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What if? [Q&A]

I had previously mentioned a technique called order-of-magnitude estimation that scientists of all stripes find extraordinarily useful, and Atul of Canara College asked me what that meant.

One of the most important characteristics of doing science is that scientists look to work on problems that can be solved. There is no point in wasting years and years of effort on pie-in-the-sky problems that no one knows what to do next to get closer to solving it. But how can you know whether something can be solved or not before it has been solved?

What one does is to set up a simplified version of the full problem, and work out the arithmetic for an approximate case. For example, to be able to launch satellites into orbit, you have to know the mass of the Earth. But you don’t need to know it accurate to the gram to figure out what kind of launch mechanism you will need. You only need to use numbers within a factor of a few of the right values to get a very good idea of what the problem looks like. The process of working that out is the order-of-magnitude estimate. It helps you define the boundaries of the problem and take the first step towards a solution. Of course, having an order-of-magnitude estimate is not a guarantee that the problem will be solved, but without one, it definitely cannot be solved.

Randall Munroe (of XKCD fame) is writing up a weekly column with brilliant examples of order-of-magnitude estimates. It is called What If?, and has so far dealt with questions like like what happens if you threw a ball at relativistic speeds, what if you put together a mole of moles, can you move the entire human population off the planet, and so on. Highly recommended reading!

ಶುಕ್ರ ಸಂಗಮ

೨೦೧೨ನೆಯ ಜೂನ್ ೬ನೆಯ ಬೆಳಿಗ್ಗೆ, ಭಾರತದಲ್ಲಿ ಸೂರ್ಯ ಹುಟ್ಟುತ್ತಿರುವಾಗ, ಒಂದು ಅಧ್ಭುತ ದೃಶ್ಯ ಕಾಣಿಸುತ್ತದೆ. ಸೂರ್ಯನ ಮೇಲೆ ಒಂದು ಚಿಕ್ಕ ಚುಕ್ಕೆ. ನೋಡು ನೋಡುತ್ತಿದ್ದಂತೆಯೇ ಸೂರ್ಯನ ಮುಖದ ಮೇಲೆ ಜಾರುತ್ತದೆ. ಸುಮಾರು ೧೦:೩೦ ಗಂಟೆಗೆ ಪೂರ್ತಿ ಹೊರಟುಹೋಗುತ್ತದೆ.

ಇದು ಶುಕ್ರ ಗ್ರಹ. ಭೂಮಿ ಮತ್ತು ಸೂರ್ಯರ ಮಧ್ಯೆ ಅಡ್ಡ ಬಂದು ಹೋಗುತ್ತದೆ. ಇದೂ ಒಂದು ತರಹದ ಸೂರ್ಯ ಗ್ರಹಣ, ಆದರೆ ಸೂರ್ಯ ಪೂರ್ತಿ ಮುಚ್ಚಿಹೊಗಿರುವುದಿಲ್ಲ. ಇದನ್ನು ಟ್ರಾನ್ಸಿಟ್ (ಎಂದರೆ ಮುಂದಿನಿಂದ ಚಲಿಸುವುದು) ಎನ್ನುತ್ತಾರೆ. ಹಿಂದೊಮ್ಮೆ ೮ ವರ್ಷಗಳ ಹಿಂದೆ, ೨೦೦೪ರಲ್ಲಿ ಆಗಿದ್ದು, ಈ ಹೊತ್ತಿನಲ್ಲಿ ಆದಮೇಲೆ ಮತ್ತೊಮ್ಮೆ ಆಗಬೇಕಾದರೆ ಒಂದು ಶತಮಾನ ಮೀರಬೇಕು.

ಈ ಘಟನೆಯ ಬಗ್ಗೆ ಬಹಳಷ್ಟು ವಿಷಯ ಸಂಗ್ರಹವಾಗಿದೆ www.transitofvenus.org ಎಂಬಲ್ಲಿ. ನೀವಿರುವ ಜಾಗದಲ್ಲಿ ಎಷ್ಟು ಹೊತ್ತಿಗೆ ಸಂಗಮ ಶುರುವಾಗುತ್ತದೆ, ಯಾವಾಗ ಮುಗಿಯುತ್ತದೆ, ಇದನ್ನು ತಿಳಿಯಲು transitofvenus.nl/wp/where-when/local-transit-times/ ಎಂಬಲ್ಲಿ ನೋಡಿ.

