎸- a set of vibrations gives rise to a particular sound .Solar oscillations first came into notice in 1961 when the observations by Mt. Wilson Observatory discovered that the Surface of Sun is slowly puffing with a period of about 5 mins . Material in the star is getting compressed and rarefied , hotter and cooler as the temperature changes , so you get intensity variations , which lead to change in the brightness of star. This flickering is so subtle (a few parts per million) that it is barely visible to naked eye. 

Vibration in stars is similar to vibration of cowbells . As big bells vibrate with deep low frequency , so do the big stars and opposite is true for small stars. So, knowing the frequency of vibration can help you figure out the size of the star. Isn't that amazing? 

Calculating the frequency was not an easy task . These few parts per million fluctuations aren't easily detectable .Hold on! Kepler satellite had got a role to play here . The satellite which was originally meant to find earth like planets near sun like system required long time observation of a patch of sky(4 years)with the precision of a few parts per million to detect the passing of planet in front of the star by detecting the change in the brightness of the star . This made the long time high precision measurement of the star possible and hence , we were able to detect the oscillations. 

Lets take a closer look into the oscillations:

It can be shown that the oscillations are separated into two categories: interior oscillations and a special category of surface oscillations. These are called p(pressure, g(gravity) and f(surface gravity modes)

p modes: 

The dominant restoring force in this oscillation is pressure. Pressure modes are basically standing sound waves. Their energy densities vary with radius inversely proportional to the speed of sound, so their resonant frequencies are determined predominantly by the outer regions of the Sun.

Sun is vibrating in a superposition of acoustic normal modes (like the patterns with which a guitar string vibrates, but for a spherical body rather than a string). The period of oscillation is about 5 minutes. The motions of these were originally believed to be due to turbulent convention in solar atmosphere. Later on , it was discovered the the phenomenon was global and are manifestation at the solar surface of resonant waves(pressure waves). About 10⁷ distinct( p modes ) are thought to be excited.

g- modes:

For these type of oscillations , restoring force is predominantly gravity. They are envanescent in the convection zone and due to their tiny energy, they are very difficult to detect. So, no g mode has been directly measured although claims about indirect interactions have been made .

The measurement of even just a few g modes could substantially increase our knowledge of the deep interior of the Sun.

f-waves:

It is essentially a surface mode and it can be expected to provide a diagonistic of flows and magnetic fields present in surface regions.

Illustration of a solar pressure mode (p mode) with radial order n=14, angular degree l=20 and azimuthal order m=16. The surface shows the corresponding spherical harmonic. The interior shows the radial displacement computed using a standard solar model. Note that the increase in the speed of sound as waves approach the center of the sun causes a corresponding increase in the acoustic wavelength.

So, Studying these oscillations or fingerprint of stars can gives us titanic amount of information let's see how :

1. These stars look very different depending upon how they flicker. For big stars , these pulsations are slow and amplitude is big , where as for the small stars, these pulsations are crowded, fast and amplitude is small. So, by clearly looking at these oscillations you can figure out that this buddy is big and this is small. We don't analyse the data as such , we take its Fourier transform- figuring out the sinusoids that the curve is made up  of and then we have a diagram called power spectrum.

2. This is known as the power spectrum of the star- making the typical frequency at which the star oscillates. It won't be wrong if we call this the fingerprint? ultrasound of the star . This curve carries an immense amount of information. Looking at the peaks , and the spacings, mass and size of the star can be predicted. Looking at subtle spacings , you can tell what's going on in the core of the star , how much H it has burnt into Helium , what is it's age . 

These oscillations have helped us in giving answer to following questions:

How big the star is 
How massive it is 

Has it started He burning?

How old a star is?

Are our models correct?

This is an astounding amount of information with such an ease .

Studying these oscillations opens new gateways to study astronomy with precision that is entirely unravelled.

These oscillations have made us sing -"Twinkle twinkle 🌟 little star , now I know what you are!"

