Tides - 6

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Although he didn't ask me for a Testimonial, I have no hesitation in saying "Newton is a Genius".

Thirty years ago I happened to read Stephen Hawking's book: "A Brief History of Time"

At the end of that book were 3 Appendixes, each with a photo and a short biographical sketch. 

These three all-time Geniuses (according to Hawking)  were:

1. Galileo 

2. Newton

3. Einstein

Obviously Hawking was being modest...he had implied that the next in the line was:

4. Stephen Hawking :)

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London in the 17th Century was hit by a plague (like Mumbai is now). And Newton fled to his village home with an orchard that had apple trees. And he was sitting under one of those trees, contemplating, like I was at Harry's often at IIT KGP (and getting hit by crows' shit).

And an apple got detached from its branch and fell down (many say on Newton's head...not true).

As Newton watched it he is reputed to have exclaimed:

"Aha! Gravity!"

Even little Ishani could have said it.

Newton, on the other hand, looked up and saw the disk of a pale moon.

And realized that Moon also was in free fall towards the Earth like that apple.

That is GENIUS!

Moon in Free Fall towards the Earth?

Question: Why doesn't it fall down like a meteor or an asteroid and hit the Earth?

Answer: Inertia (First Law of Newton).

Moon was given a tangential velocity round the Earth in its time.

There are three theories of Moon's relation with Earth:

1. Daughter:

A bit of Earth got detached from Earth and flew away 

2. Sister:

Both Earth and Moon were born about the same time

3. Spouse:

Moon was wandering and found herself close to the Earth and got sucked into a nearly circular orbit

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'Inertia' was the toughest for us to understand at our university.

1. Suppose a bird perched on a tree sees a worm on the ground. And jumps vertically down to catch the poor worm.

But Earth is spinning. A simple calculation shows that in the time the bird takes to descend, the Earth, the tree, and the worm would have gone forward about 30 feet. 

And the bird ought to miss her worm by about 30 feet.

But she doesn't ever...she always catches her worm

2. You don't have to travel all the way to New York by a Pan Am flight.

Just go vertically up in a helicopter and stay there hovering. And eventually, since Earth is spinning, New York would come right under your nose.

And then descend.

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Newton also gave a 'thought experiment' to show how Moon is always in free fall around the Earth but never falls down on the earth smashing us.

Take a cricket ball and throw it horizontally. 

It would be in free fall and would take a parabolic trajectory and fall on the Earth about 30 feet away from you (horizontal range).

Throw the ball with increasing speeds. Its range will keep increasing.

Throw it harder and harder.

It will fall 30 miles from you.

But, wait...Earth is not flat. It is curved, and the 'horizon' is only about a few miles away.

So, as the cricket ball tries to fall on the ground, the ground itself would evade it by bending.

The ball keeps on trying and trying and fails to drop on the ground.

Eventually the cricket ball would go round and round the Earth in an elliptical orbit (and would hit your back if you were not anticipating it).

You have launched an 'artificial satellite'!

Moon, likewise, became the 'natural satellite' of the Earth long long ago.

It is always trying to fall on the Earth but always misses it (by about 384,400 km...the radius of the Moon's orbit).

Don't throw your cricket ball any faster...it will escape into space once for all.

Rahul Gandhi (the fifth Genius) promised his voters that he would throw away their poverty at an 'escape velocity'.

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Once Newton realized that both his apple and the Moon are in free fall due to the same Earth's gravity, he came up with his famous 'inverse square law".

Even I could have discovered it...just a cooking up (కిట్టింపు).

All it required was taking a ratio.

He didn't need the mass of the Earth, the mass of the apple, the mass of the Moon, or even the value of his famous "Universal Gravitational Constant".

All of them cancel away.

All he needed was to time the apple's fall (Galileo had invented the principle of the pendulum clock), height of the tree, the 'height' of the Moon, and the time period of rotation of the Moon.

Of course he needed  an expression for the 'centripetal acceleration'.

That required Calculus.

And he invented it!

Genius!

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The first precise value of 'Newton's Universal Gravitational Constant' came a century after Newton.

It was measured by Henry Cavendish in a lab he constructed in his home.

That home-lab was terribly expensive.

Q: Where from did Cavendish (and other English Scientists) get their money for their costly experiments and explorations (geological mostly)?

A: A rogue called Robert Clive gave it to them.

