Science - The way I understand it

Why Moon rises 50 minutes later everyday ?

2009-03-06T11:37:00.000-08:00

[Note: Many of you may be already knowing why. But there is no harm in reading this article and checking out whether what I say is what you know :) ]

You would think - 'whats so special about this question ? The speed of rotation of earth and the speed of revolution of the moon around earth are relative to each other in such a way that moon rises 50 minutes later everyday'. This however does not explain why '50 minutes' and why 'later' everyday and not earlier ? Another answer you may find in books or on the web is "Earth rotates around itself in 24 hours, and moon takes about 29.5 days for one revolution round the earth - so divide 24 by 29.5. That's right answer, but still it does not throw any light of 'why' and 'how' aspects of the original question.

If you think a bit hard, you will realize its not that hard to figure out the answer. 50 minutes is the average time by which moon rise is delayed everyday. Depending upon where you are located on earth, the time can be less or more than 50 minutes. Why so ? That's because the plane of revolution of earth around the sun and that of the moon around the earth are at different angles. Please see the diagram below (I have modified the original diagram that's available at wikipedia.org):

The moon's plane of revolution around the earth is tilted with respect to earth's plane of rotation (around itself) by about 29 degrees. Had the orbit of moon's revolution been co-planar with the plane of earth's rotation (in other word's had moon circled around the earth in earth's equatorial plane), the moon- rise and moon-set times would be same along all the places which fell on the same longitude. In addition, all the places on earth would have experienced the same delay (of 50 minutes) in moon-rise time everyday. But since the planes are oriented in the way they are, the daily 'delay' in the moon-rise time is different at different places on earth and they average out to be about 50 minutes.

Also, moon's orbit around the earth is a bit elliptical (and not circular) with perigee (point of elliptical orbit closest to center of the orbit) being 3,63,104 km and apogee (point farthest from the center) being 4,05,696 km. The average distance of moon from earth is about 384,400 km. Let's assume a circular moon orbit to keep our calculations simple.

Let's now turn to the answer to the core question of this article. Why 50 minutes later ? Mind you, earth completes one rotation in 24 hours. That is, 360 degrees in (24 X 60 = 1440) minutes. This means earth takes 4 minutes (divide 1440 by 360) to rotate through 1 degree. The direction of rotation is from west to east. Moon revolves around the earth in the same direction - from west to east. Moon takes about 29.5 days to travel one complete cycle around the earth. That is, it travels 360 degrees in 29.5 days - which comes to around 12.20 degrees per day (Which is about 0.0085 degrees per minute. Go figure out how)

Now refer to the following diagrams. They show moon's revolution around the earth as seen from earth's 'North' pole. When seen from north pole, the earth would appear to be rotating counter-clockwise. The moon also would appear to be moving around the earth in counter-clockwise direction. The diagrams show positions of moon with respect to earth on two consecutive days.

Lets say, on Day 1 at 6:00 pm, the city that you stay in, is at point A on earth when it sees moon rising at it's eastern horizon (so 6.00 pm is the moon-rise time). The earth (and hence your city) is traveling west to east, i.e., counter clockwise as seen from top (north pole). So is the moon. But since earth is spinning much faster than the moon, it passes past the moon swiftly enough to cause the moon to rise to it's east and set to it's west within span of approximately half day.

Consider next diagram which represent earth and moon positions exactly after 24 hours - Day 2 at 6:00 pm. At this instance, your city which has advanced through 360 degrees during past 24 hours would again find itself at point A.

But moon has advanced by approximately 12.2 degrees in counter-clockwise direction around the earth (we've already seen how). In order for your city to see moon rise at its eastern horizon, it has to travel an additional distance of 12.2 degrees to arrive at point B. We know earth rotates at about 1 degree in 4 minutes. So it would take an additional of approximately '12.2 X 4', which is 48.8 minutes to see the moon rise at its eastern horizon. Got it ? But we said its 50 minutes.

Consider this: When your city is at point-A on Day-2, the moon has already advanced by 12.2 degrees. No moon-rise for you at point-A. By the time your city advances another 12.2 degrees ( 48.8 minutes) to reach point-B, the moon will have advanced additionally by approximately 0.40 degrees (Remember, the moon is continuously advancing - about 0.0085 degrees a minute. So 0.0085 X 48.8 = 0.40 approximately). So after your city has arrived at point A, in order for it to see the moon rise, earth has to advance by a total of 12.2 + 0.40 degrees, which is almost 12.6 degrees. So in all earth will have to rotate for 12.6 X 4 = 50.4 minutes in addition to completing one rotation (24 hrs) so that your city can see it's moon rise on Day-2. And don't forget, the moon's orbit is elliptical and not circular. This has to be factored in to find out the exact delay in moon-rise time. But it averages out to around 50 minutes per day.