ಜಗತ್ತಿನಾದ್ಯಂತ ಖಗೋಳ ವಿಜ್ಞಾನಿಗಳು ಮತ್ತು ಹವ್ಯಾಸಿಗಳು ಈ ಸಂಗಮವನ್ನು ಉತ್ಸಾಹದಿಂದ ನಿರೀಕ್ಷಿಸುತ್ತಿದ್ದಾರೆ. ೧೭ನೆಯ ಶತಮಾನದಲ್ಲಿ ಇದರ ಮಹತ್ತನ್ನು ಗುರುತಿಸಿದಾಗಿನಿಂದ ಪ್ರತಿ ಶತಮಾನದಲ್ಲಿಯೂ ಇದು ಆದಾಗಲೆಲ್ಲಾ ಇದನ್ನು ನೋಡಲು, ಅಳತೆ ಮಾಡಲು, ಇದರಿಂದ ಸೌರವ್ಯೂಹದ ವಿಸ್ತಾರವನ್ನು ಅರ್ಥ ಪಡಿಸಿಕೊಳ್ಳಲು, ವಿಜ್ಞಾನಿಗಳು ಪ್ರಪಂಚದಲ್ಲೆಲ್ಲಾ ಪ್ರಯಾಣಿಸಿದ್ದಾರೆ, ಪ್ರಯಾಣಿಸುತ್ತಿದ್ದಾರೆ.

ಈ ಶುಕ್ರ ಸಂಗಮದ ಬಗ್ಗೆ, ಟಾಟಾ ಮೂಲಭೂತ ಸಂಶೋಧನಾ ಸಂಸ್ಥೆಯ, ರಾಷ್ಟ್ರೀಯ ರೇಡಿಯೋ ಆಸ್ಟ್ರೋಫಿಸಿಕ್ಸ್ ಕೇಂದ್ರದ, ನೀರಜ್ ಮೋಹನ್ ರಾಮಾನುಜಮ್ ಮತ್ತು ರೇಷ್ಮಾ ಬರವೇ ಅವರು ಒಂದು ಉತ್ತಮವಾದ ಚಿಕ್ಕ ಪುಸ್ತಕವನ್ನು ಬರೆದು ನಿದರ್ಶಿಸಿದ್ದಾರೆ. ಇದನ್ನು ಭಾರತದ ಬಗೆಬಗೆಯ ಭಾಷೆಗಳಿಗೆ ಅನುವಾದಿಸಲ್ಪಟ್ಟಿದೆ; ಕನ್ನಡಕ್ಕೆ ಗೀತಾ ಕೈದಾಳ ಗಣೇಶರವರು ಅನುವಾದಿಸಿದ್ದಾರೆ. ಇದನ್ನು ಓದಲು, ನಿಮ್ಮ ಕಂಪ್ಯೂಟರಿಗೆ ಇಳಿಸಿಕೊಳ್ಳಲು, mutha.ncra.tifr.res.in/ncra/for-public/transit-of-venus ಅಥವ transitofvenusncra.wordpress.com ಎಂಬಲ್ಲಿಗೆ ಹೋಗಿ. ಕನ್ನಡದ ಅನುವಾದವನ್ನು ನೆಟ್ಟಗೆ ಇಳಿಸಿಕೊಳ್ಳಬೇಕೆಂದರೆ transit_of_venus_ncra_kannada_hires.pdf ಅನ್ನು ನೋಡಿ.

Ludi Saeculares: the Transit of Venus

On June 5 (or June 6, depending on which time zone you are in) of 2012, Venus will be seen from the Earth passing over the disk of the Sun. This is not only a rare event, but also one which has been of great historical importance in figuring out how big the Solar System is. A number of people all over the world, both amateurs and professionals, are making preparations to observe this event. Go to www.transitofvenus.org for a summary of what is cooking. You can even download an app on your smartphone to participate in a worldwide effort to time the transits.

