The big bang and my children

Sometime back I promised to give you one more reason why my children remind me about the universe. But, thanks to them, I could not get around to writing about it till today. That is the problem with children, you do not get time for much else. Don’t get me wrong. I am not saying parenthood is without its moments. The other day, I was carrying Aman around in a store, while my wife was looking admiringly at all the tablets that were on display. I was talking to him and in a bout of fatherly affection, I hugged him tight, and all of a sudden I felt a certain warmth envelop my heart. The problem with these moments are they are very fleeting. This time it ended with my wife telling me that the warmth was not from the inside, but because, Aman threw up some of the formula he just drank, onto my shirt. I digress.

Do you remember the term Entropy? I remember it from my Chemistry text book being defined as “Entropy is the measure of randomness in a system” accompanied by a diagram having two boxes, one in which small circles are arranged closely together on one side of the box, and the other box having these circles evenly spread out. The first one is supposed to have low entropy, because it is more ordered, while the second one has higher entropy, as there is less order in it. As with rest of Chemistry, I had no clue what it meant. I vaguely remember wondering, why this is even considered an important concept, but was practical enough to memorise it since it was an easy definition, and could earn me a couple of marks if it came up in my examination.

A few years back when I actually learnt what entropy meant I was blown away. In many places, entropy is defined in terms of orderliness. The higher the orderliness, the lower the entropy . A common example is that of a room neatly arranged, with all the things in their places. If you do not take any effort towards the room for some time, it will soon end up in an unordered state, what with your leaving a bowl here, a book there, a shirt on the couch, a drinking cup elsewhere and so on. Another example given is on the lines of dropping a little bit of ink into a glass of water. Initially the ink is focussed at the spot where it was dropped, but slowly it spreads out turning the entire water blue. In both these cases, the room, or the glass full of water, initially there is low entropy (high orderliness), then the entropy slowly increases (orderliness decreases). (I know that this definition of entropy is confusing, so I will try to use orderliness more frequently in the rest of this post, occasionally translating it into entropy.)

The examples are given to explain one of the fundamental laws of physics: second law of thermodynamics, which is that the entropy of a closed system will never decrease. By closed, they mean a system that does not interact with any other object outside the system. And the examples of the room and a glass of water, is meant to tell you that a room never gets organised on its own (unless you put in some effort), and though you will see ink spreading out in water uniformly, you will never see all those ink molecules come together as one blob in any part of the glass of water. But these examples are merely analogies. Not really an example of entropy. For, if you really did nothing to the room, say you locked your house and went on a vacation, the room would be as it is when you return. The example of ink in water, can be turned around with the example of oil in water. If you drop some oil into water, stir it well, the oil will spread. But once you stop stirring, the oil will accumulate on the surface of the water.

Further, this definition of orderliness stuck somewhat odd to me. After all, who decides what orderly is. If I think a spilt cup of milk on my couch is an integral feature of an orderly room, then surely orderliness can increase. So, this was never really convincing to me. Thankfully, there is a better definition.

Imagine this. You heat some water in a bowl, and you see steam coming out of it. The steam is hot. And so is the water. Have you thought of heating some milk with this heat from the steam, and the heat of the bowl of water? After all, we were told that energy can be neither created nor destroyed. So we should be able to use that energy again. If you try, you will notice that you can achieve some heating of the milk, but not really much.

The question is, can energy be recycled? The problem is that there is useful energy and the not-so-useful energy. For energy to be useful, it has to be focused in a very small area. When you heat a bowl of water, you do not lose energy. Only that it becomes more spread out. As steam and as heat in the water. The more spread out it becomes, the less useful it becomes as an energy source.

Thus an easy way to think of Entropy is to think of the amount of useful energy in a system. The way this energy and orderliness can be coupled is this: If energy is arranged in an orderly fashion, it is useful energy. If it is spread out in a random manner, then nothing much can be done with it. So if you want to increase orderliness in a place A, say, to get all those atoms in a particular arrangement, then you need to spend some useful energy elsewhere drawn from a place B. And always, the quantum of orderliness gained in place A, is less than the orderliness you lost in place B. Which means, in the overall perspective orderliness always goes down. Going back to our confusing definition this means entropy will always go up.