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MOON LANDING CONSPIRACY DEBUNKED

From 20th July 1969 to 2020 , it's been 51 years since the mankind has set the first steps on moon but still we have never got rid of these -

It's important to question Everything..but still it's important to not form any preconceived notions about your ignorance and accept the facts which have logical proofs. The idea about conspiracy started with Bill Kaysing , who worked as a technical writer for NASA Apollo Mission - published a book - We never went to the moon : America's 30 billion dollar swindle  and claimed that he has got some inside knowledge of conspiracy. It gained immense popularity since then , because  media was heavily earning from this issue and why not the questions raised are really some good ones and worth an explanation . But the problem occurs when the concept is promoted  in such a way that people don't feel any need to check facts or reasoning and are dragged in the camp of " non - believers " 

Here , lets debunk some of the most popular misconceptions that have become conspiracies now:

#1. Sun is the source of light for moon so why there are different angles for shadows ?Are Studio lights the reason ?

Explanation - 

Sun is the dominant but not the only source of light available . Surface of moon is also a reflector as well as uneven - shallow bumps are hard to notice  . Moreover , earth also shines light on moon - called Earthshine. Thus , sun isn't the only source available for light so , shadows are at different angles .

#2. Flag is waving on lunar surface even when it has no atmosphere

Explanation-

 NASA was well aware of the fact that there is no air on moon , so the flag that they constructed had horizontal rods in it . By the time we were on the moon , some serious ripples were there on fabric giving it a bent shape . Moreover , the flag appears to move only when the Astronauts touched it ( momentum conservation ) , so it was not because of wind .

#3. The most popular one - Why there are no stars? Just because it will be easy to locate the position and timing with stars so studio director avoided  that ?

Explanation -

 Obviously , no. There are no stars due to the exposure  . Exposure time is the length of time for which the camera's shutter is open when taking a photograph. If you want to catch each and every star in the background , the exposure would have to arranged ,  in such a way that it will result in  this kind of photograph. Obviously , you don't want that, so the prime Focus was on clicking pic of astronaut not the stars . 

 This is a four-second exposure taken from the flight deck of the shuttle Endeavour

Moreover , try to clicking your pic in night sky , notice no stars will be visible ,  only blackness( with some city lights maybe ) , this is the same thing that happened when we clicked photograph on moon So yeah , issue resolved. 

#4. This image was taken by Neil Armstrong when Buzz Aldrin was stepping out of Eagle . It clearly shows that the sun is in the opposite side and the astronaut is in shadow , so how is he so brightly visible ? Shouldn't he appear dark ?

Explanation  - The astronaut is bright because :

1. Moon's surface is reflective as explained above 

And the astronaut is "soo" bright because - 

Neil Armstrong is clicking the pic and the spacesuit made up of Teflon has 90 % reflective properties , so he himself is like a bright source of light . We have  got all of this tried in a  simulator and the results are the exact same as they were in official  moon landing photographs

#5 How did the astronauts survive radiation from Van Allen belt ? 

Explanation - 

Let's first understand what Van Allen Belt is - it is a torus of the charged plasma ( soup of Charged particles )around earth trapped by the earth's magnetic field .

 It has two layers with the inner one being well defined , so easy to avoid . The outer one is very large and hard to avoid , but we can find relatively less denser regions. Apollo astronauts were exposed to the radiation , but for a relatively shorter amount of time and through a relatively less dense region -similar to getting two CT scans of your head , so not too bad .

#6 Crosshairs etched into the cameras are visible in the Apollo photos; however, in some images these aren't visible ? How's that possible?

Explanation- 

Try photographing a very bright surface, and you will yourself see the crosshairs disappear. those bright objects bleed brightness , saturating the film and obligating the cross hairs . So , yes it's possible.

#9 The powerful engine of lunar module should have produced a blast crater yet it is nowhere to be seen .

Explanation- 

Yes , the engine was indeed very powerful  , landing on earth would have made a lot of hoo-haah on earth due to different rocks and stronger gravity. but on moon , the thrust was lowered down to mere 3000 lbs before landing on lunar surface. The Moon's surface is covered with a rocky material called lunar regolith, that has a unique property that the particles are very jagged, which causes them to interlock. When subjected to pressure, the regolith will resist, almost like solid rock.The exhaust stream was not powerful or centralized enough to displace the regolith and blast out a crater. The first moon landing by Neil Armstrong has been registered to be one of the softest moon landing with a  0.54 m/s velocity.

#8 Still I don't believe that moon landing happened 

Explanation - 

For you first I have some evidences , cuz till now I have debunked assumptions only and maybe visible  evidences can convince you more strong.

