A few years ago I, along with my son John who had a good SLR Camera, acquired a telescope. The object was to further his and my interest in Astronomy.
We had some hard earned early successes and some failures. Later, when we had learnt much and added to our equipment, some of the images taken with our 6″ reflector telescope compared favourably with some internet images that had been taken using larger and more expensive equipment.
We, like the many other amateur astronomers went through a learning process. On our nights out I did the navigating and, because I am retired, I had the daytime during which to research the internet so as to improve our knowledge base and thereby improving our routines, making best use of the equipment we had and acquiring equipment that would help.
Some of the sub items here are just copies of the comprehensive notes I made. At A level physics I had learnt to draw light paths that showed how various lens arrangements brought things into focus. I could reproduce those diagrams but never understood them. Dealing with telescope optics brought with it much understanding of the behaviour of light.
Nebula historically referred to extended space objects. The Andromeda galaxy was previously the Andromeda nebula before being found to be a galaxy. Nebulae are now space volumes of interstellar clouds and dust. The space volumes where the gas and dust are most dense we call diffuse nebulae; they are space volumes where stars are born.
H – Ⅱ diffuse nebulae regions are so called because a lot of hydrogen in them is in its heavy deuterium form. In this form of hydrogen its normal nuclear single proton is accompanied by a neutron so that its atomic mass is 2. Hence H – Ⅱ. Gasses in these areas are known as molecular clouds. They are a feature of spiral galaxies that contain much gas and dust in their spiral arms. The milky way, our galaxy, is just such a spiral galaxy and in our galaxy there are many such nebulae where stars are being born. The following are stages in a star’s life.
Stage 1: Molecular Cloud.
The process by which the gas and dust of a molecular cloud start to collect in clumps is called accretion. It is thought that the universe’s earliest molecular clouds were entirely of hydrogen and helium and that only later clouds contained tiny fractions of heavier elements, probably from star explosions and emissions. Isotopes and ionisations are thought to be common in space.
The process of accretion is one in which heavier accumulations become more massive as they attract more surrounding dust and gas and the more massive the clump becomes the greater becomes the pressure on its core. In this way the desire for external energies cause core materials to become increasingly agitated heat up.
Stage 2: Proto Stars.
Centres of these heated gas clumps are where proto stars are born. Being surrounded by gas they can at an early stage be observed by infra red telescopes that see the energies emitted by their cores. The star may spend a 100,000 years at this stage growing. Eventually the star starts radiating energy in excess of that it is taking on board and the cocoon of dust and gas around it gets dispersed by jets of what is called a T-tauri wind. The star has become a main sequence star and is now visible to optical telescopes.
Stage 3: Main Sequence.
The star spends 90% of its life at this stage. After a few orbits of its galaxy it will have been pulled by others, from its birth area and into a space of its own. Its core is now undergoing a fusion process, started by the pressures built up in the previous stage. The fusion process is outputting energy at the expense of the star’s mass energy.
The fusion process is not a burning process. It is a number of nuclear process by which hydrogen in the hot core of the star is converted (fused) to helium, the processes involving a loss of mass energy to radiated energy. The energy output is given by Einstein’s well known E = mc2 where c is the speed of light. There is no explosive release of energy because gravitational pressures on the core determine the rate of fusion, but the fusion energy releases then counter and diminish the gravitational desires for energy.
The processes by which stars convert hydrogen to helium vary according to star mass which is usually a comparison with our own sun’s mass (solar mass). Stars like our sun fuse hydrogen to helium via deuterium and if their core temperatures are above 15 million degrees Kelvin via beryllium, lithium and boron. The fusion in stars with masses over 1.2 solar masses may involve carbon, nitrogen and oxygen and in stars of over 3 solar masses fusion is almost entirely via these elements. .
You may think a more massive star will last longer but that is not the case because fusion energy releases are scattered energy releases and on a large star less controlling of gravity
Stage 4: Giants. The stage of giant is not an automatic phase in a stars life. Small stars, with below 0.35 solar masses, never get beyond the above described stage. helium produced in their cores is convected throughout the star and they become red dwarf stars.
For larger mass stars when all the hydrogen in the core has fused to helium the star core starts to cool and rapidly contracts as gravity wins. But the layers outside the former core contain hydrogen, which now comes under pressure, heats up and starts to rapidly fuse to helium, becoming hotter than at the main stage. At about 108 Kelvin, the helium starts fusing to carbon.