Two improbable arrangements of atoms

What you see above are two orderly arrangements of a gazillion number of atoms (of course, so are you and me). These atoms could have been arranged in a gazillion to the power of gazillion number of other ways. But very few combinations will actually form a human being that can grow, eat and function purposefully. Thus this very high orderliness in my house should mean orderliness must have reduced somewhere else. Where did my children steal that orderliness from?

It comes from the sun. In fact all the orderliness on earth comes from the sun. It is the energy of the sun that gives us all our life. So it is the useful energy of the sun that we are converting into useless energy. The energy from the sun has high orderliness, low entropy. The energy that we release (as heat) has low orderliness, high entropy. And the closed system I am talking about is the entire universe. Our universe as a whole has a finite amount of useful energy. At some point in future, all that useful energy will be lost. So, even if we could be immortal, there is a point after which you cant eat to get energy, because there are no plants. No plants because there is no sunlight. No sunlight because, there are no stars. No stars because energy is not focused at any point any more anywhere in the universe. It is all spread out in such a manner, that the entire universe has one consistent, very cold, temperature. At that point, nothing can be done. No turning back. Life cannot exist any more.

I know it sounds all bleak, but that future is very far away. We have bigger worries like the sun dying out in the next 5 billion years. So, the universe ending up with maximum entropy need not keep you awake at night. But entropy is important because, it is one idea that seems to explain why time always flows from past to future and not the other way (more on it some other time). Another interesting aspect is that, if entropy always increases towards the future, then that means, our universe must have begun in the past with very low entropy. That is why we are able to have so much useful energy. It is as if the universe is like a clock that has been wound up, and is slowly unwinding. At some point it will unwind completely and all that is left is a clock that does nothing. So how did the big bang start off the universe with low entropy?

I really do not have an answer for that (though scientists know it). But what fascinates me is that it is this low entropy start that big bang gave to the universe making life possible in this universe. You can read a short story by Isaac Asimov on this topic here.

Einstein shows the way

One of the first things that drew me to physics was the theory of relativity. It is so counter intuitive that it caught my imagination right away. After all relativity shows us that time travel to the future is indeed possible, provided you travel fast enough, and who can resist that. But this theory is by no means restricted to just some abstract physics. It is absolutely essential for GPS to work. This is what I touch on in my latest article for the New Indian Express.

Here is a video that explains the same.

Bend it like Einstein

Einstein’s theory of General Relativity is considered revolutionary because it changed our ideas of both space and time. With this theory, space became a trampoline curving under the weight of heavy objects, and time became personal, with each of us having our own version of time. But when he proposed this theory in 1915, it did not become known to the common man immediately. That had to wait for 1919 when there was an experiment confirming what Einstein’s theory had predicted.

We all know that light travels only in a straight line. That is why we cannot see a TV running in the next room since the wall in between prevents the TV’s light from reaching us. One of the consequences of Einstein’s theory is that you can, see an object even though your line of sight to the object is blocked by a barrier.

Imagine you are watching a TV with 2 of your friends, sitting on your either sides. Now, suppose your spouse, wanting to grab your attention, comes and stands in front of you hiding the TV from your view. Your two friends can continue watching the TV, because there are rays from the TV directed at your friends too which are not blocked by your spouse. In this situation there is no way you can watch TV without either you or your spouse moving.

But when you consider a similar situation on a cosmic scale, things are different. Imagine a star far away from Earth. But suppose there is a black hole in between the earth and the star blocking our view. Would you be able to see the star? Our experience with the TV tells us that we cannot see the star. But actualy you can see it; that too not once but multiple times at the same instant (as shown below).

Multiple images of the same star at the same time. (Picture from Wikipedia, originally by NASA)

What happens is this. The light that comes from the distant star towards you is blocked by the black hole and you cannot see it. But, the star is sending out light in all the directions, and some of it is directed at your neighbors too. But since the black hole is a massive object its gravitation attracts the light that was going away from the black hole. But that light is not completely absorbed. So what ends up happening is that the path of the light that started off towards your neighbors, is bent slightly so that it eventually reaches you. It is as if, the light is taking a slight detour to avoid being pulled in by the black hole.

