Wednesday, 10 January 2018


This New Year I would like to share some of the best astronomical memories.

The first visit to ARIES (Aryabhatta Instititue of Obervational Sciences) in September 2016 will always be memorable. I had never imagined the place to be so serene and filled with loads of beautiful flowers and trees covered with lavish green mosses, and lichens.

The most beautiful experience was when I saw Dr. Hum Chand sir who is a Scientist at ARIES working alone in front of a computer with soft background music. His room was filled with loads of files and papers. It was the first time I saw the Lab of a scientist.

It was also a thrilling experience for me and my sister to see the 104cm Sampurnanand Telescope, a 40 year old telescope at ARIES. There are other telescopes at ARIES like the 130 cm telescope at Devasthal and the newly installed 1.3 m Optical Telescope which is the largest optical telescope in Asia.

And actually it was not the first time that I met Dr. Hum Chand sir. Two years ago in 2014, I listened to his talk “Wonders of our Universe” in the seminar held in our college.

A small model of the 3.6 m Devasthal Optical Telescope (DOT) in the Seminar

HoD Physics Dr. L.P.Verma sir, who organised this grand seminar is giving the talk on Solar Flares which was also the topic of  his research work during his PhD.

After him Dr. Brijesh kumar sir who is also a scientist at ARIES told us about the new 3.6m Devasthal Optical Telescope being installed. I also remember asking him a question which more-or-less was, “When the new telescope will be fully installed what you will see first”.
 And he answered that we do not see things but observe them and according to the project proposals, scientists will be observing lots of things like binary stars, planets beyond our solar system etc.
Next day one of the talks in seminar was given by another scientist of ARIES Dr. Yogesh Joshi sir. He talked about “Looking for Planets beyond Solar System

It was a really amazing experience to listen to so many scientists and professors. I also made a report and wrote about almost every speaker and their talks.

The same year I built a small Galilean telescope. The most amazing experience was when we saw more stars in the Pleiades star cluster and In the Orion constellation than could be seen with naked eye. I could also see the craters on the moon which to normal eye appears just a white orb in the sky.

My younger sister observing the last Supermoon of 2017. 

I was fortunate to visit ARIES the second time in March 2017 with mommy and my younger sister. This time I met other scientists and PhD students. And I was able to talk to Dr. Biman sir who is a scientist there.

And I hope in future I will meet more scientists and people working in the field of Astronomical Sciences.

Friday, 22 December 2017


Snowflakes are really awesome, and I realized it when I first saw these amazing pictures by Alexey Kljatov.

The size of these snowflakes is only a few millimeters!

We can make paper snowflakes or kind of snowflakes as shown in this 5 year old video by Vihart. 

I also tried to make some patterns. Not all them were perfect but I made some good ones also! 

Snowflakes have sixfold symmetry that is if you rotate a snowflake by 60 degrees it will look the same as before. 
Here is a paper snowflake with sixfold symmetry!

Happy Mathematics Day!

Sunday, 10 December 2017

Mathematics Day

To celebrate the birthday of famous mathematician Shrinivas Ramanujam or Mathematics Day (22nd December), I would like to share some interesting stuffs,

First of all this year Ramanujam's birth date is more special because 22-12-2017 is a prime number! And it would have been his 130th birthday.

What is shown here is a Magic square. It is an n×n array whose row, column and the diagonal numbers add up to the same number.

The magic square shown above was made by Ramanujam. Its very first row contains his Birth Date. So its also known as Ramanujam's magic square.

If you add the numbers along the row, column or along the diagonal they will add up to 139 (a prime number).

Friday, 1 December 2017

Semi Eulerian Graph

Inspired by this standupmaths video I made some shapes and figured out whether they can be made without taking pen off the paper.

So if a shape has got all odd number of lines going from its every point you can never make it without taking your pen off.
If it has only two such odd points it's called Semi-Eulerian Graph and then you can make the shape by beginning on one odd point and ending on another, as in the very first shape of the following picture.

Tuesday, 22 August 2017

Colliding black holes inside a computer

When we see a picture of scientists in lab or at a research centre, we notice that there are computers everywhere. And we think that they use these computers to analyze the data from the experiments in particle physics or cosmology. But there are lots of other things that are done with the aid of these computers, like landing of a rover, communication with a satellite orbiting mars, etc. 

SpaceX/Dragon CRS-12 Launches to the International Space Station

I was curious how physicists, cosmologists, and mathematicians use computers to solve problems. Like how the simulations of colliding black holes or galaxies is produced. How can it reveal something which has not happened yet? Like how our sun will explode at the end of its life and become a white dwarf.

The stars we see at night are just a small part of our galaxy. And our closest star, the sun can be seen throughout the day.

But how a black hole looks like?

We know that the planets are illuminated by star. Similarly Black holes are illuminated by the accretion disc surrounding them. So how does a black hole look like with its accretion disc? 

First computer images of the appearance of a black hole surrounded by an accretion disc were obtained by J.P. Luminet in 1979.

He had to produce the final image by hand using the numerical data.

Almost 38 years have passed since then. 
So now we should have a real picture of black holes, right?

But still we do not have one.

Although the simulations of black hole have become more beautiful and precise, and Luminet’s original work has now been done with a computer and shows 3D model of similar picture he created with his own hands.

And the black hole Gargantua in the movie INTERSTELLAR with its distorted accretion disc due to gravitational lensing is also now a famous visualization of such black holes.

But we do not have to be disappointed, because the Event Horizen Telescope, which is a large collection of telescopes, has started working on it and within few years we’ll see the first picture of a black hole!