Authored by: Mandar Garge

E = MC2: PART 1: What should we understand from it ?

2008-11-22T11:32:00.000-08:00

You will find lot of articles about this equation on the internet. This is my attempt to put in my own words, what I have understood out of this revolutionary phenomenon called E = MC²

E = MC²: The most famous equation from Albert Einstein as a part of his work on 'Theory of Relativity'. In this equation relating Mass and Energy, E stands for 'Energy ', M for 'Mass' and C for the 'Speed of light in vacuum'. One of the simplest and tersest equations ever formulated but in the world of Physics, it has unleashed an impact inversely proportional to its size. But what does it really mean?

Section A :

Lets look at each of these terms E, M and C:

What is 'mass' ? Every matter, object or a thing has mass. But what is 'Matter' ? - 'Matter' is anything that is made up of atoms and molecules (matter is not just the things we see. Air or oxygen or any other gas is also 'matter'). Anything - solid, gaseous or liquid - which takes up space and has volume is 'matter'. And 'Mass' is a measure of how much matter there is in that object/body/thing.

What is 'energy'? Some of the common forms of energy that we know are 'thermal' and 'light'. When you burn coal, you release enough 'thermal energy' to heat water or cook a meal. When steam is pressurized at high speed, it has enough 'kinetic energy' to rotate a turbine. Water stored in dams has enough 'potential' energy. In addition to this it gains enough 'kinetic energy' when it flows down from a significant height. This energy enables it to rotate turbines and produce electricity.

What is 'C (Speed of Light in vacuum)' ? - Light is an electromagnetic wave just like xrays or microwaves, or radiowaves that transmit data between wireless devices like cellphones or waves those that bring songs to our radios from far off radio stations. All these waves are part of something called 'electromagnetic spectrum' and *all* electromagnetic waves have the same certain 'speed of travel'. Remember that light takes about 8 minutes to reach from sun to the earth? 'Light' also is one type of electromagnetic radiation which can be seen in different colors unlike xrays or other radiowaves. The fact is that 'Light' (just like any other electromagnetic waves) travels at a speed of 3, 00,000 Kilometers/second (in vacuum) . So when we talk about speed of light in vacuum it is actually speed of any kind of electromagnetic radiation in vacuum.

How do they fit in the equation E = MC² ? The equation really means that 'matter contains energy' (even when the matter is not moving) . Before Einstein’s time, the assumption was that energy can be exhibited by a body only when it is moving or when it is emitting some form of radiation like heat or light. A body at rest is simply a piece of matter with zero energy. Einstein dared to change this thinking. He proposed that matter is a chunk of mass with dormant energy trapped inside it even when it is *not* moving. When the mass moves, it has kinetic energy in addition to this trapped energy. Fine - mass has energy. But how much energy ? The energy trapped in a matter (in which 'M' is the measure of the mass) is equal to: 'M' multiplied by C² ( square of the value of C).

Universe is made up of Active energy (kinetic energy, heat, light and other electromagnetic radiations) and Passive energy (which is in form of 'Mass' or 'Matter'). One meaning of the equation E = MC² is that Mass and Energy are inter-convertible. When Einstein proposed this idea the world was not really ready to digest it. How can something that can be visualized and weighed, be converted into energy which in its most forms is not visible to the naked eye? Inter-convertibility also meant that energy can be converted to mass. How was that possible? And what has 'speed of Light' got to do with Mass and Energy? E, M and C - all were well understood terms at the time when Einstein formulated this equation in 1905 as a part of his work on ‘Theory or Relativity’. Also, relating mass and energy was not a new thing when Einstein started working on his theory. But it took a genius like him to knit these terms together in a simple and exact equation.