...All of them had shares in a profitable thievery called the  "East India Company"

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To be continued

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శంకరార్పణం - 3687

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శంకరాభరణం సమస్య - 3687

“తేలును ముద్దులాడు బడతిం గని మెచ్చఁ దగున్ ముదమ్మునన్”

జాలిగ కోపమున్ విడిచి చక్కగ నవ్వుచు నాథునిన్ గనన్

పూలను దాల్చుచున్ జడను పొంకము మీరగ కౌగిలించుచున్

మేలుగ పచ్చ రూపమున మెల్లగ గాంచుచు ఛాతి మీదదౌ 

తేలును ముద్దులాడు బడతిం గని మెచ్చఁ దగున్ ముదమ్మునన్

పచ్చ = tattoo

(కంది శంకరయ్య గారి సౌజన్యంతో)

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Tides - 5

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"This is because tides in our seas are due to an interplay of the combined gravities of the Moon and the Sun.

In a sense they are the highly visible terrestrial events due to celestial bodies."

This is great!

"High tide and low tide occur twice a day one followed by the other about six hours apart.

Thus there are two high tides and two low tides alternating every day."

Oh! No! That is terrible!

Why so ?

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It is like this:

Suppose I am sitting on the rock on the beach of Vizagh, with the Bay of Bengal giving me company.

And it is midday on a New Moon Day (అమావాస్య; Amaavaasya).

Then the Sun and the Moon are aligned with each other more or less in a straight line above my head. Their gravitational forces on me and the sea are assisting each other pulling us towards them. My rock and I are fairly rigid bodies attached to the earth and do not tear us away towards the Sun and the Moon so easily...

But not so the sea water which is a fluid that can flow. So the sea water accumulates towards the Sun and the Moon and there is a bulge in the sea level. And the sea floods the beach. 

We have a high tide. 

Fine!

About 12 hours later, at my midnight, the Sun and the Moon have rotated (as I see them) and are almost overhead at a point on the other side of the Earth (antipode) where it is midday.

So there must be a bulge (and a high tide) there, and, since the sea by my rock is pulled away there flowing towards my antipode, my sea level must have a shrink (low tide).

But this is not what happens in practice:

My sea bulges again and we have another high tide although the Sun and the Moon are nowhere to be seen by us...they being above my antipode.

How come?

Strange!

That is not all...

Suppose my rock and my sea and I are sitting at midday on a Full Moon Day (పూర్ణిమ) when the Sun and the Moon are roughly opposite to one another...with the Sun on my head and the Moon on the head of my antipode.

I would expect then that their gravitational pulls of the sea by my side try to cancel each other to some extent; and my antipode as well as I should have a low tide.

But that is not what happens!

Both of us have high tides again (like on the New Moon Day).

How does one explain these anomalous tides?

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First of all we should note that none of the heavenly bodies is nailed to the heaven. All of them are free to move. And their motions are governed by the gravitation at their site (local).

Apart from gravity, their motions are not influenced by other forces...so Celestial Mechanics is simple :)

99% of their motions can be explained by Newtonian Mechanics and Newtonian Gravity (no need to invoke Einstein's Mechanics and Einstein's Gravity...except near blackholes).

Moon rotates around the Earth captured by it. Earth and other planets (along with their satellites) rotate around the Sun. Sun with  its extended family rotates around our Milky Way Galaxy. And our Galaxy rotates around other galaxies. And all galaxies slowly move by and large away from others (Expansion of the Universe).

All bodies that move only under gravity are said to be "freely falling".

Fortunately most of us on our Mother Earth do not experience free fall.

It was only in my Muthukur school days that I was jumping down for a fraction of a second from a low-hanging branch of a tree playing "Monkey Business".

The apple that fell down from its tree (Newton) is under free fall, ignoring air friction. 

The youth who springs from the diving board into his swimming pool is under free fall (Einstein).

The passengers in the lift undergo free fall if the cable of their lift suddenly snaps.

And the ditched lover jumping from the balcony of his 13th floor flat is under free fall.

Free falls never hurt anyone....it is the landings that do it.

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On the other hand, in our Earthly Mechanics, Gravity is just one of the forces. 

The bob of a simple pendulum moves under gravity plus tension.

The block on the inclined plane moves under gravity plus normal reaction plus friction.

There are no tensions and normal reactions in the heavens.

Indeed as I progressed from my first year to the final year labs in our university, gravity ceased to matter much at all.

It was only in our first year lab that we had Borda's Pendulum, Compound Pendulum, Kater's Pendulum, cantilevers loaded in the center or sides, and the viscometer which had weights falling under gravity plus viscous friction.

In the second year, we moved to Heat...Copper Voltameter, Stefan's Constant, Newton's law of Cooling, Planck's Constant etc, ignoring gravity altogether.