Saturday, 27 May 2017

Black Hole (Gargantua) and Event Horizon Telescope

Murph's bookshelf, Blight, Wormhole, Gargantua (The Black hole), Singularity, Tesseract, Bulk Beings... 
So many misconceptions were cleared after reading the Awesome book by Kip Thorne.
One of the best things about the movie Interstellar is the Awesome and Fascinating view of Gargantua, the black hole...
And the Tesseract is just unbelievable!!

I am writing some beautiful lines straight from the book which I found really interesting and also eye-opening!

Tuesday, 28 February 2017

Black holes

“Astronomy is older than physics. In fact, it got physics started, by showing the beautiful simplicity of the motion of stars and planets, the understanding of which was the beginning of physics. But the most remarkable discovery in all of astronomy is that the stars are made of atoms of the same kind as those on earth.*
Richard Feynman 

How can a star turn into a Black Hole? From an object that shines due to nuclear fusion to something which does not allow light itself to escape from it. It becomes something so mysterious that cosmologists need to combine one of the greatest theories – General theory of relativity and Quantum mechanics to understand what is inside it. 

As Michael describes in his video "Travel INSIDE a black hole", theoretically anything, you, me or the Earth you are sitting right now can become a black hole if you shrink it under the Schwarzschild Radius. fortunately there is no means of doing it. But a star can do it at the end of its life.

But how? How can a star turn into a black hole.
To understand it we have to see what happens inside a star.

Stars emit electromagnetic radiation during nuclear fusion.
In our Sun during nuclear fusion Hydrogen nuclei fuse into Helium nuclei and produce electromagnetic radiation which we feel as heat. Photosynthesis starts as the radiation falls on leaves.
Thus everything we eat here on earth is just Bottled Sunshine!

Here are some of my favourite lines from Carl Sagan’s book “cosmos”,

It was more awesome to listen it in his beautiful voice in the video series Cosmos Episode 2 - One Voice in the Cosmic Fugue

Stars are very stable due to the thermal equilibrium that exists between the outward pressure and gravitational force. Outward pressure is maintained by heat generated in the nuclear reactions. But as more heavier elements form in the center of star, different layers start forming, star begins to swell and becomes a red giant. In the end it collapses into a dense core.

This is how we are told that the stars die, but its still described as one of the unsolved problems of physics"What is the exact mechanism by which an implosion of a dying star becomes an explosion?"

So, every star becomes a black hole in the end?
No, two things are important for a star to become a black hole,
  1.     Chandrashekhar limit
  2.     Schwarzschild radius

If a star’s mass is less than 1.4 times the mass of sun (Chandrashekhar limit), it will settle down to a white dwarf, which will remain stable due to the balance between gravitational force and Pauli Exclusion Principle which is the repulsion between electrons. That is the the dense core left at the end will be so dense, it will have only electrons!

But if its mass is above Chandrashekhar limit, it will become a neutron star which is stable by the Pauli Exclusion Principle followed by neutrons. The dense core will be made of neutrons! But if the mass of a star is more than 10 or 20 times that of the sun it will collapse in on itself to a point! This is what is called a BLACK HOLE!

So what is inside a black hole?

We don't know!

One of the solutions of Einstein’s field equations is “Schwarzschild metric”. It describes spacetime surrounding a non-rotating massive object. Schwarzschild black holes which are simplest kind of black holes are described using this metric.


Schwarzschild metric described by Matthew O'Dowd of PBS space time,

Metric is another word to describe the distance between two points in space. Metric can be different for different space. 
In spherical polar coordinate system the Schwarzschild metric is,

In the above equation, 2m=Rs (Schwarzschild Radius).
According to this metric, there is a Schwarzschild Radius surrounding a black hole where the escape velocity is greater than speed of light. This Schwarzschild Radius is actually whats written in many books as event horizon of a NON-ROTATING black hole.

As nothing can travel faster than light, this region surrounding a black hole looks black.

Usually when we see a picture of a black hole, we see the surroundings distorted and the black hole itself shown literally black. But as we know, all these images are not real. But they tell us what really is true. What we actually see when we look at a picture like this is the Schwarzschild radius or the sphere, from which nothing can escape, not even light.

And because of black hole's immense gravity, the galaxy behind it also seems to be distorted due to gravitational lensing.
In gravitational lensing, when a heavy object comes in front of a star, galaxy or quasar it bends the light coming from them and thus distorts is totally. Sometimes it forms a ring and sometimes multiple images. Like in yesterday’s APOD -
And the following picture shows other gravitational lenses taken by Hubble Space Telescope.

The video shows how the bottom of a glass can be used to see a ring of light when the source of light and the bottom of glass are aligned.

As this experiment was inside my mind, I saw another way of looking at the effect using only water in a bowl.
You can see in the image below, when the light from LED falls in the center of bowl a ring is formed even though its not a full circle.

Schwarzschild black hole is the simplest black hole. Its assumed to be non-rotating and with no charge. So what would it be like to travel inside it?

There are some mindbending simulations on this page made by Andrew J. S. Hamilton.
But there are other black holes which are not formed after death of stars, they are called supermassive black holes.
And astronomers have found these supermassive black holes at the centre of every galaxy. So how these black holes are formed? And what came first galaxy or black hole?

As theoretical physicist Michio Kaku explain in this video, the latest theory tells us that supermassive black holes formed first and then the galaxy itself formed around it. But its still difficult to tell which formed first.

Theoretical physicist Carlo Rovelli in a course at World Science U describes that a quantum theory of gravity is needed to explain the interior of black holes. 

So we have still many mysteries to unravel as in Newton's time.