Light from a star bending around a massive object (Picture from Wikipedia, originally by NASA)

Since the light comes from the side of the black hole, we would see the star as if it is by the black hole’s side and not behind it. Moreover, since such light would have started off in all the different directions, you can see light all around the black hole bending towards you. Thus what you see is multiple images of a single star. In many cases, what we observe is only a brightening of the star since the light that was meant for different directions is grouped and directed towards the observer.

This phenomenon called Gravitational lensing was the key experiment. It is called lensing, because a lens too alters the direction of light. The amount of this bending that relativity predicted was different from that of what was predicted by Newton’s theory of gravity. Only when this test was done, was the theory experimentally confirmed and the theory shot into limelight.

Re-testing super luminal neutrinos

If you missed it, the news is that the CERN experiment which observed neutrinos travelling faster than speed of light, is being done again. The goal is to eliminate one kind of possible error from the experiment.

I will try to explain what the error is, very briefly. What happened in the initial run was this. They had beamed 10²⁰ protons (that is one followed by 20 zeroes, a 1oo billion billion), that collided into atoms to produce neutrinos. The number of neutrinos eventually detected was 16,000. These neutrinos, the scientists observed, reached the detector, 60 nano seconds (a nano second is 1 billionth of a second) ahead of the estimated time (the estimate was based on the speed of light).

The crucial point was that these 10²⁰ protons were not released at the same instant. They were released as one single pulse, that spanned more than 1000 nano seconds. The detection of the neutrinos was also a spread. So what was measured was the average release time of the 10²⁰ protons and the average detection time of the 16,000 neutrinos. But, we don`t know whether the detected 16,000 neutrinos were from protons that were released early in the 1000 nano seconds pulse or in the later part of the pulse, or were they too spread out in an average manner. If the source protons of the detected neutrons were spread out evenly in the initial 1000 nano seconds pulse, then the observations are correct. This is important since the neutrinos were detected only 60 nano seconds ahead of their scheduled arrival, which is very small compared to the duration of the initial pulse. Thus, it is possible that due to some unknown, all the 16000 neutrinos observed could have been from the later part of the initial pulse, thus invalidating the average starting time of these neutrinos.

This is what is being checked now. What the scientists are planning now, is to send multiple pulses of 1 to 2 nano seconds duration, instead of one single pulse of 1000 nano seconds. Moreover, in between these pulses, there will be a gap of 500 nano seconds. So there will not be any confusion on which is the source pulse of the detected neutrinos. Since the pulse duration of 1 to 2 nano seconds, is far less than the supposed early arrival period of the neutrinos (which is 60 nano seconds), this test should verify if the the results observed were indeed true.

I learnt a good deal about the experiment from these blog posts by Ethan Seagal, who explains the intricacies with a lots of pictures. His posts usually have a lot of pictures which are very helpful in visualising what he says. His post on this re-run have some very good pictures explaining this pulse duration problem and the possible bias of it. Have a look.

It could turn out that in this re-run, neutrinos arrive on time and not 60 nano-seconds ahead, as was previously thought. In that case, the whole thing can be scrapped, and we can get back to our work. But if this re-run confirms the earlier finding, there is still a possibility of a systematic error, which can be detected only if other teams of scientists replicate the observations. This re-test will take a few weeks. So it wont be long before the results are out.

More on the faster-than-light neutrinos

I had previously mentioned the news that an experiment in CERN has suggested that some neutrinos are travelling faster than light. If you want some perspective on it, you can refer to two articles, one by Victor Stenger and another by Sean Carroll, both physicists and popular writers.

The beauty of the whole thing is that the experimenters themselves admit that they could be wrong. That is one of the strengths of science. The process involves looking at all results skeptically, and look for evidence. Ask for confirmation and re-check. Science actively works at proving others wrong and thus, what we end up with is only those ideas that have withstood numerous attempts at falsification. That is what makes it such a good method of acquiring knowledge.

Back to the topic, both the authors are saying that the result is probably the result of a systematic error, but also add that even if such a violation was confirmed to be true, it will not disprove Einstein much.  I learnt something there that I didnt know before. It seems, Einstein only says that you cannot make a particle travel at the speed of light, but if some particle is already travelling at the speed of light or more from the beginning(?), that does not violate Einstein’s equations.