• Apollo astronauts brought sample of moon rock back to earth and the rock with this particular composition is nowhere to be found anywhere on Earth. Tests have shown that the lunar meteorites match exactly with the rock samples from moon , except from the features that distinguish them from meteorites. 

•The most solid proof is here - American flag isn't the only thing that astronauts carried on moon . We also have 'Laser Retro - Reflector' - these are a series of corner cube reflectors which have a special property of reflecting the light in the direction where it came from . They are still working today :)

•Some Logical Proofs - 

If it would have been so easy to build a special Hollywood set for moon landing , The Soviet Union ( Russia now ) - the major competitor of would have never accepted this and might have staged Mars landing in response.

400 thousand people have worked on this program ,  so many missions have been there before to make the landing happen . With so many people reporting to the mission constantly , maybe reporting everyday , why it is that no one has spilled tea so far .

600 million people watched the launch , that includes so many people at the launch site watching live. The rocket did launch and there is no place to where it did go except space .

Those pictures have all the smallest details in them and getting these perfectly would have been much easier by going on moon than filming in any Hollywood set .

With so many fallacies explained ,  I guess the conspiracy theories have finally been debunked. Still if there are things left to be explained , try to do some search , instead of jumping right to conclusion.

 20 July 1969 , indeed marks "One small step for man , one giant leap for mankind ". 

COPYRIGHTED IMAGES CREDIT - NASA

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SPACE ELEVATOR

"The space elevator will be built about 50 years after everyone stops laughing.”

— Arthur C. Clarke

Ever thought about taking a lift from ground to space ? Well the idea might sound sic-fi and unusual but let me tell you NASA has commissioned the study of elevator in 1990s which concluded that it will be feasible to build one and use it for exploring outer space . In Sept. 2018 an experiment was launched to International space station to test idea that the movement of climber. Not only this , countries like Japan , China , US they all have plans regarding the same . Let's see how did the idea came into existence ?

Birth of Idea of space elevator -

First proposed by a Russian Physicsist Konstantin , the idea finally came into limelight with the novel ' Fountains of Paradise ' by Arthur Clarke . Research was finally started with enthusiasm in this area with the discovery of Carbon Nanotubes ; they play the most important role in realisation of concept of Space Elevator

Building Space Elevator 

This is where the things start getting interesting and complex .

Let's first understand the design -

Space elevator is basically a tall cable rising from Earth to Space , terminating in a Counterweight.

The components are - Cable , Counterweight , Anchor and Climber

We need our elevator to be static wrt. to us so we need to assure that all the forces acting on it are Zero. 

You must have heard about geostationary satellites - as the name says , they appear static wrt  earth        ( the time period of rotation of satellite is same as that of Earth 🌎 ) They are placed directly above equator , at a particular height , at which the Gravitational ( force pulling satellite towards earth ) and Centrifugal force ( force pushing it out of Earth ) become equal , that height from surface of earth is = 35786 km . 

But the situation is not as simple as satellite in this case . We have cable attached to the satellite which carries its own weight . Upward force - centrifugal force must increase to balance this out . So either increase mass of counter weight ( maybe capture an asteroid ) or increase the height of cable. L

So lets talk carefully here -

The Design 

Each portion of tower should be such that total force on it = 0 

Total forces acting on a small element of the giant tower are - 

Fu : Force due to the portion of tower above the element

Fd: Force due to the portion of tower below the element

W: force due to weight of element  and 

Fc : Centrifugal force ( Cuz of rotation of Earth ) 

For the element below geostationary level 

W> Fc , which implies to balance this Fu > Fd .

This means that the thickness of tower should increase with increasing height below geostationary level

For the portion of the tower above geostationary level  implies W< Fc . To balance this we should have Fu < Fd 

LINEAR SCALE HAS BEEN USED TO SHOW INC. AND DEC. IN HEIGHT INSTEAD OF EXPONENTIAL FOR EASE OF REPRESENTATION 

This means that thickness of tower should decrease with increasing height below geostationary level.

Thus , a free standing tower is the one for which tension drops to 0 at both the ends with maximum value at Geostationary height.

Building from ground mathematically , the tower area should first increase exponentially , maximum height at geostationary level and then decrease exponentially. 

We should have something to hold this large structure right ? Here comes the role of anchor .

