Twinkle twinkle little star – How I wonder what you are !

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Astronomy – a simple science?

“Simplicity is the ultimate sophistication.” – Leonardo da Vinci.

Astronomy may not sound like a very simple science. But in reality, many things in astronomy require only basic fundamentals that we all learn in high school. The sky is a natural laboratory for astronomers and fundamentals of physics are used to study the properties of objects in space. To give a demonstration of this, we will take a look at how simple it is to get a rough estimate of the properties of a star which is probably billions of light years away from us.

How do we know about the stars

Even an astronomer having access to state-of-the art technology can obtain values of only two variables – apparent brightness of the star and it’s distance from us.

Apparent brightness and spectrum[1] can be measured and recorded by a variety of light sensitive devices. The distance can be obtained from simple methods like parallax. To demonstrate parallax, hold your index finger at eye level. Shut your left eyelid first (right eyelid open) and look at your finger, then shut your right eyelid and look at the finger. Your finger will appear to move against the backdrop of a more distant object such as the wall of your study room. This apparent motion is called parallax. Astronomers use a similar technique to find distance to the star. Astronomers make one observation each two times a year, when the Earth is on the opposite sides of the sun.

Now let’s go from what we can measure to what we can infer and calculate. We will have a look at how a star’s three most important properties – Luminosity, Surface temperature and the radius – are calculated. Brightness, spectra and distance can be used to obtain these properties.

Let’s first learn a little bit about these quantities and why we are interested in them. Luminosity is an important measure of brightness, which is the power of a star — the amount of energy (light) that a star emits from its surface. It is usually measured in terms of how much more/less bright a star is as compared to the sun. Surface temperature of a star is used for classifying the star into different types. The radius of a star is very important from the point of view of assessing the star’s evolutionary phases[2]. The equations for these quantities are what we learnt in high school or early college years. Let’s get a recap of those:

Equation for Luminosity:
L= 4πD2b
L= Luminosity of the Star
D = Distance of the star from Earth
b = Apparent Brightness
Equation for Surface temperature:
T =  0.0029  ⁄ λmax   
T = Surface Temperature
λmax = Maximum wavelength from spectra
Equation for Radius of Star:
L = σT44πR2
R= Radius of the Star

We already have the values of the inputs (D, b, λmax ). So calculating the outputs (L, T, R) is an easy task.

Astronomers: We work hard too!

Well, now you might say if stellar astronomy is just about three simple equations, then why are astronomers spending hours on research and taking thousands of measurements using precious telescope time? Well, it turns out that getting the initial measurements is not so simple.

When we look at the sky, the stars appear like they are distributed on a huge 2D black canvas. But in reality, there is space between us and the stars. Therefore it’s not uncommon that our view of the stars may be obstructed by some interstellar gas or dust cloud. When starlight passes through this interstellar cloud before reaching earth its spectra will get distorted. Now it’s a challenge to separate which part of the spectrum comes from the stars and which one from the interstellar cloud. This is a real problem and requires several observations. There are various techniques that astronomers use to separate the two. But all of them rely upon using what we know about the stars to infer which parts of spectrum belong to the interstellar cloud. After that astronomers can subtract that part of the spectrum to give them the spectrum of the stars. Once astronomers have learnt about the interstellar spectrum they can use this to correct spectra of other stars in that direction.

Overall, we can see that although the fundamentals are simple to grasp, the practical challenges in astronomy are immense and require a lot of ingenuity and also dedication to the goal of advancing our knowledge about the universe. And in our opinion, that’s what makes it so challenging.


Footnotes:
[1] When astronomers split the light beam coming from a star using a spectrograph (prism like device), the resulting collection of wavelengths of light is called a spectrum.
[2] A star goes through various evolutionary phases starting from a big gas cloud to a huge supernova explosion.  Right now, our Sun is in a phase called the ‘Main Sequence’ which is roughly in the middle of the two aforementioned limits.
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India-Pakistan…Why war may not be the solution

The spark for the fire..

26th November 2008, a horrifying day for the people of India. For three days, horror unfolded as people watched 10 armed terrorists ravage the Indian city of Mumbai by attacking some of its iconic landmarks. This attack which targeted people of all races, religions and cultures indiscriminately, brought India’s ‘financial capital’  to a halt. Military assistance was called in to stabilize the situation and many civilians lost their lives or were injured. After learning that the perpetrators were from a Pakistan based terrorist outfit Lashkar-e-taiba, most of India wanted only one thing – revenge against Pakistan. This was the breaking point for many Indians. A rage that had been boiling over for years because of frequent acts of terrorism (most of which had been attributed to Pakistan based terrorist outfits) now had its biggest outpouring.