Einstein’s equations fully allow for particles to travel faster than light — provided they never travel slower. Physicists have speculated about such objects for years. They are called tachyons. Many searches have been conducted, with no significant signals until now.

Einstein showed that it was impossible to accelerate a particle moving less than the speed of light (in a vacuum) to the speed of light or higher. Similarly, a tachyon cannot be decelerated to or below the speed of light. Only massless particles, such as photons, travel at exactly the speed of light.

Says Victor Stenger and continues:

So, if confirmed, the reported result from CERN or any future observation of superluminal motion will not lead to the overthrow of Einstein’s theory of relativity. Its significance will be to overthrow the distinction between cause and effect. At the worst, Einstein might be faulted for taking causality a little too seriously.

How does this happen? Let us try this simple thought experiment. Imagine that a ball could be thrown at a speed faster than the speed of light. Imagine a scenario similar to something as seen below. A is throwing a ball at B and the whole process is observed by E.

Can effects precede causes?

Let red line be the path of the ball from A to B. Since as per our assumption, the ball travels faster than the speed of light. Let us assume that this motion from A to B takes 9 seconds (note that B is very close to E).

Let the green line be the line of vision of E looking at A throwing the ball. This information needs to reach E for him to know that A has thrown the ball. Let us assume this takes 10 seconds (less than the nine seconds of the ball since the ball is travelling faster than the speed of light).

Let the purple line be the line of vision of E looking at B receiving the ball. Since B is very close to E, this information reaches E in just half a second.

Now you can see what happens. Once the ball leaves A’s hands, it reaches B in 9 seconds. The information that B has caught the ball reaches E in half a second. That is, E sees B receiving the ball in 9.5 seconds. But the information of A having thrown the ball, reaches E only at 10 seconds. So, to E, it appears that the cause, A throwing the ball, appears after the effect, B catching the ball. This is the problem with superluminal objects.

But then again, Sean Carroll, in another post, argues that even faster than light particles will not violate cause and effect relationship. Frankly, it is all over my head. But there is one thing that I firmly understand.

The universe is positively weird.

Note: For more details on the experiment, you can also look at this webcast from CERN where the scientists have presented their findings. I am yet to watch it, it is almost 2 hours long.

Eight, not nine.

That is the number of planets in our Solar System. I know we have all been taught that there are nine planets. That is what the CBSE, still says, as can be seen from page 22 of this activity book. But in 2006, the International Astronomical Union(IAU) decided to remove Pluto from the list of planets thereby officially reducing the number of planets to eight. Pluto is now only a dwarf planet. Let us see what the IAU had against Pluto.

Pluto was discovered in 1930, more than 85 years after the discovery of the previous planet, Neptune. But Pluto has always been an oddity in the list of planets. For one thing, its orbit was weird.

Pluto's orbit (in red). Notice how it crosses the orbit of Neptune (the outermost blue orbit)

From the top view, you can see how Pluto’s orbit crosses Neptune’s orbit. No other planet has an orbit like this. So, there are times when this planet is closer to the Sun than the Neptune.

But that is not all. If by the previous paragraph, you were wondering, why Neptune and Pluto with criss-crossing orbits, did not collide into each other, there is another oddity of Pluto that is hidden when seen from the top. The problem is that while orbits of all the other planets lie almost on the same plane, the orbit of Pluto alone, is tilted by about 17 degrees. Look at the two side-on pictures below, to see what I am saying.

Looking at the orbits on the plane of revolution of the 8 planets. Pluto's orbit is tilted.

Looking at the orbits along plane of revolution of the Pluto's orbit. The orbits of the eight planets appear tilted.

The other thing odd about it was, that the 8 planets discovered so far, fell into two families. The 4 planets closer to the Sun: Mercury, Venus, Earth and Mars, were rocky planets. They were made mostly of rock and metal and hence were called Terrestrial planets. The next 4 planets: Jupiter, Saturn, Uranus and Neptune were primarily made of gases. These latter 4 planets are also referred to as gas giants. Pluto was made of rock and ice, but it did not belong to the family, its neighbour Neptune belonged to.

But what most embarrasses Pluto is its ridiculous size. Look at this picture from NASA.

Planets and other objects, scaled to size. Pluto is just barely visible. Note that the distances are not scaled.

