Monthly Archives: July 2004

The Belt and the Cloud

 

      Most of us think that the Solar system ends at Pluto. In fact most astronomers thought that this was the case. But then somebody asked the question: where from do the comets come from??? We will try to answer this question in this VERITAS and we will learn about worlds beyond Pluto.

      In 1950 a Dutch astronomer Jan Oort suggested that comets come from a vast reservoir of icy bodies at the distance of 50,000 AU( AU means Astronomical Unit. 1 AU is the distance from Earth to the Sun). About a year later Gerard Kuiper suggested that 50,000 AU is too far away for comets and that comets are placed just beyond the orbit of Neptune ( Neptune is placed at about 30 AU).

      Today we know that both these theories are true. There is a belt of icy bodies just beyond the orbit of Neptune. We call it the Kuiper belt. We know of atleast 70,000 objects in this belt each with a diameter of atleast 100 kilometres. Astronomers are sure that there are more.

And there are zillions of more objects with diametres between 10 and 50 Kms in this belt. The Kuiper belt extends from 30 to 50 AU. Many astronomers  are of the opinion that Pluto should not be called a planet but a Kuiper Belt Object(KBO). This is because of its small size and its funny rotation ( it does not rotate on a North-South axis but on a East-west axis i.e it rotates on its side).

        Most of the short period comets come from the Kuiper belt.

Helley’s comet is a short period comet( just 76 years) and it comes from the Kuiper belt.

The long period comets come from the OOrt Cloud. There are comets humans have seen just once. These comets might have the priod of thousands of years. When Jan OOrt observed these long period comets he realized that thay come from somewhere very far away. He also noticed another strange things: these comets come from any direction in space. These facts made him hyphothesize that these comets come from a spherical cloud about 50,000 Au from us. Note that all the planets and the Kuiper belt lie on one plane and this is the plane in which the equator of the Sun is at the centre. This is because the Sun’s gravity is strongest here. But at the distance of 50,000 AU the sun is just a small spec of light and thus the oort cloud is not located in a plane. It is spherical.

So we are surrounded by a spherical cloud of small icy worlds.

They are held in that spherical cloud by the gravity of Sun.

See how far Sun’s Gravity can be felt. The diameter of the Oort cloud is about 2 light years!!!! The sun’s gravity has trapped things even to a distance of 1 light year!!!!!!!!

      But wait a minute! How far is the nearest star? It is just 4 light years away. This OOrt cloud is affected by that star too. So every once in a while this star(Alpha centauri) perturbs an object of the OOrt cloud. Remember that the OOrt Cloud objects are very loosely bound to Sun’s gravity. So a small push by a passing star is enough to move them. When perturbed this object falls “down”.But where? It falls towards the sun. It is this object that comes hurling towards the sun that we call a comet. What a traveller. What a sight from Earth.   

      Short period comets are formed when a Kuiper Belt object is perturbed by one of the outer large planets.

      OOrt cloud and Kuiper belt are remains of the formation of the solar system. The giant planets Jupiter, Saturn, uranus and Neptune created a lot of left overs when they were being formed. Some of this debry was set into orbit and formed the Kuiper Belt. The rest of the debry way kicked out of the solar system. It however could not escape the gravity of sun altogether and went to form the OOrt Cloud.

      See the attached illustration of the Kuiper belt and the OOrt cloud. See how little the Sun is. And what a small portion of this entire thing is the solar system till pluto. Also see the spherical OOrt cloud surrounding the sun and planets.

 

      Friends, The earth is a small place in this grand scheme of things. It is no doubt our home but lets not restrict our thinking to just our little home. Lets explore beyond the farthest reaches of space and time. The human brain constantlyt searches for infinity.

Lets not deny it its pleasure:

 

            THE BRAIN is wider than the sky,

              For, put them side by side,

            The one the other will include

              With ease, and you beside.

 

            The brain is deeper than the sea,       

              For, hold them, blue to blue,

            The one the other will absorb,

              As sponges, buckets do.

 

            The brain is just the weight of God,

              For, lift them, pound for pound,       

            And they will differ, if they do,

              As syllable from sound.

 

                              ( – Emily Dickenson)

 

Kuiper3

Kanwar

 

 

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  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             

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Zeno’s paradox and the modern effect

 

      Zeno was a Greek philosopher who lived in 5th century BC. He belonged to the Eleatic school of thought. This school believed that the Universe is unchanging and any appearance of change or motion is merely an illusion. Zeno thought of about 40 “thought experiments” which are designed to show that motion does not exist.

     In one of these paradoxes there is a story of a tortoise and Achilles. The tortoise challenges Achilles to a race and claims that Achilles would be defeated if the tortoise gets a small headstart.

Achilles laughs. Now Achilles is a mighty warrior and is very fast and the tortoise is very slow. Achilles asks the tortoise “how much headstart do you need”. The tortoise says “10 metres”. Achilles laughs and says that that is nothing and will overtake and win the race in no time. The tortoise says that by using simple arguments he can prove that Achilles can never win. The tortoise says : “You say that you will cover the 10 metres of my headstart very quickly. But I would also have moved a little by then. Lets say that by the time you cover 10 metres I would have moved 1 metre. Now you will cover the 1 metre fast but I would have moved 10 cms. And so on… The distance between us will keep decreasing but it will never become zero. I will always be ahead!!!”. Achilles understands the tortoise’s argument and accepts defeat.

      In another paradox Zeno “proves” that an arrow shot from a bow cannot reach its destination. Because to reach the destination it must first cover half the distance. And to cover that it must cover half of that distance and so on forever. And since there are an infinite number of points between the start and end points so the distance cannot be covered!!! And thus motion does not exist!

      We of course know that motion exists and that we can move.

The Zeno effects were formed due to lack of knowledge of infinitisimals and limits which calculus corrected.

      After people realized that Zeno “paradoxes” are nonsense they lived happily for thousands of years. But then in 1976 this paradox raised its head again: in the quantum world! Two Indian scientists Mishra and Sudarshan published a paper in which they showed that a quantum system if measured continuously will NEVER change/evolve.

      In Quantum Mechanics a system evolves in time based on the Schrodinger’s equation. However if it is measured then it collapses into one of the stable states with a certain probability. Mishra and Sudarshan showed that if a evolving system( such as some atoms undergoing radioactive decay) is continuously measured then it may never evolve( decay). It may sound strange but if the laws of Quantum Mechanics are right then the Quantum Zeno effect HAS TO BE TRUE! ANd it is true.

It has been experimentally observed in several lab experiments.

      Let the initial state of a system be represented by |A> If left to itself this state evolves to another stable state |B> after say T secs. If I observe the system before T then there is a finite probability that the system may collapse into the initial state

|A> or the final state |B>. If I observe it just after it starts

evolving then the chances of collapsing to |A> are much more then collapsing to |B>. If I observe the system at very short time intervals then each observation will collapse it into the initial state

|A> and it would never get time to evolve into |B>. So if I measure the system continuously then it will never evolve.

 

      And there is another effect: The Quantum Anti Zeno effect. According to this effect a monitoring of another system( prepared in a different way) will cause an increase in speed of its evolution. THis effect is the opposite of the Quantum Zeno effect and this too has been observed in experiments.

      Welcome to the strange world of the ultrasmall. Life will never be the same again.

Kanwar

 

 

 

|======================================================|

  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             

|======================================================|