The government was under immense pressure to mount an offensive against Pakistan and the terrorist outfits. But it didn’t do so and was widely criticized for it. Pretty understandable when one looks at the emotional turmoil that many Indians had to go through.Not waging war was interpreted as a sign of timidity.

Similar is the case with the North Indian state of Kashmir. It has been a disputed region between India and Pakistan for decades. Both nations claim a part of it which has led to many violent cross border incidents. Pakistan was once a part of India and the two nations have had a long history of violence since they split apart. Major part of Kashmir is largely under India’s control today but faces frequent insurgency from Pakistani militants.

Let us picture a hypothetical scenario where the Kashmir or the cross border terrorism issue leads to enraged public reaction and  becomes a catalyst for a larger conflict between two nations and India decides to attack Pakistan. Its important to remember that we are only discussing possibilities from one nation’s decision making perspective. A conflict in the region will most likely be critically damaging for all the players involved.

Analyzing a potential India-Pakistan war:

Any offensive started by India against Pakistan will most probably lead to Pakistan retaliating and beginning of a war. It is common knowledge that India has more troops and allegedly more nuclear warheads than Pakistan. So India is going to win the war. Sounds so easy, right ? Maybe it is. But there are many indications that it is never so simple. Lets dig a little deeper. We will concentrate on four major points-

The possibility of a ground battle

When it comes to a ground battle between the two countries, India definitely has the upper hand. India is probably much better prepared on the north western borders to repel any Pakistani attacks. The only problem can be Kashmir where the terrain can be a hurdle. But overall, starting a ground war won’t be a rational thing for Pakistan to do as they will only be playing into India’s hands.

The role of United States in Indo-Pak politics

United States has always looked upon Pakistan as a potential ally which can help it combat the Al-Qaeda and other terrorist/militant groups which are so prevalent across Pakistan’s Northwest. Any attack on Pakistan (like India attacking it) will cause Pakistan’s civil state to become even more unstable than it is now. Instability is a natural fuel for militancy to thrive in and we don’t think the US will be very happy with that. India has a lot of international relations with U.S and any kind of sanctions or pressure that the US puts on India could prove to be very harmful.

The potential role that China plays

For many years now, China has been a big ally of Pakistan mostly due to the the feuds that they share with India. China and Pakistan have been collaborating on a lot of military technologies and also nuclear power. Based on a report in Wall Street Journal, Pakistan and China recently agreed a deal in which China will sell two nuclear reactors to Pakistan. It is feared that China has collaborated with Pakistan on Nuclear defense technologies. However true this is, it is definitely worrying for India. Ties between India and China have long been characterized by mistrust. Tensions boiled over into a brief war in 1962, following which China gained control of a 14,600 square mile territory known as Aksai Chin. It’s not in China’s interest to start a war with India under normal circumstances. The repercussions are likely to be costly for China considering it has to maintain ties with rest of the world. But let’s say that there is still a small chance that China with its ally Pakistan might want to start a war with India. Or China can even try to exploit India’s vulnerability in such a situation and attack the disputed Northeast regions of India. In such a case things can go badly for India. India cannot afford to repeat the losses that it sustained in the Indo-Sino war in 1962.

The possibility of a nuclear war

Both India and Pakistan being nuclear armed nations, we cannot rule out the rather extreme (though not improbable) possibility of any conflict escalating into a nuclear war. Now according to International estimates, Pakistan has about similar number of nuclear warheads as India. So we can see that in this case, India is not an an advantage. Also Pakistan has the additional advantage of having a lot of uncertainty over how much control is being exercised over it’s nuclear arsenal and by whom.So it is going to be very hard for India to detect a potential launch. Consequently, the chances of some retaliation plan are greatly reduced especially if Pakistan manage to hit some very important targets where there is a stockpile of nuclear arsenal. India is not fully prepared for having a robust second strike capability when it comes to nuclear attacks. So as we can see, this is a scenario India would be looking to avoid.

Is the risk worth taking ?

We won’t go deep into math and risk functions; But we feel it is imperative for India to assess the risk of choosing the war option for minimizing the occurrences of cross border terrorism.

Society as a whole has a certain “well being” and bad events such as war or terrorist attacks reduce that well being (good events like better healthcare, infrastructure etc increase well being). From the above discussion, we can see that the potential risk for heavy losses in well being from a war situation is higher than that from more frequent random terrorist attacks against the nation. So this potential hostile approach might actually turn out to be far more damaging to India than the current sporadic incidents of terrorism.

Let it be noted that we are not advocating a “soft” approach to minimizing the risk of terrorist attacks. Making a country safe for its citizens is the duty of every government and same applies to India. The objective of this discussion is to impress upon the readers that the solution is not as simple as it is painted. Bill Clinton once described Kashmir as the “most dangerous place on earth”. It is going to require a lot of work to make it a “heaven on earth” again. And hopefully the solution won’t require guns.