Talking of inter-convertibility between mass and energy, one should try to understand this conversion with the same ease as the conversion between feet and meters, or between kilograms and pounds. It’s very easy to visualize a system which measures a distance with either ‘feet’ or ‘meters’. A Meter-long distance can be broken down into 100 equal units (centimeters) or 3.3 equal units (feet). 1 meter is approximately 3.3 feet. So 3.3 is a constant called the ‘conversion factor’. Applying the same logic to mass and energy conversion, C²> (a scalar constant) is the conversion factor between E and M. But unlike 'distance', E and M are still fundamentally different things, and far too distinct from each other to undergo any kind of conversion amongst themselves. But Einstein disagreed. He said that they are just two manifestations of the same phenomenon.

If we analyze this equation from a different angle, it suggests that the sum of all the mass and energy in the universe is *constant*. Or another way to put it is - out of the total energy contained in the universe, some is present in form of active energy and remaining is in form of mass or matter and that mass can change into energy and vice versa.

Section B :

Let’s go back to the first fact - Mass contains energy equal to M X C². How much energy is that really? Let’s consider an example. The most common unit to measure energy is 'Joule'. 1 Joule of energy is what is required to lift up a small fruit in your hand. So how much energy does 1 gram of mass (matter) have? 1 gram of matter at rest has following amount of energy as per the equation E = MC² (C is approximately equal to 3, 00,000 Kilometers/second. Remember, 1 Kilometer = 1000 meters)

Energy in 1 gram of mass = 0.001 Kg X 300000 Km/s X 300000 Km/s = 90000000000000 Joules (or 90 TeraJoules)

To get an idea of the magnitude of this energy, consider following two scenarios:

- 90 Tera Joules is equal to 25000 Megawatt-hrs. This means converting 1 gram of mass completely into energy would fulfill the power requirement of city of Pune (Population: around 37 lacs or 3.7 million) for an entire month, and that too without any load shedding :)

- 'Little Boy', the nuclear bomb dropped over Hiroshima in 1945 had a yield of around 15 Kilo tons of TNT. That amounts to approximately 63 TeraJoules. The bomb contained 64 kilograms of uranium, of which only 0.6 grams were converted into energy. And how many people were killed? About 1.4 lac (or 140000).

That’s the sense of massiveness, magnificence, vastness that this equation has unleashed upon mankind. As of yet there is no means to extract 100 percent energy from mass. But mankind is hoping that it becomes a reality in future. The research is costly but it needs to be done, given that natural resources and fuels are fast depleting. It could one day open doors to cleaner energy. May be in future we could have a technology - where at one end of a fission reactor, you put in a raisin and on the other get energy enough to light up New York City (Population – around 20 million or 2 crores) for a day. You may say that this idea will forever stay as pure fiction, but so was the perception about cell phones in 80s when we used to watch Captain Clark of Star Trek series talking to his folks through a hand-held wireless device.

Part 2: Conversion of Mass to Energy / Energy to Mass

Authored by: Mandar Garge

E = MC2: PART 2: Converting Mass to Energy / Energy to Mass

2008-11-15T10:55:00.000-08:00

Continued from Part 1 ....

It’s easy to get examples of mass being converted to energy. When you burn coal into ash, you are using up the binding force (which holds the ‘molecules’ of that substance together) to get energy. You are releasing the energy that is holding up atoms and molecules together. Molecules break down and atoms recombine to form new molecules of resulting byproducts. Weight of byproducts after burning process is lesser than that of original coal. This is nothing but mass converted to energy. The amount however is extremely minute with respect to original mass of coal. On the other hand when you trigger nuclear fission you are basically breaking down the atom (nucleus) of an element and converting some atomic (nuclear) mass into energy. The mass of the nucleus before fission is slightly more than the sum of the masses of the separated elements of the nucleus. The difference is what got converted to energy. In other words, this energy is dormantly trapped inside the nucleus, and as long as it stays trapped, it shows up as that 'differencial' mass.

Nuclear reactors and nuclear bombs work on this principal of 'nuclear fission'. However, for the same original mass, the percentage of mass converted to energy is much higher in case of nuclear fission than conventional ways like burning fuels. Hence fission process has much higher yields. The process of fusion is also associated with mass-to-energy conversion. When you fuse two atoms (protons) of hydrogen to form helium, the united protons together weigh less than the sum of individual protons. The difference is converted to energy. 'Hydrogen' (or thermo-nuclear) bomb works on the same principle and so does the Sun of our solar system.

