A note on the Hydrogen spectrum

The emission spectrum of atomic hydrogen is given by this amazing spectral series diagram:

image

Let’s take a closer look at only the visible portion of the spectrum i.e the Balmer series.

image

If a hydrogen lamp and a diffraction grating just happen to be with you, you can take a look at the hydrogen lamp through the diffraction grating, these lines are what you would see:

image

Source

These are known emission lines and they occur when the hydrogen atoms in the lamp return to a state of lower energy from an excited energy state.

image

           Representation of emission and absorption using the Bohr’s model

Here’s another scenario that could also happen:

image

You have a bright source of light with a continuous spectrum and in between the source and the screen, you introduce a gas (here, sodium)

image

Source: Harvard Natural sciences

The gas absorbs light at particular frequencies and therefore we get dark lines in the spectrum.

This is known as absorption line. The following diagram summarizes what was told thus-far in a single image:

image

The absorption and emission spectrum for hydrogen look like so :

image

Stars and Hydrogen

One of the comments from the previous post was to show raw spectrum data of what was being presented to get a better visual aid.

Therefore,the following spectrum is a spectrum of a star taken from the Sloan Digital Sky Survey (SDSS)

image

                                 Plot of wavelength vs median-flux

Here’s the spectrum with all the absorption lines labelled:

image

Source: SDSS

You can clearly see the Balmer series of hydrogen beautifully encoded in this spectrum that was taken from a star that is light-years away.

And astronomers learn to grow and love these lines and identify them immediately in any spectrum, for they give you crucial information about the nature of the star, its age, its composition and so much more.

image

Source: xkcd

Have a great day!

*If you squint your eyes a bit more you can find other absorption lines from other atoms embedded in the spectrum as well.

On the strong 5577Å spectrum line


The above is a plot of the Wavelength(in Å) in the x-axis vs the flux of some objects from the Sloan digital survey ( consists of galaxies, young stars, Quasars, etc)

But  there is one strong peak in all of those plots that seems to stand out: 5577 Å

image

And if you like, the color that it represents is the above  (Made with Stanford’s color matcher app)

A nightmare for the astronomer

image

This line at 5577.338 is what astronomers refer to as a ‘skyline emission’ or a ‘mesospheric night-glow’ and arises from the recombination of atomic oxygen in the mesosphere.[2]

image

                                               Source

This line is of no significance to an astronomer who is looking to find out properties about a far away astronomical object. Yet, this line pops up in every spectrum of any object that you look at in outerspace!

In addition since the line is so strong, it contaminates the nearby pixels making the nearby data unusable and also messes up the scaling of the plot.

image

Example of contaminated pixel columns in an image because of bright object

Wavelength Calibration

What do you do with something that is always there but has no use for you? – Re-purpose it!

image

Having noticed that this peak was consistent at 5577.338, Astronomers decided that they would use this peak line in the data as a reference to calibrate their actual data. (known as ‘zero-point correction’).

This ensures that all the spectrum lines in the data are aligned and any errors that might have occurred during observation are corrected for.

Other lines ?

There are other lines at 6300,6363, etc which are sometimes as bright or brighter than the 5577 line that are also used for calibration.

If you are interested in learning more, the following are three papers that this post was inspired from and they dive deeper into more technical details that underlie this fascinating topic:

[1] Night-Sky High-Resolution Spectral Atlas of OH and O2 Emission Lines for Echelle Spectrograph Wavelength Calibration

[2] Mesospheric nightglow spectral survey taken by the ISO Spectral Spatial Imager on ATLAS 1

[3] Variability of the mesospheric nightglow sodium D2/D1 ratio

Have a great day!

Parallax method, 61-Cygni and the Hipporcas mission

It is trivial for most astronomy textbooks to illustrate the parallax method as follows:

This is absolutely fascinating, but it was really hard to find actual images of stars in books that illustrate this.

This is the proper motion of 61-Cygni, a binary star system over a span of couple of years.



61 Cygni showing proper motion at one year intervals

 

But Bessel discovered that in addition to this proper motion, 61-Cygni also wobbled a little bit from side to side because of the parallax during observation.

