Tides - 8

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"Sitting on that blessed rock near the Scandal Point on the Vizagh beach, I would see 4 tides every lunar month (two spring tides and two neap tides) on Amaavaasya, Shukla Ashtami, Poornima, and Bahula Ashtami.

And since my Earth is spinning around itself in 24 hours, I would see these high and low tides repeating every 6 hours.

Phew!"

At last we have succeeded in understanding the origin of ocean tides on Earth, somewhat.

Actually, the details of tides are infinitely more complicated.

What we have done is more like the Eka Shloki Raamaayan:

आदौ रामतपोवनादिगमनं हत्वा मृगं काञ्चनं 

वैदेहीहरणं जटायुमरणं सुग्रीवसंभाषणम् |

वालीनिर्दलनं समुद्रतरणं लङ्कापुरीदाहनं 

पश्र्चाद्रावणकुम्भकर्णहननमेतद्धि रामायणम् ||

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All of us know that our Earth, seen form outer space, is spinning lie a top. And we are clinging to its surface somewhat precariously.

Because we should experience a centrifugal force tying to throw us out into space. But we rarely feel it, because Earth's gravity pulling us towards its center overwhelms the centrifugal force.

That is because the spin of the Earth is so very slow...once in 24 hours. That makes the ratio o the two forces about a few parts in a thousand. Still, it can be detected by the lessening of the 'acceleration due to gravity'  at the equator compared to the poles. 

The theory of spinning tops in classical mechanics is very very complicated. The Guru-Chela duo, Felix Klein and Arnold Sommerfeld, used to go to the sea beach and collect pebbles of various shapes, spin them in their lab; and they came up with a 4-volume definitive text: "Theory of the Spinning Tops"!

John Perry's Demonstrations at the Annual Royal Society Exhibition (meant for lay spectators) can be found compiled in the fascinating booklet: "Spinning Tops and Gyroscopes" (I had read it with great gusto in the Central Library of IIT KGP).

Every child riding a merry-go-round in the Kid's Play Area feels the hilarious centrifugal force as soon as it is revved up. That is because the merry-go-round goes round once every second maybe (instead of once in 24 hours).

And all molecules (like the Ammonia molecule) spin themselves once in about a microsecond. So the quantum theory of polyatomic molecules can't do without incorporating the centrifugal and other 'ghost' forces, making an already complicated subject infinitely more complicated.

I happened to chance on the celebrated tome of Townes and Schawlow:

'Microwave Spectroscopy".

That was full of symmetric tops and asymmetric tops and stuff like that. That work of Townes led to the first Maser (the Ammonia Maser) and won him the Nobel for it.

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All of us who played with tops know that when spun fast on the ground, the axis of the top remains vertical ('sleeping top').

But soon, due to friction with the ground and air, the top loses its kinetic energy and its axis starts tilting towards the ground and goes round in a cone. 

This is called 'precession' of the top axis.

The cone's semi-vertical angle increases gradually. This is the 'nutation'. 

And finally the top topples and falls on the ground.

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Something similar (but not as catastrophic) happens with the 'spin axis' of our Earth as seen from space.

The axis doesn't remain static but precesses in the celestial sphere, with about 25 deg as the semi-vertical angle of its cone.

And the time period of this 'precession of the equinoxes' is about 26,000 years (I can wait).

It means that the present 'pole star' (Polaris) will no longer remain a pole star in a few centuries. That position is taken over by some other star in the heavens.

Till, after 26,000 years Polaris once again becomes our pole star.

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The theory of this 'precession of the equinoxes' is as complicated as any theory of the spinning tops...more so because our Earth is not a perfect sphere...more like an oblate spheroid (pumpkin).

There are many cosmic reasons why our Earth-Top precesses.

One minor actor is our oceanic tides.

The continual ebb and flow of the seas on the land against the friction between the beaches and the seas generates heat.

And this heat energy is lost by the Earth into space by radiation.

Also, the solid Earth itself is not immune to tides. Although we treated Earth as a rigid body, we know that 'rigid body' is an idealization...all bodies are deformable to some extent or the other.

That much for tides (for now)...

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