But it’s hard to imagine processes where pure energy gets converted into mass or matter. What is Matter? Matter in its simplest form means - protons, neutrons (and electrons because they also have mass, although minuscule). Protons and neutrons form the nucleus and electrons are moving around the nucleus. These three act as building blocks in making up atoms, which in turn make up molecules that make up different elements and compounds. If you pull out a proton (or a neutron or an electron) from a nitrogen atom and replace it with a proton (or a neutron or an electron) from an oxygen atom or any other element’s atom - Nitrogen would still remain Nitrogen. Hence matter boils down to protons, neutrons and electrons.

When the big bang happened approximately 13.7 billion years ago, all you had was energy (thermal and electromagnetic. Remember, light is electromagnetic radiation). That energy spread over and in bits and pieces, started getting converted into 'Matter' or 'Mass'. First Hydrogen was formed since it is the easiest one to be created when it comes to creating matter from scratch. Why easiest? Construct a nucleus with only one proton and you have Hydrogen atom. (That’s also the reason why Hydrogen is most abundant in universe). Then gradually other elements were created and chunks of these elements started grouping together to form different compounds and celestial bodies mainly stars and planets. So there you go - energy got converted to matter.

But where did that initial energy that triggered the big bang come from? The accepted answer is 'God'. But assuming that God also is made up of matter, how did he get created? I don’t know :)

I don’t think human quest would reach that far. But the Particle Accelerator experiment at CERN, is attempting to get closer to the time just after the big-bang. It aims to create a miniature big bang which will lead to creation of 'matter’ from scratch. But wait a minute. How would you create the big-bang without having enough energy to cause that big bang in first place ? Of course, you can’t create energy but can covert it from some matter, cant you? The CERN equipment will try to do exactly that. It will try to energize protons (which is matter in its simplest form) to travel at speeds close to that of light. These protons would then have enourmously high amount of energy. These high energy protons would be banged into each other to create a mini big-bang. So here, matter (protons) is being converted into energy (big bang) and that energy is expected to be converted back into new matter (or ‘mass’).

But one important thing is that big-bang will produce two types of matter - 'normal' matter as well as 'anti-matter'. Normal matter is positively charged. Antimatter as a matter of fact, is still ‘matter’ and has the same 'mass' as its corresponding matter, but has 'negative' electric charge. Yes, it is matter with mass that has ‘negative electric charge’. (Note - its ‘negatively charged’ and not 'negative' mass, which supposedly does exists. But its a totally different theory and no need to worry about it here). How can that be? Does mass have a charge? Yes. It does and we don’t usually have to worry about it, because the positive charge of the mass will be detectable only if there is a negatively charged mass in its vicinity and we don’t have any negatively charged matter around us. An electron (with negative charge of 1 electron-volt) will not let us know that it has a negative ‘electric’ charge unless we let a positive charge venture into its vicinity. And what happens when positive and negative ‘electric’ charges combine? ‘Nothing’ - may be a spark. The charges neutralize.

So what would happen when matter and anti-matter come together? No, not ‘nothing’ this time. Remember, we are dealing with masses (positive scalar quantities) with 'opposite' charges. The charges will neutralize but mass quantities will add up and annihilate to create ‘Pure Energy’. Union of matter and anti-matter will create energy with 100 percent efficiency (meaning 100 percent of matter gets converted to energy)

Thinking of the reverse process, we know that matter got created during big-bang 13.7 billion years ago. But does it also mean that equivalent amount of anti-matter was also got created under the rules of E=MC²?. That’s what scientists at CERN are assuming. A section of the scientific community has always believed that antimatter was also created with matter when big-bang happed. They conclude that anti-matter is somewhere out there far away in the universe, dormant like a sleeping dog but when you get closer to it, it would growl and pounce on you to cause total annihilation and creation of 'pure' energy. The other section of scientists disapprove this theory (of equivalent amount of anti-matter being present somewhere in the universe)

So you get the idea - how mass and energy are inter-convertible and how they are two different forms of the same thing? Einstein proposed this theory in 1905, but rest of the world took decades to grasp this revolutionary concept.

If you come so far, I believe you will be interested in knowing more about what has ‘Speed of Light’ got to do with this Energy and Mass conversion? If you are, please visit the following link:

Part 3: How is 'Speed of light' involved in the conversion ?

Authored by: Mandar Garge

E = MC2: PART 3: Why is 'Speed of Light' involved as the conversion factor?