It is so small, that its mass is less than one-fifths of that of our moon. Of course, mere difference in size would not have been much of a problem, since the Earth too is puny, when compared to Jupiter. But Pluto’s moon, Charon, was discovered in 1978 and it was half of the size of Pluto itself (Pluto now has four moons). For contrast, the size of our own Moon is 2% of that of the Earth. Soon many other bodies were discovered beyond Neptune, having sizes comparable to that of Pluto. This made astronomers realise that Pluto did not belong to the planets, but was part of a different group whose members were being rapidly discovered. Finally the worst happened. Eris was discovered in 2005.

Eris is a celestial body which orbits the Sun, and its mass is 25% more than that of Pluto. This was the first object discovered orbiting the sun that was more massive than Pluto (of course, apart from the other 8 planets). This posed a dilemma. Either Eris should be added as a planet, and along with it many other bodies, or drop Pluto from the list of planets. The definition of what actually constitutes a planet, became crucial, and hence in 2006, the IAU met, to decide on a formal definition. In that meeting, the IAU laid down the following as the eligibility criteria for a planet. From wikipedia:

The definition of planet set in 2006 by the International Astronomical Union (IAU) states that in the Solar System a planet is a celestial body that:

1. is in orbit around the Sun,
2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape)
3. has “cleared the neighbourhood” around its orbit.

The first 2 points are clear and Pluto satisfied both. But the third one was its undoing. What the third rule means is that the body should be the dominant (in terms of mass) object in its vicinity. This Pluto was definitely not, since similar sized objects were present near it. Thus Pluto lost its status as a Planet. Pluto joined the group called dwarf planets, in which it is the second largest, with Eris being on top.

Interestingly, the whole debate was sparked off, when a planetarium in New York (Hayden Planetarium) prepared an exhibit in 2000, with only eight planets, leaving out Pluto. The brain behind this was its director, Neil De Grasse Tyson. Here is what wikipedia says about him.

As director of the Hayden Planetarium, Tyson bucked traditional thinking to keep Pluto from being referred to as the ninth planet in exhibits at the center. Tyson has explained that he wanted to look at commonalities between objects, grouping the terrestrial planets together, the gas giants together, and Pluto with like objects and to get away from simply counting the planets.

Neil Tyson is an amazing science communicator. His interest science and his enthusiasm in communicating both make him a tremendous person. I recently saw a video of his. A must-watch. It was informative, and absolutely hilarious. Here is the video for you. His talk (more of an interview) starts 15 minutes into the video and goes on for 1 hour. Trust me. You wont regret the time spent watching the video. Look out for the last point he makes in his talk. It is disturbing, but also fascinating.

Note: I got the first three pictures from a free simulation software, Celestia. I recommend you too download and install it. It is fun.

Neptune was discovered only this year

Do you know that Neptune was first discovered by us, less than a year ago. It is shocking, is it not, considering what we have been taught in our school, but it is true. Let me explain.

Neptune was discovered in 1846. As of today, it is the outermost planet of the Solar System after Pluto was declared not to be a planet. It is, on average, 30 times as far away from the Sun, as the Earth is from the Sun. Since the Earth is, about 150 million kilometres from the Sun, that means Neptune is roughly 4.5 billion kilometres away.

A picture of Neptune taken from Voyager 2 mission. The original can be downloaded from http://photojournal.jpl.nasa.gov/catalog/PIA02210

The interesting thing is that since it is so far away, it takes about 165 Earth years for it to complete one revolution around the Sun. Now you might wonder that, if the planet is 30 times as far away from the Sun as the Earth is, then it should take about 30 Earth years to complete its revolution. Then, why is Neptune taking 165 years to go around the Sun?

The answer lies in that, our expectation is valid, only if both Earth and Neptune are travelling at the same speed. But, that is not the case. Earth is going around the Sun at a speed of 30 kms/second (pretty good speed, isn’t it?) while Neptune is orbiting the Sun at 5.5 Kms/second. Since it is about 5.5  times slower (30 / 5.5  kmps = 5.5) than the Earth, its time to make one orbit would be 5.5 times longer than our usual expectation of 30 Earth years which means it would take about 165 (30 x 5.5 = 165) years, which is what is its correct orbital duration.