The above happens as a helium flash in stars up to 2.57 solar masses but in a more controlled fashion in more massive stars. Star luminosity increases at this stage by by a factor of 1,000 to 10,000 and its outer parts swell so that the star becomes a sub giant, red giant or super giant. Betelgeuse is a super giant. Although the core and lower layers are now generating more energy than at the main stage the increase of size brings decreased surface radiation and such stars usually appear red.
In medium stars like our sun the heat is sufficient for the fusion of Helium into heavier oxygen and carbon. This process is much shorter than the hydrogen to helium fusion. Again, there is loss of mass and energy is output.
Stars, at main stage more than 5 times the mass of our sun will go on to fuse carbon and oxygen into neon, sodium, magnesium, sulphur and silicon and maybe into calcium, iron, nickel, chromium and others, with each stage shorter than its previous one.
Stage 5a: Planetary Nebulae.
When gravity is insufficient for further fusion, stars, that were at the main sequence stage up to 7 times the mass of our sun, now have their hot cores sending out increased photons. These photons push the outer carbon and silicon elements into space creating a glowing planetary nebula (it looks like a planet) with a white dwarf star at its centre.
Stage 5b: Supernova.
Stars that had masses above 7 times that of our sun (when at the main sequence) go the supernova route. When fusion ceases their iron cores implode from about earth size to about that of the size of a city in less than a second. Outer gasses are pulled in to strike the core and are compressed in the process. The compression causes the gasses to heat up to billions of degrees and within 15 minutes an explosion results. The super heated gasses carry heavy elements like gold, platinum and uranium into space. The star Betelgeuse is said to be near following this route.
Stage 6: Core Remnant of Supernova
The core remnant after the outer layer has been thrown off at the above supernova stage determines what happens next and is as per the following table.
In mathematics and physics vectors have both magnitude and direction. If a car was travelling at 65 mph when an accident occurred that 65 mph is seen as a scalar quantity. If we also know the direction the car was travelling in then we can treat this combined information as a vector.
We manipulate scalar information all the time using plus, minus, multiply and divide operators. We can even add, subtract and multiply unlike scalar quantities if it suits our purpose. For example we could add a count of pears to a count of apples and give the answer as pieces of fruit. It would make little sense to multiply them but their are many unlike quantities we multiply together to get a result. For example we multiply voltage by current by time to get energy. But can we and how do we apply operators to vectors?
Before we go any further, let us consider a practical example. The diagram shows the basic operation of an electrical motor. View the currents as going away from you and coming toward you. The role of a commutator is to arrange for such current flows. The force, and therefore the rotating torque, is related to a multiplication of the magnetic field strength and the current flow.
The field strength, current and force are all vectors. The resultant force vector is at right angles to the other two vectors and in this case, but not in all, they too are at right angles to one another. As such they deliver the greatest possible forces and hence the greatest rotary torque. I hope my inclusion of this example helps in establishing that vector multiplication has some purpose.
Clearly one way of showing both size and directions is to draw the vectors on graph paper using a coordinate system. We use the length of an arrow to represents the size or scalar element of the vector and its alignment plus arrow head to represent the direction of the vector.
If the vectors are about forces that you and I exert on an object, then when we push in the same direction the magnitudes of our pushes add and if we push in opposite directions they subtract. However our pushes on the same object point can be in all manner of directions. Each one can be in any compass direction and include an element of thrust upward or downward.
If I am pushing northward and you are pushing with an identical force toward the south west we can guess that the pushed object will move both to the north and west. Combining vectors geometrically gives us the combined force in both size and direction as long as we draw the vector lengths to some scale and with the right relative directions.
It may be more convenient to work out the result algebraically.The top triangle from the above is illustrated here and we can use the equality of the cosine rule( as determined in my blog on trigonometry) and as shown to determine the size of the result.
Once we have R we can determine the part of it that acts to move the object west and the part that acts to move the object north. These are as shown in green. Like the M and Y forces that actually delivered R these two component vector forces would deliver the R result. We have if you like resolved the vector R into two components, an east/west one (x axis on a graph) and a north/south one (y axis on a graph).
We can look at these green component vectors in another way and consider them as scalar multiples of unit vectors. One is a scalar multiple of the unit west vector shown in red and the other a scalar multiple of the unit north vector in blue.