 

For building a tower so high and with such a large counterweight , there is a risk of disturbing the orbit of Earth around sun by disturbing Centre of mass , so we need to add an anchor attached to the counterweight through cable , down to earth to prevent it. Our anchor is not a simple hook , it will be located on a mobile , ocean - going platform in Pacific in a specific location . Reason ? By doing this we can avoid space debris , lightening and collisions with satellites . 

Let's now discuss about the most crucial impediment to our elevator - the material 

We have an important lead here - the taper ratio - which is the ratio of area of tether at the bottom to area at the highest point . Steel , the seemingly promising material in the construction has taper ratio

 = 1.6 × 10 ^ 23 

Building structure with steel , the area of top of tether is greater than the width of universe by a factor of 10^27 . Steel fails in terms of strength as well.

We require a material which has low density and has high tensile strength . That material is Carbon Nanotubes -

 

basically rolled up sheets of graphite. There are some major problems with this though -

*The ultimate tensile strength is still arguable outside laboratory and is sensitive to slightest foldings and twists 

* We haven't constructed nanotubes in bulk , we have achieved to about 3 cm length 

Good news , research is on !! 

Finally , let's turn to the climber 

Climber will be like a slight  modification to a Spacecraft , in terms of locomotion , cable deployment and power systems.

Calculations show that the mass ratio of cable to climber should be 0.86 .

Let's now talk about power source to space lift now -

It's challenging to power the climber to go up . The only possible way comes out to be photovoltaic cells ( a little ) and (mostly) powerful lasers .But still things like prevention of power dissipation have still a lot to work upon.

Ah..so much complications..

Nevermind , let's imagine to have built the one. So, how will we be using the space elevator ?

Space elevator is like one time risky investment , but if it will be stable and successful, we will be jumping into a new era of space  exploration 

Launching stations can be set up there , we won't have to spend too much fuel in getting rockets out of Earth 

Space travel will be cheap enough to $200 / kg as compared to billions of dollars today .

Stations and labs can be setup there with daily supplies

Global monitoring of earth and it's environment can easily be done. 

It will open gateway to a new way of living life !!

So many complications , is this realistic and worth research ? 

In my opinion , space elevator is quite realistic . Like maybe there is risk on Earth 🌎 , but the situation will be easier with Moon and maybe other planets in terms of low risk factor and type of material required ( like we can go with kevlar instead of Carbon Nanotubes on moon )

Just so many benefits , rely on some innovative Physics- Engineering Research . I think we should never stop research on this topic , goal is not about building an elevator on Earth only , it will bring with it revolution in the field of Material Physics , study of lasers , mechanics and so on ! We aren't losing anything.

What we have found is

interesting , innovative , takes relatively less money and has ability to completely change our ways of living more than any national budget . So let's have a positive attitude and determined approach :)

REFERENCES:

*The physics of the space elevator-P. K. Aravind

Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609

*The Space Elevator-Bradley C. Edwards, Ph.D.

*1-Source -The physics of the space elevator-P. K. Aravind

*2-Source- spectrum.ieee.org

*3-Source -The physics of the space elevator-P. K. Aravind

*4-Source-matmatch.com

*5-Source-amp.ibtimes.co.uk

*6-Source-theconversation.com

*7-Source-themeparksandentertainment.com

*8-Source-extermetech.com

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HOW FAR AWAY ARE STARS?

"...Looking at the stars always makes me dream , as simply as i dream over the black dots representing towns and villages on map. Why, i asked myself shouldn't the shiny dots of sky be as accessible as black dots on the map of France"

-Vincent Van Gogh

Study of heavens is older than study of navigation, agriculture and even language itself. It is one of the oldest sciences ever studied . From the dawn of civilisation , humans have wondered about twinkling dots above their heads , far far away from the reach. Study of these twinkling dots has laid down the most important building blocks in arousing the curiosity of mankind into knowing - who we are ?

Stars are all born in nebuli , the cloud of dust. With the gravity working is magic , dust and gas start to collapse. As the temperature rises further stellar evolution continues ; thermonuclear fusion begins, forming helium and we get heat and light .

How far away are stars?

It seems impossible to understand stars, unless one has an understanding of tackling distances between them. Taking the understandings of Greeks in measuring the distance of moon forward , we reached the stars . 