But its distance has not deterred us from reaching out to it. NASA’s Voyager 2 mission, has gone closest to Neptune on August 25, 1989 and it took about 12 years to reach Neptune from Earth. But that spacecraft will eventually go out of the solar system and into interstellar space. The FAQ section, tells me that this could happen in about 2020, but by then, it will exhaust all its supply of energy to power its instruments. After that point, neither will it be able to move on its own, nor will we be able to communicate with it. It will be lost forever. These spacecrafts will be the first human-made objects to go out of the Solar System. You can track the progress of these spacecrafts here.

Now let us come back to our topic. On July 12th 2011, 5 days from now, Neptune will complete one revolution around the Sun, counting from the day we discovered it in 1846. We count one year as the time it takes us to go around the Sun once. Measuring the Neptunian year the same way, not even one Neptunian year has passed since we discovered it. Now, tell me. Is the title justified or not?

Who discovered the planet going in reverse?

All planets rotate on their axes while orbiting their Sun. Ours does too. But the axis on which our Earth rotates is tilted an angle of about 23.4 degrees, as can be seen by the way globes are mounted. And it is this tilt that causes the seasons. This tilt also leads to scenarios where near the Northern and Southern poles, we can experience 24 hour days and 24 hour nights (visiting one of these places at such a time, is on my things-to-do-before-I-die list).

But interestingly, the planet Uranus is tilted at angle of 97.7 degrees. If we imagine the usual plane of rotation of planets around our Sun as a table top, then the Earth will be seen as a spinning top whose axis of rotation is slightly tilted. In comparison, Uranus must be seen as lying flat on the ground rotating on its side. That is, the axis of rotation of Uranus is roughly along the plane of its rotation around the Sun. To see why that is interesting, imagine how day and night will be on that planet. When the axis of rotation of the planet is directed towards the Sun, then one half of the planet will get continuous day light. The other half is completely in the dark (this is just an extreme case of our planet having continuous days and nights near the poles during 2 seasons). During the two other seasons, its day-night pattern is similar to that of a normal planet. Uranus is, in that sense, unique.

But a newly(?) discovered planet that I read about in Times of India, a few days back, is unique in a different way. Normally a planet goes around the star in the same direction as the direction in which the star spins. That is all the planets travel in the same direction around the Sun. This is because, during the formation of the planetary system, all planets arise out of the same cluster of particles. These particles aggregate to form planets. Hence they all rotate in the same direction. But the new planet discovered rotates in a direction opposite to that of the direction of the spinning of the Sun.

This planet was discovered using the same technique as we discussed last time. The cause for this reverse motion is not very clear and still remains an open question. But the article itself is somewhat odd. The article refers to an astronomer, Daniel Bayliss, from Australian National University. When I googled for his name so that I could read more about this news item, I saw that all the news items refer only to Indian newspapers like this, this, and this.

Confused as to why I did not find any international news items, I searched with the planet name which was WASP-17B (BTW, WASP stands for Wide Area Search for Planets. The star around which it rotates is called WASP-17, which is about 1000 light years away from us.) and I saw many news items, but they were are dated in the month of August 2009. These were from the big news sites like National Geographic, BBC and New Scientist. And they all credit the discovery to scientists in the UK. The planet has a Wikipedia entry too.

It is curious that a planet that was discovered a couple of years back is being touted as a discovery again (at least that is what it appears to be unless I am missing something). When I went to the website of the Australian National University, I saw this press release about the planet. It is from this press release that a news agency prepared the news item which was used by the newspapers. But the press release also had contact details of the astronomer. So I emailed him a couple of days back asking for a clarification. I have not received a reply so far.

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UPDATE (Jun 19th 2011): The scientist replied to my email a few days back, saying that the initial article was based on a paper which was only speculative of the reverse orbit of the planet and that his work covered a full transit and confirmed that the planet was indeed going in reverse. But the news reports were definitely messed up. The Times of India Report says, “now astronomers have stumbled onto one that goes the wrong way”, which clearly suggests that the planet itself was a new discovery.

NASA’s Kepler mission

NASA is searching for Earth-like planets in a specific area of the Milky Way galaxy, the galaxy to which we belong. This is being done by putting a spacecraft outside the atmosphere of the Earth. Even as you are reading this, the Kepler spacecraft is collecting brightness information from about 100,000 stars. This information will then be analysed to find out if there are any planets orbiting it.