Multiplication of Vectors
In normal multiplication we multiply scalars together and get a scalar. We can do so because they are on the same scale. We have seen above how we can componetise vectors into north, south, east and west and we can likewise do so for up and down. All such component vectors have a scalar element and we can multiply scalars together to get a scalar or dot product, as long as we confine ourselves to multiplying the scalar elements that lie on the same linear scale.
For example, consider two vectors A and B that have scalar components along the x, y and z axes as indicated by the suffixes that describe them and as converted to vectors via the unit vectors i , j and k along those same axes. Be aware. in what follows, that we are doing scalar multiplication and that the scalars of the three unit vectors i , j and k are all equal to one.
When written out in full the dot product of the two vectors is as under A . B = (Axi + Ay j + Azk) . (Bxi + Byj + Bz k) and to expand that product we have to multiply every term in the first bracket by that in the second bracket. However, whilst we can multiply i scalars together, j scalars together and k scalars together because they are on the same scale all other scalar multiples are not possible because they are on scales orthogonal to one another (at right angles) So the scalar dot product A . B = Ax Bx + Ay By + Az Bz
To multiply two vectors together and get a third vector we again set out to multiply all the bracketed components as above but changing the dot to a cross to signify that we are doing a cross product. We now multiply just the terms that are orthogonal. In our example above the motor force only arises when there are components of magnetic field and current acting across one another. so in the cross product we ignore i x i, j x j and k x k.
There is a cyclic rule for multiplying the other unit vectors as shown. So for example i x j = k and k x i = j whereas in the opposite cycle j x i = -k and i x k = -j
A x B = (Axi + Ay j + Azk) x (Bxi + Byj + Bz k) = Ax Byij + Ax Bz ik + Ay Bxji + Ay Bzjk + Az Bxki + Az Byk j = Ax Byk – Ax Bz j – Ay Bxk + Ay Bzi + Az Bxj – Az Byi = i ( Ay Bz – Az By ) – j( Ax Bz – Az Bx) + k( Ax By – Ay Bx )
The above result we can express in the form of the matrix left. We will learn more about matrices in a later blog. On the right, we show a cross product vector geometrically. It is at right angles to those multiplied and its magnitude is that of the yellow area and equal to AB sinθ.
In our motor example the angle between current and field is a right angle ( sinθ = 1) and the force that delivers the torque is at right angles (orthogonal) to both of them. The force is also related to the product of current and field. The yellow area is in this case a square whose sides are vectors with different scalar measures (field strength and current) and whose cross product is a vector that has another scalar measure (force).
Every particle movement in a structure is an energy change but too small for us to notice. However many particle movements can involve energy changes that are substantial.
Changes of state as between, for example, solid ice, liquid water and gaseous steam happen naturally because structure particles always want an arrangement that best suits their environment.
In winter when the environment is low in energy water will become ice. As the environment warms the ice will take energy from it and use it to change its particles to the structure that is water because that structural arrangement now better suits its energy needs in the changed scene. If we now put water next to a heating element in a kettle the water changes its particle structure to that of steam because that now better suits it in its changed environment. The released steam in the now changed environment soon reverts to tiny unseen molecules of water in the air or will condense on your window or hand, if held in the path of the steam.
Changes of state are energy changes but not chemical or nuclear changes because particles are not lost, gained or shared with another structure, they are just either closer together or further apart. Chemical changes are changes that involve the loss, gain or sharing of electrons whilst nuclear changes involve the loss or gain of nuclear particles.
We do not bring about chemical or nuclear change. Particles decide when it is in their interest to make such change. What we do is provide the environment in which it suits them to make such change. Particles are always in search of a more energy efficient arrangement because it is a one in which they have most stability.
Chemicals in a battery want to rearrange their particles in more energy efficient structures. Those rearrangements involve releasing electrons at the negative terminal and taking electrons from the positive terminal. They are restricted in doing this because the terminal particles also want efficiency and stability. Connect a circuit that allows electrons to flow and the battery chemicals can start to rearrange themselves in more energy efficient ways. Particle and photon interaction energies proactively make the changes. We just create the enabling environment.