The following is a plot of the motion of 61 Cygni – A which beautifully  elucidates the proper motion and the effect of parallax (i.e the wiggle of the blue line with respect to the mean free path)

         Source

In addition, if you would like to actually play around with data for yourself, the The Hipparcos Space Astrometry Mission might interest you a lot. The mission was Launched in August 1989 and successfully observed the celestial sphere for 3.5 years before operations ceased in March 1993 employ

The documentation and the catalogue are fairly clear ,  instructive and easy to use. Have fun!

 

 

Using Complex numbers in Classical Mechanics

When one is solving problems on the two dimensional plane and you are using polar coordinates, it is always a challenge to remember what the velocity/acceleration in the radial and angular directions (v_r , v_{\theta}, a_r, a_{\theta} ) are. Here’s one failsafe way using complex numbers that made things really easy :

z = re^{i \theta}

\dot{z} = \dot{r}e^{i \theta} + ir\dot{\theta}e^{i \theta} = (\dot{r} + ir\dot{\theta} ) e^{i \theta}

From the above expression, we can obtain v_r = \dot{r} and v_{\theta} = r\dot{\theta}

\ddot{z} =  (\ddot{r} + ir\ddot{\theta} + i\dot{r}\dot{\theta} ) e^{i \theta}   + (\dot{r} + ir\dot{\theta} )i \dot{\theta} e^{i \theta} 

\ddot{z} =  (\ddot{r} + ir\ddot{\theta} + i\dot{r}\dot{\theta}  + i  \dot{r} \dot{\theta} - r\dot{\theta}\dot{\theta} )e^{i \theta} 

\ddot{z} =  (\ddot{r} - r(\dot{\theta})^2+ i(r\ddot{\theta} + 2\dot{r}\dot{\theta} ) )e^{i \theta} 

From this we can obtain a_r = \ddot{r} - r(\dot{\theta})^2 and a_{\theta} = (r\ddot{\theta} + 2\dot{r}\dot{\theta}) with absolute ease.

Something that I realized only after a mechanics course in college was done and dusted but nevertheless a really cool and interesting place where complex numbers come in handy!

 

 

ISS is the third brightest object in the night sky!

It often comes as a surprise to people when i tell them that the space station can be seen with the naked eye! Flying at 400 km above your head, the ISS looks like a really fast moving airplane in the sky.

The ISS isn’t brighter than the day sky and hence cannot be seen during the day. But in the night, it’s the third brightest object in the sky! It reflects the sunlight off the solar panels on its surface.

Spot the station!

If you would like to see the ISS for yourself, NASA ‘s Spot the station! is at your disposal. Register with your email address/mobile number and every time the ISS passes by your town/city, you will get a notification with the time, duration and inclination.

image

Have fun!

(Extras: There are mobile phone apps which you could use too, like the ISS detector satellite detector for android. At the end of the day all that matters is what is convenient to you.

ISS tracker– Real time tracking of the ISS)

Celestial Wonders- Binary Stars.

image

The twins of the stellar world are binary star systems.A binary star is a star system consisting of two stars orbiting around their common center of mass.When two stars appear close together in the sky, the situation is known as an “optical double”. This means that although the stars are aligned along the same line of sight, they may be at completely different distances from us. This occurs in constellations; however, two stars in the same constellation can also be part of a binary system.

image

Artist’s impression of the sight from a (hypothetical) moon of planet HD 188753 Ab (upper left), which orbits a triple star system( yes, a Triple Star system!). The brightest companion is just below the horizon.

image

Binary star systems are very important in astrophysics because calculations of their orbits allow the masses of their component stars to be directly determined, which in turn allows other stellar parameters, such as radius and density, to be indirectly estimated. This also determines an empirical mass-luminosity relationship (MLR) from which the masses of single stars can be estimated.

It is estimated that approximately 1/3 of the star systems in the Milky Way are binary or multiple, with the remaining 2/3 consisting of single stars.