Let's first understand the term parallax - Its the apparent shift in position of an object when it is viewed along different positions. Eg.  hold a pencil in your  hand and extend your arm. Notice the shift in position of pencil as you view it through your one eye keeping the other closed at a time. Your eyes have a certain distance between them that causes this parallax . Similar shift in the position of star occurs when it is viewed from different locations of earth and the astronomers didn't spare this and made it one of the most powerful tools of astronomy !

Let me show you how -

As seasons change, the location of stars in the sky changes - this apparent change in the position of the star when viewed from different points on earth is called - Parallax. 

We take the benefit of this observation and by measuring the position of the star in the sky 6 months apart , by simple mathematics , we get the distance to stars .

we already knew the distance from sun to earth( 1 AU ) 

we measured the angle' alpha 'from earth and putting all in formula - 

alpha= (1 AU)/d  , we get the distance to the star.

But the process is not as straight forward as it looks , twinkling of stars - though soothing to eyes are a major trouble for astronomers because it limits the accuracy to which the position of star is known .

One way to solve this problem is to have thousand of observations to get the accurate position of star and the other is to position our telescopes outside the atmosphere of earth to avoid turbulence due to atmosphere and get the measurement of accurate position. That's why we have most of the telescopes placed higher up in atmosphere.

Everytime we need to measure the position of a star , it's tedious to take thousands of observations . This parallax method surely has limitations . Is there a better way?( yes obviously , else why would i be having this question here ) . It lies in measuring the brightness of star.

How bright are stars and how to measure the brightness?

Let's first talk about brightness in daily life. You go to market and purchase 1000 W bulb. This bulb gives off 1000 Joules of energy in one second. Physicists call this term luminosity.

The other term is apparent brightness. It describes how a star gets dimmer and dimmer as it gets far away. We use this relationship between distance and brightness to a great extent in astronomy.

 How Astronomers measure the brightness?

Stars radiate enormous amount of energy so thy don't use units like Watts cuz that will be very inconvenient. 

The apparent luminosity of of a star is descirbed as

 apparent magnitude (m) and

                                                 

 total luminosity is described as absolute magnitude (M)-magnitude of an object placed 10 pc     away.

                                                 

 Where parsec(pc) is the distance which a star has to travel for it's parallax to be 3.26 light year(light year is equal to the distance light travels in one year = speed of light(m/s) * no. of seconds in an year)

The construction of magnitude scales was done on the basis of the most fundamental logic-

Our eyes are more sensitive to geometric than arithmetic progression.

This fact can be understood very easily as you will be able to distinguish more clearly in between two bulbs if brightness of one bulb is greater than that of other by a factor 5 i.e b1=5*b2

 than if the brightness of one bulb is 5 + greater than the other , i.e b1=b2+5.

There are two things which we need to note about these magnitudes here -

The scale runs on logarithmic scale ( magnitude of one star is dimmer than other by same factor)and backwards( higher the magnitude , dimmer the star )

Here is the mathematical expression for apparent magnitude- 

m1 - m2 = -2.5 * log( B1/B2) where m1 , m2  and B1 , B2 are magnitudes and brightness of objects respectively. 

and here is mathematical expression for absolute magnitude- m-M = 2.5 log (d/10)^2

 If the object is at a distance d pc, then (10/d)^2 is the ratio of its apparent brightness and the brightness it would have if it were at a distance of 10pc. 

Starlight deciphering the mysteries of cosmos

Stars send us message encoded in the starlight. We decode this message by studying the spectrum of stars, we can encode many things, like what is the star made up of , the age of star .

 

Suppose two stars have same spectrum, one is near and one is very far away . If spectra of two stars is identical then experience has shown astronomers that the two stars will also be very similar in their other properties, such as their mass, radius, and total luminosity. If it turns out that the second star has apparent luminosity that is only one ninth that of  1st one , then it is likely that this is because the star is thrice as far away, so that its light is spread over a sphere whose area is nine times as large as that of the first one. Noticed how cleverly we figured out distance here ? This is what astronomers use to take account of very large distances.  

well..this is not the end to the story still , we got a lot of information from a single twinkling speck on the sky , that realisation is awesome in itself. I wonder , what it would be like decoding every single bit of information that is given to us ! Our ancestors were definitely excellent at it ; we owe our understanding to all those curious , passionate and brave minds who decoded the biggest mysteries without any basic tools. There is still a long long way to go .. Every piece of the sky tells a story , just be curious enough to decipher one.