The transit of Venus always occurs in a pair, separated by 8 years. The next pair then repeats a century later. This year’s transit happens to be the second of this cycle’s pair. The previous one occured in June 2004. The next pair will occur in December 11 2117 and December 8 2125.

The reason for this odd periodicity lies in the geometry and dynamics of the Solar System. First, note that the orbital period of Venus (i.e., a Venusian year) is 224.65 days, and for the Earth of course it is 365.24 days. So in the time that it takes the Earth to go around the Sun once, Venus would have done so 1.6 times. This ratio is approximately 13/8. That is, after the Earth has done 8 full orbits, Venus would have done 13, and both planets would be back where they started relative to the Sun.

Of course, during these eight years, Venus would have crossed the Sun-Earth line 13 times, so we should have seen 13 transits, right? No, because the orbit of Venus is tilted by 3.4 degrees relative to that of the Earth’s. It’s orbital plane cuts across Earth’s along a line (called the line of nodes) which the Earth happens to cross in June and December. Now, the diameter of the Sun as seen from the Earth is only half a degree, so for Venus to get in between the line of sight from the Earth to the Sun, it can be at most a quarter of a degree away from the orbital plane of the Earth. So transits of Venus can only occur when Venus is close to the line of nodes. As we have seen, if it happens once, we will have to wait 8 years for the next one.

But then why does it not keep happening every 8 years? Why is this the last transit of our lifetimes? Well, first of all, the 8 year period is not exact, and Venus shows up at slightly different locations every cycle. Second, there is a slight drift in the line of nodes as the orbit of the Earth circularizes. So the Sun-Venus-Earth line will not have quite reached the exact same configuration as the previous conjunction, and will have lagged a little bit, and Venus will not be at the same position for transit as before. After another 8 years, it will have drifted sufficiently far away that it no longer transits the disk of the Sun. But as it continues to drift, by approximately half a degree every 8 years, it drifts up its inclined orbit for 3.4 degrees and back down again to the other node, in about 14 8-year cycles, and so in slightly more than a century, we can expect the pair pattern to repeat.

Here is a nice 2-minute explanation, with paper plates, of how it works (from transitofvenus.org/):

Space Math [try it]

I came across this brilliant collection of math problems in a variety of practical settings in the context of space exploration and astronomy. It is a fantastic resource for teachers setting up realistic math problems. The site is called Space Math @ NASA. There is even a page with the problems sorted by NASA missions and programs.

Fundraising

With a major Science Fair behind us, we at CREATE Gurukula are now setting our sights on our next goal. To start construction on the school buildings. In order to begin, however, we need to raise funds, and the amount needed is beyond the individual capacities of the CREATE members.

We therefore ask you go to our Donations page and contribute to the best of your ability.

Thank you!

If you are a United States resident, know that CREATE Gurukula is a 501(c)3 organization, and your donations are tax deductible.

CREATE STEM2 Fair 2011 – Photos

Photos from

STEM2 Fair 2011 – Results

The winners of the various competitions at the First CREATE STEM2 Fair, held on Dec 31, 2011, at the FMKMC College, at Madikeri:

ESSAY CONTEST

Juniors: Implementation/Importance of hygiene in local communities

I – Rishira S. M., Lions Nursery and Primary School, Gonikoppal

II – Chandan D.C., General Thimmaiah Public School, Madikeri

III – Roohani B., Lions Nursery and Primary School, Gonikoppal

Seniors: Nuclear Energy – pros & cons

I – Poojitha Uthappa, Lions High School, Kalthmad, Gonikoppal

II – Yamini K.L., Murnad High School, Murnad

III – K.V. Yashaswini, Triveni English Medium School, Virajpet
QUIZ CONTEST

Juniors:

I – General Thimmaiah Public School, Madikeri

II – Shantinikethana Primary School, Kodagarahalli

III – Sarvadaivatha High School, Arvathoklu

Seniors:

I – St. Michael’s High School, Madikeri

II – Sri Rama Trust English Medium School, Napoklu

III – Lions High School, Kalthmad, Gonikoppal
MODEL BUILDING

Juniors: To build the tallest tower with soda straws

I – Lions Nursery and Primary School, Gonikoppal

II – General Thimmaiah Public School, Madikeri

III – Shanthinikethana Primary School, Kodagarahalli

Seniors: To build a functional school model using cardboard and paper sheets

I – Sarvadaivatha High School, Arvathoklu

II – St. Joseph’s High School, Madikeri

III – Shanthinikethan High School, Kodagarahalli

Cash prizes for 1st, 2nd, and 3rd place finishers, ranging from Rs.1000/- to Rs.6000/-, as well as consolation prizes of Rs.1000/- each, were awarded in all categories.