And then on to the Electricity Lab...Wheatstone's Bridge, Rayleigh's Bridge, Anderson's Bridge, Potentiometer etc

And then on to Optics...Newton's Rings, Fresnel Biprism, Lloyd's Mirror, Straight Edge Pattern etc.

And then on to Electronics...Amplifiers, Oscillators, Modulators, Demodulators, Superhet Receiver etc..

...None of which required Gravity...unlike our Celestial Mechanics in which we can  forget all these devils...

We the experimenters (trying to cheat) and the apparatus on its table  (trying to misbehave) were firmly grounded by the Normal Reaction and Friction....

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To be continued

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శంకరార్పణం - 3686

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శంకరాభరణం సమస్య - 3686

“తిట్టెడివారి కెల్లరకు దీవెనలిమ్ము శుభమ్ముఁ గోరుచున్”

రట్టును జేయగా మిగుల రాక్షసి వోలుచు తిట్లతోడనున్

గట్టిగ జుత్తు పట్టుకొని గాభర నొందక లాగి తెచ్చుచున్

పట్టుకు వచ్చి నాకడకు ఫక్కున నవ్వుచు నత్తగారినిన్

తిట్టెడివారి కెల్లరకు దీవెనలిమ్ము శుభమ్ముఁ గోరుచున్

(కంది శంకరయ్య గారి సౌజన్యంతో)

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Tides - 4

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"Time and tide wait for no man"...Proverb

There is a tide in the affairs of men
Which, taken at the flood, leads on to fortune;
Omitted, all the voyage of their life
Is bound in shallows and in miseries.
On such a full sea are we now afloat,
And we must take the current when it serves,
Or lose our ventures. 

...Shakespeare

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Tides are periodic bulging and shrinking of seas.

In the high tide sea level rises, and the sea floods the beach.

In the low tide the sea recedes far away from the beach.

High tides and low tides occur twice a day one followed by the other about six hours apart.

Thus there are two high tides and two low tides alternating every day.

High tides at times can be very impressive.

One night I was walking back to my home in Krishna Nagar by the road in front of the RK Mission in Vizagh.

There were no street lights and it was pitch dark...maybe New Moon (Amavasya).

Suddenly I found my feet wet. And I realized that the sea had swallowed the beach entirely, jumped over the low embankment in that spot, and was trying to swallow the road as well...like a hungry cobra.

And I had to take a non-existent sidewalk and cling to the trees and bushes and inch my way forward through those patches...not to get wet or lost...

At places where a river joins the sea, and the river's mouth narrow, the sea in its high tide can flow back vengefully into the river, reversing its course, and flooding its embankments far far into it. 

That is the Tidal Bore in rivers.

The leading edge of the bore is highly visible like a traveling hump.

This is a common enough occurrence in the river Hooghly by Calcutta....the bore having traveled inwards all the way from Ganga Sagar maybe.

The tidal bore can at times be so high that it could devastate the small boats sailing under the Howrah Bridge.

And then travel to Dakshineswar where Sri Ramakrishna Paramahamsa would be waiting on the bank with his team of followers in order to watch it. His abode was by the river Hooghly which he used to call reverentially: "Ganga".

And also scare the monks of Belur Math on the other bank:

https://timesofindia.indiatimes.com/videos/city/kolkata/watch-high-tide-causes-panic-in-belur-math-in-west-bengal/videoshow/68558540.cms

https://www.youtube.com/watch?v=C6XdTxyUH68

World's highest tides (about 50 feet) are seen in the Bay of Fundy (Nova Scotia):

Twice each day, 160 billion tonnes of seawater flow in and out of the Bay of Fundy — more than the combined flow of the world’s freshwater rivers! The Bay of Fundy’s tides transform the shorelines, tidal flats and exposed sea bottom as they flood into the bay and its harbours and estuaries.

https://www.youtube.com/watch?v=OP0cpXpw8yk

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Tides are complicated events. Their size and extent depend on the longitude, latitude, lay of the shore, seasons, and rivers flowing into the sea...

But science can now predict their timings fairly accurately...unlike earthquakes, tsunamis, and Didi's tantrums.

This is because tides in our seas are due to an interplay of the combined gravities of the Moon and the Sun.

In a sense they are the highly visible terrestrial events due to celestial bodies.