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INTERPLANETARY TRAVEL

"The first day or so we all pointed to our countries . The third or fourth day ,we were pointing to other countries . By the fifth day , we were only aware of earth"-Sultan bin Salman Al-Saud

Curiousity about space is the essence of human existence. So , this blog post is about some of the tricks that we are using for interplanetary travel.

Well why do we need to use them though ?

Because they are more efficient . Planets, let alone galaxies are millions of kilometres away from us and exploring them requires efficiency in fuel and time . This is what is provided by these tricks.


Getting away from Earth ; The pale blue dot

Want to escape from solar system , make the total energy of trajectory = 0

What's total energy ? It's the sum of -

Kinetic Energy - energy due to motion +
Potential Energy - energy due to configuration
Putting total energy 0 we get escape speed from Earth = ( 2* G *M /R) ^ (0.5) where ,
G = Gravitational Constant -6.6× 10^ (-11) Nm^2 kg^2
M = Mass of Sun = 1.98 * 10^30 kg 
R = Distance of sun from Earth = 152.09 million km

Putting all these values we get escape speed from earth - 11.2 km /s 

Long story short, The spacecraft launched in any direction will reach the out of the Gravitational pull of earth when launched with the speed 11.2 km/s.


Getting to other planets :

Hohmann Transfer

Credit:Wikipedia

Hohmann ( a German scientist) showed that the lowest propellant path between any two orbits is an elliptical orbit which forms a tangent to the starting and destination orbits.
(Pic)

Insight - Spacecraft to Mars and Chandrayaan-Spacecraft to moon used this technique

Calculating launch speed to other planets

Suppose we launch from the Earth, at a distance R1 from the Sun, at a target planet a distance R2 from the Sun. 

Let r denote the ratio R2/R1; then r is just the orbital radius of the target planet expressed in astronomical units (AU).
v⊕ = orbital speed of the planet from where the spacecraft is to be launched 

To reach the outer planet, the spacecraft is required to have a speed relative to the Sun after escaping the Earth of:
v = (2r/r + 1)^ 1/2 * v⊕ 

For Jupiter we have this speed = 38.6 km /s
To get launch speed from Earth , subtract earth's orbital speed 29.8 km/s and add the escape speed.
Thus launch speed to Jupiter is 20 km/s 

Similarly, launch speed to a planet from any other planet can also be calculated.


Gravitational Slingshot -

 Using gravity of planet to reach to other planets

Now we have successfully sent our spacecraft to Jupiter , we will gravity of Jupiter to send it further and out of Solar System.
Wait ! If we send a spacecraft on a trajectory
around Jupiter , and we follow its orbit as it falls towards the planet and then comes
back out, we always find that it returns to the same place as we started it with exactly
the same speed. There is no gain! But we see Voyagers speeding up gaining speed from Jupiter. How's that possible?
Well answer lies in the 'frame of reference' .
We need to look at the change in speed through frame of reference of Sun:

It seems like breaking the conservation law, it seems like planet is taking energy out of the system out of nowhere . Well that's not actually the case .

The gain in speed of spacecraft is accompanied by slowing down of Jupiter a tiny bit , 

because Jupiter is very large , this slowing down isn't prominent enough . But yeah , with millions and trillions of similar slingshots , we can slow the planet to even such an extent that it will start dropping towards Sun's gravity .

This is pretty much what Voyagers have used to escape the boundaries of solar system.
Taking spacecraft approaching along different direction , we can slow down the spacecraft as well and make it fall close towards sun and speed up the planet.

Thus we see how we can use planets like controllers for our journey to the outer world.This realisation so freaking awesome in itself !
Not the gravity but time dependency of gravitational field due to motion of the planet has helped us in taking some advantage out of it . The conservation laws you see , are built on principle of invariance , invariance of gravitational fields , time .

The relation between conservation laws and invariance is built into the laws of physics at their deepest level. How can we mold them into our benefit is totally upon our understanding of phenomenon and curiosity in understanding the nature of Universe .