2008-11-15T02:24:00.000-08:00

...Continued from Part 2

This could be hard to explain. Its definitely not as easy as explaining why the conversion between meters and feet is ‘3.3’. But I will try my best. Remember, the equation E=MC² is a part of Einstein's work on his ‘Theory of Relativity’ and ‘C’ was a term pivotal to that theory. Einstein was particularly fascinated by Light, its speed, its properties. During his work on Theory of Relativity, it dawned upon him that C - the ‘Speed of Light’ (or an electromagnetic radiation) in vacuum has to be constant in all frames of reference (The fundamental basis of Theory of Relativity)

- The first assumption in his theory of relativity was that C, the speed of Light in vacuum, was always constant for observers in all frames of reference. So me, standing on earth (one frame of reference) and you travelling in a rocket at around 15-20 times speed of sound (second frame of reference), or our friend travelling at half the speed of light (third frame of reference) – all will measure the value of C to be the same (approximately 300,000 km/s).

- The second assumption was that laws of motion should apply the same way to all systems travelling at constant speed ‘relative’ to each. So if you are travelling at half the speed of light and I am at rest on earth, you can say that you are at rest in your spaceship and earth is travelling at half the speed of light. So we are travelling at constant speed ‘relative’ to each other and both can apply the laws of physics (for example Newton’s laws of motion) the same way in our own systems.

So C is the only thing that remains constant in all frames of references, the only thing that is ‘absolute’ with an ‘absolute’ value of 300000 km/s. Everything else is ‘relative’. For laws of motion to hold in all frames of reference (which measure C to be the same) – Time, Distance, Mass, Energy - have to adjust in order to maintain the constantness of C. Einstein proposed that, for a system moving at constant speed with respect to a system at rest – ‘Time’ would slow down, ‘Distance’ would be compressed, ‘Mass’ and ‘Energy’ would increase (with respect to the same terms measured in a system at rest). The “extent” by which time, distance, energy, mass differ in two systems moving ‘relative’ to each other – is determined by formulas - all of which contain the term ‘C²’.
For example assume that system is moving at a speed of 'V' m/s. Then as per equations of theory of relativity, the slowed-down time (t') of that system with respect to time (t) measured in system at rest is:

t' = t (1-V²/C²)^½

So as an example assume that you are travelling at 60 % the speed of light from point A to B, and I am at rest. If ‘I’ measure 10 minutes in my watch as your travel time from A to B in my frame of reference, then ‘I’ would measure 8 minutes (80 % of 10) in your watch which is operating in a system that is moving relative to my system at 60 % the speed of light. That means ‘time’ in your frame of reference, has slowed down, as observed from my frame of reference.

Based on the same principle, In order to keep C (Speed = distance/time) constant for both frames – distance (or length) must also reduce in value (compress). So if the spacecraft in which you are travelling is actually 10 meters long, I would see it compressed to 8 meters from my frame of reference (applying the same equation for distance). But you in your own frame of reference would measure yourself as 10 meters. Confused? The point is that time and distance that I measure in your system, are different than what I measure in my system.

It’s not important that you understand how Einstein arrived at these equations. What is important is the role played by the term ‘C²’. Apply the same logic to Energy. Yes you guessed it right. The difference between energies of the two systems moving relative to each other at constant speed must be having term ‘C²’ involved somewhere. Einstein figured out that when objects emit energy in form of heat, sound, light etc (or decay and emit radiations) they were actually losing mass. The form of energy being emitted was not important. So for purpose of calculation of this equation, Einstein considered a system where a body emitted light (radiation):

From frame of Reference of Object at Rest:

"Energy of an Object _{before emission} = Energy of that object _{after emission} + Energy emitted"

Then he applied the same equation for the frame of Reference that was moving with respect to object at Rest.

"Energy of a moving Object _{before emission} = Energy of that moving object _{after emission} + Energy emitted by moving object"

Then he compared the observations in the two systems for calculation of the emitted energy and arrived at a conclusion that - when a body emits energy 'K', its mass diminishes by an amount = K/C². This means the mass of the object depicts how much energy it contains.

This explanation is surely a very short excerpt. But the gist is that Einstein formulated E=MC² as part of Theory of Relativity where the term ‘C’ plays a pivotal role. The equation was proved decades later in 1938 when German scientists successfully carried out fission of uranium for the first time and found that the energy released during the fission due to loss of mass was exactly in line with this equation (A Swedish physicist named Lise Meitner was the one to prove this).

Even today most of the mankind doesn’t see what terrific revelation is hidden in this equation, but Einstein visualized it more than a century ago. What a revolutionary and mind-blowing concept it has been.

Authored by: Mandar Garge