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In our university physics we heard of two pinnacles of precision:

1. Astronomical

2. Spectroscopic

1. Astronomical:

For instance we learned that medieval astronomers tracked the movements of planets over centuries accurately and recorded them. Copernicus used them to propose his heliocentric theory (planets, including our Earth, move around the Sun rather than the other way round) and so destroyed the primacy of our Earth, its pundits and politicians. Newton used his 'Inverse square Law of Gravitation' to account for the intricate motions of planets due to their mutual gravitational interaction, called perturbations. And predicted the next arrival of the Halley's Comet accurately. That was his crowning glory.

But Newton's Gravity Theory failed to account for a tiny tiny tiny anomaly in the motion of the innermost planet, Mercury, difficult for us to see unaided in our lifetimes, mostly due to the arrival of electricity and sky lights :)

Mercury was found to revolve around the Sun in an elliptical orbit (as predicted by Kepler and derived by Newton). And due to perturbations of the gravity of other planets, its orbital ellipse slowly slowly slowly rotates like in a rosette pattern.

Most of this precession of the perihelion of Mercury could be accounted for by Newton's Gravity Theory, except for a wee amount that came to be correctly calculated two centuries later by Einstein's Gravity Theory (wrongly called The General Theory of Relativity).

How tiny was the discrepancy?

It is mind-blogging (I had checked Einstein's calculations and gave them out as an MSc Project...along with the two other classical tests of Einstein's Theory):

It was 43" of an arc per century (hundred years)!

One second (") of an arc is 1/60 of a minute ('). One minute of an arc is 1/60 of a degree (deg). And a circle has 360 degs (when I heard last). 

How the hell could the Middle Age Western Astronomers measure and record it (while our Kalidas was busy writing his Meghdoot, as lovely a thing as any)?

2. Spectroscopic:

We had 6-hour labs in our Spectroscopy in our University at Waltair.

In our MSc Exam in 1963, for appearing in this lab, we had to wake up early to catch the first bus and reach the Lab by 7 O' Clock. And then for all of 6 hours we were stuck there (no coffee-breaks).

Most of those experiments involved taking emission spectra of carbon, copper etc sticks when they were lit up by arcs.

And we measured the wave numbers (frequencies) of the spectral lines we recorded on our glass plates (developing them in our dark room) using 7-figure log tables (4 figures were no use...not accurate enough).

That meant that the good old spectroscopists measured spectral lines of various elements and recorded them accurately to seven decimals (that was called 'Term Zoology' for fun, and youngsters like Heisenberg who invented Quantum Theory had it at their finger tips).

The latest measurement of the 'Fine Structure Constant' has an accuracy up to 14 figures!

Like "pi" was taught us to be 22/7, this 'fine structure constant' was first measured to be 1/137 and led to many hilarious "Magic Number Theories", all wrong.

It is nothing so simple. Its value a decade ago was:

The team in Paris measured the value of the fine-structure constant as 1/137.035999206, to an accuracy of 11 digits. The result appears in a study published in Nature.

And it agrees fairly well with the super-duper-hyper computer calculations of the Quantum Electrodynamics popularized by Richard Feynman.

Phew!

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To be Continued

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శంకరార్పణం - 3685

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శంకరాభరణం సమస్య - 3685

“సాఁకఁగ లేక బిడ్డలను సాకులఁ జెప్పెడి వాఁడె భర్తయౌ”

తేకువ మీర పెండ్లిగొని తీరిచి దిద్దెడి సాఫ్టువేరునన్

ప్రాకట మొందినన్ సతిని బంగరు బొమ్మవు నీవటంచునున్

వేకువనందు లేచి కడు ప్రీతిని బోవుచు మందు కొట్టులన్

సాఁకఁగ లేక బిడ్డలను సాకులఁ జెప్పెడి వాఁడె భర్తయౌ!

(కంది శంకరయ్య గారి సౌజన్యంతో)

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Tides - 3

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My first encounter with tides was hilariously humiliating.

It was a bright sunny winter morning in Vizagh with not a speck of cloud in the sky.

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Well, there, I am exaggerating. Bright and sunny is ok...but not 'winter'.

There is no winter either in Vizagh or Muthukur or any other south Indian coastal town. It is either 'hot and humid', or 'rainy and humid'.

The only woolens I saw in my school days in Muthukur were two.

1. My Nagpur Auntie brought what she called a 'woolen sweater' that she had knitted as a gift to my father. It was not a pullover, nor a turtleneck, nor a cardigan. It was like what we now call a T-shirt (without 'slogan'). Father wore it at once to show it off to Auntie, but grimaced, and took it off, saying: "Beautiful! Beautiful". He never wore it saying it was too hot and 'sweaty' (Humpty-Dumpty of Alice would say that is why it is called a 'sweater').