                                 ________________________________________________

For astrophysics geeks, i would here like to mention the list of top 25 astrophysics blogs of 2020 by feedspot. Go check them out by clicking here- top25astrophysicsblogs

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ORANGE IS THE NEW BLANK : CMB : THE MAP OF UNIVERSE-(BB-5)

Ever tried switching between channels in antenna tv ? You must have heard that static buzz and be like .. ah ! such a mess

Well , about 1 % of that buzz carries information about the whole of universe. We have built a cosmic map out of that !
I have introduced it a bit in the previous blog(*1) and now we will dig into it in bit detail.
Cosmic microwave background is a information about baby universe(3,80,000 years after Big Bang ) in the from of radiation filling entire space. It's the first light ever!

How did it happen ?

Just before recombination , the universe was a hot dense soup of baryon-photon plasma . Most of electrons were not free to travel very far due to constant interaction with ionised particles. There was no light !
Eventually the universe cooled down to a point where electrons can combine with hydrogen and helium nuclei to form neutral atoms-event known as 'recombination'.

 The light didn't interact with newly formed atoms very much and was free to stream through the whole universe.The photons released had the temperature / energy of 4000 Kelvin .

The early photons that streamed through the universe were orange in colour . Universe looked orange !🔶

Then how the the universe black now ?
Answer : Expansion

The expansion cooled down the universe , stretched the wavelength of photons to microwave region . As our eyes cannot see this radiation , it is dark or transparent to us. Orange is the new black

 The temperature of this radiation has dropped down to 2.7 Kelvin🌡

How did we measure the radiation ?

It was first predicted theoretically by Ralph Alpher and Robert Herman .

But , was an accident that sparked the research. In 1964.

 The Holmdel Horn Antenna was designed to be used for satellite communications by Bell Laboratories. But when Arno Penzias and Bob Wilson tried to calibrate the instrument, there was a noise that just couldn't go . No matter where and when they point the antenna there was a constant low level "hum" having an excess temperature of 4.2 Kelvin . All the tricks were tried to get rid of it but in the end it was discovered that this Buzz is due to CMB winning Penzias and Wilson Nobel prize in 1978.

The theoretical predictions about inhomogeneities and and the nature of CMB were all examined in great detail by satellites and telescopes and they all reproduced the big bang model of universe.

Features of CMB
Understanding the image - 

CMB is like the map of universe , this picture pretty much tells us every thing about the universe .
Before the time of recombination, in the very early Universe , small density inhomogeneities lead to baryons and dark matter flowing inwards into dense regions . (*2)The photons were coupled with baryons till then and they exterted outward pressure . This play between gravity and pressure produced the first sound waves oscillations in universe , the bouncing shell of matter flowing inwards and outwards till it was decoupled from light and froze where it is. These overlapped frozen shells of matter then collapse into galaxies as we see them today . Cosmic microwave background is the image of universe at time of recombination .

When Recombination hit, most were caught in the middle of in and out flow - like between maxima and minima of oscillations . But some oscillations were caught at maximum density - where matter flowed in the middle of fluctuation and some were at minimum density where matter is most spread out - called maximum rarefaction. These maximas and minimas define the most obvious points on the picture.
Now lets have the information in the form of graph to get a better sense .
This graph is called the power spectrum of cmb .

Each of these peaks tells us something unique. The peaks of this size had exactly had collapsed just once before recombination .Which means it's size is equal to speed of time (0.58c) × amount of time they had to collapse (3,80,000 years ) × expansion factor = half a million light years .When we go to actually measure the size of these spots by telescope , the measurements correspond to flat universe. Thus there will be no big rip , the universe will expand forever.

The first peak tells us about the total energy present in the universe.
The second peak tells us about the amount of Baryons present in the universe (roughly 5 % of total energy of universe ) and the other peaks give us the information about dark matter - the amount of dark matter compared to radiation .
Thus , we get to reproduce this pie chart from CMB

                                 

This static buzz has helped us in understanding the colour of early universe , the composition and temperature of universe , the geometry and the ultimate fate of universe. It is a strong support to big bang model and has helped us clearing our assumptions about the model of universe directing us to the ''till now the best model of our existence".
We get an insane amount of information from it !

Every portion of the sky tells a story , be curious to detect one !
Never stop questioning , curiosity has it's own reason for existing

(*1),(2*)-CHECK PREVIOUS BLOG HERE

  -STORY OF FIRST SOUND WAVES OF UNIVERSE-(BIG BANG-4)

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