CREATE STEM2 Fair 2011

The CREATE Team successfully ran their first major operation, the CREATE STEM2 Fair, on Dec 31, 2011. Here is a preliminary report by a rather satisfied sounding Jagadeesh Moodera:

Happy New Year! … the Fair went very well – successful! … There were 17 schools participating and 200 students, including three that morning… In my view it was WAY WORTH ALL EFFORTS. It was lovely to see the whole action. We pulled it together!!!!

… Gen Thimmaiah School bagged quite a few awards. So also Lions in G’koppa. The kids had great time. They were all very enthusiastic and already look forward to the next one. The quiz masters were Dr.Narasimhan, Karthik, Akshay and Hari Prasad. Modeling was a hit as well.

We provided them lunch as well as coffee/tea both in the morning and evening.

As you can imagine the workload was really huge. Jagannath and his students rose up to the occasion splendidly.

Update 1/4: Some photos from Hari Prasad: https://plus.google.com/photos/111125312661145247284/albums/5692651012725133025

Update 1/21: Results here — blog.creategurukula.org/2012/01/stem2-fair-2011-results/, and more photos here — blog.creategurukula.org/2012/01/create-stem2-fair-2011-photos/

But what is the Universe expanding into? [Q&A]

It is probably the most common question astronomers encounter: “Fine, you say that the Universe is expanding. OK, I buy that. But what is it expanding into?”

There is really no good way to answer this because the correct answer, that it is not expanding into anything, that there is no outside to the Universe, simply doesn’t make any sense to the questioner, and just sets up a recursive mystification: if there is no outside, what is it expanding into?!

The problem is, that is not how we look at it, and there is a disconnect in how the mathematics is set up and how it gets translated to plain English.

To begin with, people have an intuitive, common sense idea of what expansion means. When you see something expanding, that is, literally see it with your eyes, what you see is a change in the size of an object which has a well-defined boundary that is gobbling up more and more of whatever medium it is located in. The key words here are size, boundary, and medium.

But the Universe is everything that there is. It has no spatial boundary, or edge, where it stops being the Universe and starts being something else. So what is really going on?

It is probably fair to blame Einstein for this. His genius lay in realizing that it is not possible to describe the structure of the Universe in totality, but it is perfectly possible to describe it in locality. You can be very precise in saying how two nearby points in space-time behave. That is what the General Theory of Relativity is: a description of the metric of space-time over small distances. All cosmologists do is take this metric and extrapolate it as much as they can given what we have seen of the Universe. So when they say that the Universe is expanding, what they really mean is that the metric is changing.

Think of it this way. At any given instant, it is easy to imagine the Universe as everything there is. Now imagine you can draw a grid of lines on it to define a spatial, 3D coordinate system. The lines are just the paths along which light would travel. Now pick a couple of points in this grid and measure the spatial distance between them. Now blink, and look at the Universe in the next instant. It looks pretty much the same, but if you measure the distance between the two points you had picked out before, it will be slightly different, slightly stretched. Locally there is more space that light needs to traverse to get from here to there. But even in this new instant, the Universe is still everything that there is. You see how that works?

The bottom line is that this is not a material expansion we are talking about, i.e., not an expansion of stuff, but a change in the geometric properties of space-time.

Commentary [meta]

I have noticed a rather large uptick in comments in the recent past, most of them saying they liked these posts. Thank you. Our goal here is to educate, and to spur curiosity. These posts are deliberately designed to not be the final word on any subject, but to give the non-experts and the learners an easy path pointing to more detail.

That said, I would like to emphasize that the comments here are moderated, and will be limited to those that contribute materially to the posts to which they are appended. If you would like to communicate with us, you may send us email at blog @ creategurukula . org