All chemical changes are energy changes. Electron energy collections can be shared by the protons of two atoms. We call it covalent bonding. Electrons can move from one atom so as to predominantly supply the energy needs of another in what is called ionic bonding. The illustration shows chlorine atoms as having taken electrons from the sodium. When discussing electricity we met metallic bonding in which electrons can’t make up their mind which to supply.
A lot of high energy holds nuclear particles together and when they decide they can find a better and more stable energy arrangement it usually involves considerable energy release.
When calculating electrical energy we use formulas that are hard to reconcile with those of mechanical energy yet each can be converted to the other. Electrical energy can be equated to mechanical energy because we have chosen electrical units to make them so. Whilst mechanical energy is mostly about the interactions of whole particle structures via photon energies, electrical energy is mostly about the interaction of the outer electron particles of structures via photons.
Electrons gather energy from the environment on behalf of nuclear particles. To perform that duty they need their own space and therefore interact with other electrons via photon energies so as to keep at a distance. Electrons are energy linked to protons because of their energy desires but less so when they are obliged to occupy positions furthest away from nuclei. In fact outer electron can link to more than one nuclei as with covalent, ionic and metallic bonding.
The metallic bonding in silver, copper gold and aluminium is such that outer electrons cannot make up their minds where they can best serve protons and they wander from atom to atom moving other electrons as they do so but all the while providing an energy feed from the environment that links them to protons.
Such electrons are not free but we can give them a directional flow that moves them in a cascade fashion round a circuit via their light speed photon energy interactions. We do so by providing a voltage source that delivers surplus electrons to one of its poles and removes electrons from its other pole.
Any move one outer electron makes almost immediately instigates movements in other electrons via light speed (300,000 kilometres a second) photon interactions. It is why energy can be conveyed over vast differences very quickly.
We should not think of electrons continuously on the move. They are generally spending considerably more time in atoms linking to protons than they are moving between atoms. Typical progress of an electron along a wire is a half metre every hour. When the moving electrons encounter an electrical load like a motor, heater or light electrons have to gang up and jointly a push that drives that load.
Electrons have a property called spin. I believe it is the result of their internal energy fragments spinning and related to the direction in which the electron is travelling. Some of the photons exchanged by electrons are spun off them and when many electrons have like directions of motion they spin out low level photon energies in the anti clockwise direction to their travel that are attracted back into the photon flows being exchanged by electrons.
The magnetic field that we see circling clockwise around a current carrying wire is actually photon energies being flung out from electrons with like direction spin as a result of their many like direction motions. We see the magnetic field as circular, related to the current flow and diminishing with distance from the wire but the field is really of photon energies that spiral outward from electrons and then spiral inward to electrons.
When the current related energy links are rising some of the driving energies go toward growing the magnetic field energy and when the current related energy links are falling the now collapsing magnetic field energy is trying to sustain the current flow. This is precisely what self induction is.
When two adjacent currents flow in opposite directions the circling photons passing between have like direction but want their own space and in pushing one another apart push the wires apart. When currents flow in the same direction photon flows between them are in conflict and many choose to go around both wires and that draws the wires together.
We should not think of neutrons, protons and electrons as being of fixed mass energies as they take on board and release photon energies that are general tiny relative to their mass energy. Nor should we think of photon energies as fixed. Like particle energies that interact via photons, photon energies interact by exchanging tiny portions of their energies. Magnetic photon energy interactions enable all electrical machines to work.
Electromagnets are just wire coils producing high volume photon flows. Soft iron is much used to support such photon flows because its outer electrons will align with and support such flows, even when they are reversing rapidly as with alternating circuits.
Permanent magnets are hard, rigid particle structures whose outer electrons have been given a like alignment during the manufacturing process by a powerful electromagnet.
Wikipedia describes the scientific view of kinetic energy as follows. “In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes”
The work-energy principle, we also learn, is that an increase in the kinetic energy of a body is caused by an equal amount of work done on the body by the force acting on it.
E = 1/2 mv2 is how we calculate kinetic energy. It is applicable when a steady force produces a steady acceleration on a mass M over a distance so that it achieves from a standstill a speed v. It is equally applicable in decelerating that mass steadily to rest. You can immediately see why it was thought that the accelerating energy must be acquired by the moving object and released in the deceleration process.
But what I cannot understand is why we still think this way. Do you really feel as if you have gained some energy when you are running and if so where do you think that energy has come from ? Does a 30 mph car engaging with a 90 mph train environment have more energy than when the same car at 30 mph. engages with a tree.