The Brightest star in the sky is a binary.

image

This is true. When it was discovered in 1844 by the German astronomer Bessel, the system was classed as an astrometric binary, because the companion star, Sirius B, was too faint to be seen. Bessel, who was also a mathematician, determined by calculations that Sirius B existed after observing that the proper of Sirius A (the main star) followed a wavy path in the sky, rather than a uniform path. Sirius can now be studied as a visual binary because, with improving technology and therefore improved telescopes, Sirius B was able to be seen, although not for 20 years after Bessel had correctly predicted its existence.

Black Holes in a binary System ?

image

The term “binary system” is not used exclusively for star systems, but also for planets, asteroids, and galaxies which rotate around a common center of gravity. However, this is not a trick question; even in star binaries, the companion can be a black hole. An example of this is Cygnus X-1.

The universe is pretty amazing huh?…

The Miura Fold

.

The Miura fold is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Koryo Miura.

Why it is awesome?

The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat.

This property allows it to be used to fold surfaces made of rigid materials; for instance, it has been used to simulate large solar panel arrays for space satellites in the Japanese space program.

The fold can also be unpacked in just one motion by pulling on opposite ends of the folded material, and likewise folded again by pushing the two ends back together.

In the application to solar arrays, this property reduces the number of motors required to unfold this shape, reducing the overall weight and complexity of the mechanism.

Other cool stuff.

Miura folded maps. Snug it into your pocket when not in need and open it up in style when you are lost !

image

(Source : http://www.bun-sho-do.co.jp/english/nextg/miura-fold/ , wikipedia )

Mars: Red Planet, Blue sunset?

Mars has always been an interesting planet to us earthlings. The possibility of life, rovers leaving no stone unturned(literally), it’s demanding reddish appearance and now those breathtaking sunsets.Mesmerizing isn’t it ? But,

Why are martian sunsets blue?

image

Here on earth, sunsets are bright with Yellow, Orange and Red colors dazzling in the sky. During sunsets, the light from the sun has to travel a longer distance in our atmosphere to reach the earth.

Consequently, all the blue and violet light is scattered( thrown in various directions) by the particles in our atmosphere leaving behind only shades of yellow, orange and red, which is what you see. This phenomenon is known as Rayleigh scattering.

image

On mars, the reverse effect occurs. The martian dust is smaller and more abundant than on earth and it incidentally happens to be just the right size that it absorbs the blue light whilst scattering the red ones across the sky. This makes martian sunsets blue :).

Stay tuned, there is more space stuff coming your way.

( Source: http://io9.com/5906367/why-are-martian-sunsets-blue

Which would fall first in vacuum: A feather or a ball?

If you take a feather and a ball, and drop them simultaneously from your hand or from the top of a building what would you observe? Obviously the ball drops faster than the feather. But why?

Air resistance is the result of air molecules bombarding onto the object as it moves through the layer of air. The feather offers more air resistance and hence it falls slower.

Now you can up the ante and ask what if you remove the air resistance?

If you remove all the air molecules from the air,you would just get vacuum, a space devoid of any matter. With no molecules to bombard the object,

The feather and the ball would fall at the same rate as you can see in the animation. The demonstration was carried in the world’s biggest vacuum chamber.

( Extra: The same demonstration, but this time done on the moon :

image

Source video: https://www.youtube.com/watch?v=E43-CfukEgs

Have a good day!

Why did the Earth start spinning?

Our Solar System formed about 4.6 billion years ago when a huge cloud of gas and dust started to collapse under its own gravity.

As the cloud collapsed, it started to spin. Some of the material within this cloud gathered into swirling eddies and eventually formed into planets. As the planets formed, they kept this spinning motion. This is similar to what you see when skaters pull in their arms and spin faster. As material gathered in more closely to form a planet, like Earth, the material spun faster.

Why does the Earth still Spin?

To put it bluntly, the earth is still spinning because there are no forces acting to make it stop spinning! This is known as Inertia – an inherent law of nature.

Inertia is the tendency of an object to remain in motion unless and until acted upon by an unbalanced force.

( Source : http://coolcosmos.ipac.caltech.edu/ask/59-Why-does-Earth-spin-)