2. His uncle "Kashi Mama", who was a practicing 'Giant Panda' in Varanasi brought what he called a "బూర్నీసు" (rough cheap red woolen blanket) as a gift to his fond nephew. Father never used it...saying he was allergic to wool and the 'rug' was itchy.

And none of our classmates and friends in Vizagh ever wore sweaters, or shoes, or socks, or monkey caps, forget about rugs and rajais.

All this stuff I got to see first in Kharagpur. 

There I found the hands of most of the ladies of my North Indian friends always busy while sitting in front of TV or in a cricket stadium. They had balls of wool on their laps and were busy knitting pullovers for their pathetic hubbies and kids, while chatting away with their friends.

Once there was this musical performance in our Faculty Club at KGP. As usual I went late to the hall and found all chairs occupied by ladies while their hubbies were standing in the verandah gabbing and smoking. I found my friend Bidhan Mohanty standing behind his wife dutifully; and joined him. Mrs Mohanty was sitting on a chair in the last row, knitting a sweater for him (and listening to the music 2-in-1).

And I whispered in Bidhan's ear: "Your wife reminds me of Madame Defarge". 

And he burst out laughing. He had read his "Tale of Two Cities" which was all about the French Revolution:

The knitting represents the start of the Revolution. Madame Defarge knits a "Hit List" all day in the wine shop which serves as a list of people the Revolutionists must kill during the Revolution. 

Mrs Mohanty turned back and both of us shut our traps like a couple of turtles withdrawing into their shells:

यदा संहरते चायं कूर्मोऽङ्गानीव सर्वश: |
इन्द्रियाणीन्द्रियार्थेभ्यस्तस्य प्रज्ञा प्रतिष्ठिता ||

One who is able to withdraw the senses from their objects, just as a tortoise withdraws its limbs into its shell, is established in divine wisdom.

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Anyway it was a bright sunny cool morning in Vizagh. There were only 7 such mornings there in the whole year (starting Christmas and ending New Year), when one would love to sit down for a couple of hours in the sun and enjoy his sunbath.

I looked out from my window and found the sea as still as a millpond. No roar...just a hum. No waves. No huge breakers. And the water sparkling like a million jewels reflecting the sun.

I picked up my copy of "Man-Eaters of Kumaon" and walked down to the beach and to a rock just beyond the Scandal Point. This rock was about 7 feet high and had a flat perch on its top, ideal for sitting down and reading...my favorite haunt to escape the madding city crowd.

The beach was vast with the sea far away to about 50 feet.

I got up, sat, opened my novel and started reading it. It was about 10 in the cool breezy morning.

And I got completely lost in the charming world of strange and melodious names: 

Chamoli, Champawat, Haldwani, Devprayag, Rudraprayag, Pithorgarh, Tanakpur, Almora, Naintal, Tehri Garhwal....

Two hours passed by and I was through.

And I wanted to get down the rock and go home.

But found that my rock got submerged meanwhile to a height of about 5 feet by swirling sea water that must have encircled it in a silent embrace meanwhile.

There was no way I could jump into the water without getting fully drenched...pant and shirt.

Moreover I was not fully aware of my bearings...I may slip and fall down and get dragged into the sea. 

The edge of the beach was now about 20 feet away.

Luckily I spotted a few fisherman sitting and knitting their nets on the beach close to the road.

And I shouted and flailed my arms in a desperate gesture that must have been familiar to those smiling fishermen. 

One of those kind souls waded into the water and reached my rock. And stood by it and asked me to get up his neck, hang my feet round his chest, and hold his head firmly.

He knew every inch of the beach like the back of his palm.

And then he waded back to the shore with the precious load on his shoulders.

And bent his head down and asked me to jump off and get lost.

I paid him all of ONE rupee (good enough for a plate of upma, a dosa, and a plate of four poories with free side dishes of chutney, sambar and curry; and a cup of coffee to top them all,  in the Ajanta Hotel).

And I walked glumly back to the RK Mission Bus Stop, boarded a Sputnik Bus #10 and reached home wondering what happened to me and why:

"I wonder why.

I wonder why. 

I wonder why I wonder

I wonder why 

I wonder why"

....Feynman

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There was no Google then; nor an Encyclopedia Britannica that I could lay my hands on.

But I guessed I was caught in what I heard was a "high tide"

And since then tides fascinated me and the more I wondered the more they became mysterious, till I reached IIT KGP...and got the hint from Prof MS Sikand...Glory Be To Him...

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To be continued

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