No wonder many scientists regard energy as a mathematical construct because that is precisely what we are making it into by saying a body has energy on account of its speed and then in gravity situations we allocate an object at height a higher potential energy than the same object at a lower level.
There is no force that accelerates an object at height toward the earth. There is a desire by the particles of the object for earth energies and that is what accelerates a free to do so object toward the earth. The object gathers speed but there is no force pulling it or pushing it toward the earth. There is no external energy driving its motion. The motion is born of particle energy desires for a more stable energy state. The structure will gain a little in mass energy as the earth emitted photons and air particles apply a motion restraining tiny upward force but insufficient to overcome the desire.
When the speeding structure nears the earth the influence of earth emitted energies on the falling structure rapidly increase and influence the motion of the structure decelerating its particles and accelerating them away in a vibrating pattern where mass energies gained are released as heat photons into the atmosphere as the object settles into a more repetitive vibrating state that we see as stability and which it prefers.
Though impossible to achieve two identical bodies travelling at different yet steady velocities through space and free from any external influence will have exactly the same particle mass energies and be exchanging the same photon energies. I repeat, there is no motion energy store. We are wrong to teach children there is and they grow into scientists who do the calculations and think there is a motion energy store.
Energy exchanges that act to separate structures will add to the mass energy of those structures. However that mass energy will increase significantly more for structures that cannot part easily than for structures that can part easily. The inner balls on a Newton’s cradle have their mass energies increased at the expense of motion.The outer balls gain little in mass energy because they are able to move away.
At school we learn about protons and electrons and how they have the same but opposite charge. Charge is the reason negative electrons want away from negative electrons, it is why positive protons want away from positive protons and why negative electrons and positive protons attract one another. We learn little at this stage about neutrons, only that they have no charge.
We hear how atoms have nuclei that contain protons and neutrons and that electrons are distributed in shell like energy formations around and away from the nucleus. No explanation is offered as to why electrons are not drawn right into the proton containing nuclei or how it is that protons can remain relatively close to one another in a nucleus. To me an understanding of the scale of particles and the relative spaces between them is a must in developing a working picture of matter and all things physical, yet it barely gets a mention.
At a later stage, we learn of beta and beta positive radioactive decays in which neutrons can become protons and electrons or vice versa. The emphasis is on what happens, not why it happens. I will tell you that such things happen when neutron particles in a nucleus seek to better their energy exchange arrangements. They either create a proton and electron to improve their energy exchanging state or get rid of a proton and neutron if their energy exchanging state is excessive. In the first second after the “big bang” that created our universe phenomenal numbers of neutrons were becoming protons and electrons as energy expanded. Neutrons are quite clearly not the inactive particles that the charge picture paints.
On earth, gold particles are more heavily compacted than lead. Gold has a density of 19,3 grams per cubic centimetre. Compare that to a neutron star density estimated at about 100 million tons per cubic centimetre. On neutron stars, neutrons seem content to exchange energies and satisfy their energy desires with a minimum of support from protons and electrons. In the less compacted energy scene of earth neutrons require the support of protons and neutrons in the satisfying of their energy needs and they adjust proton and electron numbers to suit those needs.
The much lighter and thereby more mobile electrons provide the means by which nuclear particles can energy link to the environment. They are the “slave” particles of the atomic world, each with their own space volume so that they can effectively collect suitable photon energies from the environment on behalf of their nuclear particle clients. They may be slaves but they are living proactive slaves always acting to perform their role in the most efficient manner.
Electron energy desires have them moving toward photon flows, gaining in energy and then retreating. Protons encourage energy bearing electrons to them but then as the proton’s energy desires are satisfied the approaching particle energy exchanges become excessive causing them to withdraw, more so the lightweight electrons. Such energy exchanges are the photon emissions that enter space.
Protons have an intermediary role, receiving energy from electrons, processing it and feeding it to the energy desiring neutrons. Electron accelerations toward protons are governed by the energies of the environment and protons respond to those accelerations by releasing levels of energy intent on decelerating and accelerating away those electrons. Protons gather suitable energies in the process and release it toward close by neutrons, whose energy attractions are consequently high.