The technique used is explained in this animation. What they do is essentially this. They continuously observe the brightness of the stars. If a planet moves across a star (called a transit) then the planet will block some of the light that comes out from the star and hence the brightness will go down. After the planet has passed, the brightness will come back to its normal level. It is these drops in brightness that will tell us that some planet is rotating the star being observed.

Of course a solitary drop in brightness does not suggest a planet. A planet is confirmed only if there are multiple transits, each having the same amount of drop in brightness, the same duration of drop, and a constant interval between the drops.

But the reason why I am writing this post is to show you the picture below. Click on it. The enlarged picture is worth spending some time looking at.

Planets discovered by Kepler Spacecraft

These are the 1235 candidate planets that were identified till March 2011. The second row gives a picture of the Earth so that the rest can be seen relatively. But if you thought that the picture was the Earth, then join the club. No, the picture is that of the Sun. As discussed above planets are observed in transit against the background of their stars. Here, the bright disk is the Sun. Do you see a dark dot in that disk? If it is not very clearly visible click on that picture and look at the full size pic. Now the dot is visible, right? That dot is…

No, neither is that the Earth. That is Jupiter, the biggest planet of our solar system. If you really want to see the Earth, download this full resolution picture that NASA has uploaded to flickr. It is 9.3 MB in size. But me being the large hearted soul, I have downloaded it and cut out that part alone for you to see it below.

Earth, Jupiter and the Sun

Do you see the Earth now? I still recommend that you download that full resolution picture. It is fun.

Now, coming back to the Kepler mission. One interesting point about this is that the drop in brightness can be observed only if the orbit of that planet is aligned along our line of sight. If not the planet will not obstruct our view of that star and hence no drop in brightness will be observed.

I will let the Kepler FAQ take over here.

For Kepler to detect a transiting planet, its orbit plane must be lined up with our line of sight. Most of the time, the extrasolar planets’ orbital planes do not line up. For Earth-size planets around Sun-like stars, the chances of randomly oriented orbital planes being in the correct orientation for Kepler to see a transit is about 0.5%. That is why the design of Kepler called for a very wide field telescope to be able to observe more than 100,000 stars. If all those stars had Earth-size planets, about 500 (100,000 x .005) would be in the correct orientation to transit. Statistically, we can infer that every planet Kepler detects represents hundreds more planets that are out there but not detectable due to inopportune orbital orientation.

Thus, if we have discovered 1235 planets, then there must, about 245,675 undetected planets out there. There are many more such interesting pieces of information on their FAQ page. Spend some time there to see what humankind is trying to do.

But if any of you reading this is thinking of moving to one of these planets once we exhaust our energy supplies here and pollute it sufficiently enough to render it useless for human habitation I am sorry to say that there is bad news.

The stars that Kepler is observing are in the range of a few hundred to a few thousand light-years away. One light year is about 6 trillion (6,000,000,000,000) miles.

In plain English, the theoretical minimum to reach even the closest of these stars is a few hundred years. There you go (pun half intended).

Sidereal

This time, we will learn both some Science and a new word in English. We will see what the word sidereal means. In the process, we will learn something new about Earth.

But let us get there slowly and begin with one basic question. How many rotations does the Earth make on its axis in a single day? Sounds like a stupid question, right? After all, is not the very definition of a day, based on the time taken for the Earth to complete one rotation? That is, if the Sun is on top of your head today, the time taken for it to again be at the same position is what we call a single day. Yes, the definition of a day is the time taken for the Earth to come back again to the same position with respect to the Sun. But what is interesting is that Earth makes more than one rotation in a day. Let us see how.

By definition, the Earth revolves around the Sun once a year, that is 365 days. But for understanding how Earth does more than one rotation to complete a day, let us consider for simplicity, that the Earth takes only 4 days to go around the Sun. Keep in mind that after a rotation the Earth gets back to the same position as it was at the beginning of the rotation. So earth will have to go through the following stages to complete a rotation. To see the effect of rotation, I have coloured 2 halves of the Earth in two different colours.

Picture - 1. Different stages of rotation

 

This is pretty straightforward and elementary. But keep this image in mind when we look at the next picture.

Assuming, that one day is one rotation (which is incorrect as I am trying to convince you), given below is the position of the Earth with respect to the Sun, on all these 4 days at the end of each rotation.

Picture - 2. How the Earth would be if it rotated only once each day, and completed a revolution in 4 days

One way to look at picture-2 is the normal way, that is to look at it from your perspective. The other way is to look at it from the sun’s perspective. All the positions A, B, C and D look the same to us, but as you can see, at position A, parts of both the blue and green halves are exposed to the Sun, but at position B, only the blue half is exposed to the Sun, similarly at position C, the other parts of the 2 halves are exposed, and at position D, only the green half gets to see the sun.

At position B, the green half is completely hidden from the Sun. But since a day has passed, and our assumption was that 1 day is 1 rotation, should not the same parts of the Earth be exposed to the Sun again, since one rotation is over? But that does not seem to happen. Therein, lies the problem.

For the Earth to be in the same position with respect to the Sun (which is more important to determine the time of day, than it being in the same position with respect to us), one rotation is not sufficient. To see how much extra is needed look at picture – 3.

This is how it should ideally be, for the Earth to be looking at the Sun the same way, at the end of each day. At position B, though we see only the green half (the blue half is hidden from us), the sun is able to see parts of both the blue and green halves (a little bit of visualisation on your own is needed here).

Picture - 3. Ideally, this is how a 4 day revolution should happen. With the Earth showing the same face to the Sun at the end of each day.

But to come to position B, the earth has to make an extra quarter rotation (refer to Picture-1).

The extra quarter rotation it needs to make is because, in that one day, the earth has done 1 quarter of its revolution around the sun (remember in our example, it takes 4 days to go around the Sun).  Since it has made a quarter revolution, it has to make a quarter rotation extra to get the Earth back in the same position with respect to the Sun.

Thus, the earth should have rotated a quarter rotation more, at the end of a day, for it to be at the same position with respect to the Sun, since that is when the green and blue halves are again exposed to the Sun. As in Picture – 2, a single rotation does not suffice. Thus, a day would not mean 1 rotation but 1 + 1/4 rotation.

So 1 day≠1 rotation.

QED.

The Earth’s revolution around the Sun is the key here. Since the Earth keeps moving around the Sun (apart from its rotating on its own axis) the way it is exposed to the Sun keeps changing. Thus rotation has to compensate for this change caused by revolution. Thus one rotation is not sufficient for a day.

Now coming back to our real Earth, which takes 365 days to complete a trip around the sun. In this case, the Earth will complete 1/365 ths of a trip (revolution) in a day. So the Earth has to make an extra 1/365 rotation on its axis for it to be at the same position again with respect to the Sun.

Thus 1 day = 1 rotation + 1/365ths of a rotation.

I forgot something. Wait a minute, let me recollect. Ah, yes. Sidereal. I had told you I would explain what it is, and we are almost there. Throughout the post,  I kept saying that the Earth must be at the same position with respect to the Sun, and not with respect to “us”. But who are “us”? Imagine you are on a star other than the sun. From there if you see, the Earth will be in the same position after just 1 rotation itself. It does not need any extra time, since the Earth is not revolving around the star from which we are looking at it. Thus, with respect to that star, a day is equal to 1 rotation (not exactly, there too, day lengths will change for each star, but it is a good approximation for the purpose of this article).

Now we have arrived. Sidereal means, with respect to any fixed star. The sun cannot be a fixed star, because relative to us, it moves. But the stars other than the Sun are relatively fixed. Thus a sidereal day is about 23 hours 56 minutes, which is, less than the average solar day (which means a day with respect to the sun) of about 24 hours.

A small teaser to end the post. If the Earth is rotating in the opposite direction as it is rotating now, then revolution would be helping rotation to complete a day, so to say. That would mean that a day would require less than one rotation. That is, some of the rotation needed to be achieved for one day, is contributed to, by the revolution. Thus even before a rotation is complete, the Earth comes back to the same position as it was a day before. In such a scenario, a solar day is shorter than a sidereal day. Try thinking that out yourself.

With the pictures that are present above for our Earth, and imagining how that will change if the direction of the Earth’s rotation changes, this hypothetical situation, too, must then become as clear as, if I may say so, day.