At the nuclear level neutrons and protons are said to each comprise of three quarks but the total mass energy of those three quarks is only about 1% of the mass energy of a nuclear neutron or proton. The rest of the mass is described as virtual gluons that account for the force that binds the quarks together but also for the strong force that keep the nuclear particles together.
We are told that quarks behave differently in that when you try to part them they pull together more strongly. Is that not precisely what a living desire does? It relaxes when its needs are being satisfied and acts when they are not. The gluons behaviour is like that of a photon but no one seems to be able to measure its energy.
My gut feeling is that gluons are simply a multiplicity of lower photon energies and therefore not showing up as a single frequency. High volumes of low energy photons passing between much larger attracting and repelling nuclear particles would certainly account for the strong limited range nuclear force. It would also avoid the need for a conversion from photon based interactions to gluon based interactions because if gluon energies are not photons energies then a proton would have to make that conversion.
I remember at school drawing force diagrams. They always had forces that balanced which enabled the doing of calculations. A typical scenario was that in the diagram of a cyclist following a curved path. On it centrifugal force equaled centripetal force and weight was balanced by the opposing normal hold up from the ground.
One day at college our mechanics lecturer asked us to draw just such a diagram but showing only actual forces. Without exception everyone drew a diagram. like that shown. We had come together from various parts of the country but all of us had learnt of centrifugal force and not one of us had questioned its reality. The lecturer explained that there was no such centrifugal force, that the centripetal force was accelerating the cyclist toward the centre of the curved path he was following. Centrifugal force was an invented force just for the purpose of creating a balance and equal to the mass of the combination times its acceleration.
I tell the above tale because mathematics can be a wonderful tool but it sometimes doesn’t truly represent reality. In fact on this diagram we also show the force that is weight. We say it is the force of gravity and responsible for the acceleration due to gravity but is it a force and if so where is the downward acceleration in this scene.
We humans are energy structures just as the chair we sit on is an energy structure. When we sit on it, its energy structure reacts to our energy structure and we feel its pushing on our bottoms. The chairs energy doesn’t want our energy structure getting too close to it and so it pushes us away. Likewise our energy structure is pushing the chair energy structure away. It is the basis of Newton’s third law “for every action there is an equal and opposite action”. The difference between us and the chair is that we convey energy signals, from those interactions to our brain that let us feel and respond if we wish to.
If you previously thought your particles made contact with the chair particles, think again. What we feel as multiple contacts are just as much photon energy exchanges as are the photon energies of visible light that in their exchanges with our bodies give us sight. What we hear, the warmth we feel, our sense of smell and sense of taste are all similarly so.
The same sort of photon energy exchanges that stopped our particles from further engaging with the chair hold particles apart in structures. Particles don’t want to come too close to one another and they respond to ever closer approaches by releasing and exchanging ever higher levels of photon energy. It is why when you sit on a chair with someone on your knee you feel more pressure.
Of course pushing particles away is not the whole story. If it were structures would fall apart and they don’t; in fact many structures only part under extreme pressure. So particles in a structure clearly have an attraction for one another but what is its nature? Is it charge attraction or an energy attraction?
The external energy we have to input to break apart a structure is called binding energy and clearly equal to the attraction that holds a particle structure together. My view is that attraction is the desire that particle nodes of energy have for the energies released by the particles of their surround. Particle energies attract surround photon energies to them and in so doing attract the nearby particles releasing those energies. Window particles that attract raindrop particles are no less a part of the gravity style attractions between energies.
When we humans have filled our energy stores do we continue eating? No we don’t and neither do particles. They have extremely tiny energy stores that they rapidly fill in moving toward and attracting energies. When they have satisfied their needs they withdraw from, discourage and release energies. They are doing this billions of times a second, more so if the photon energy supplies coming their way are larger, less so if those energy supplies are smaller
Particle desires for photon energies extend to particles in other structures. They are what hold us together as an organism and what hold the earth together as a space structure. They are also responsible for our being attracted back to the earth when we jump up. The attraction is mutual but the more massive earth does little moving.
The desire of particles toward energy flows is the attraction that we call gravity. There is no force pulling or pushing us toward the earth. The accelerating motions of bodies toward one another is the result of particle desires and when the bodies come up close to one another and those desires are more than satisfied they push each other apart and quickly settle into some interacting vibrating state.
The earth in space is a particle structure travelling at a speed that would take it away from the sun but its particles desire photon energies and the sun as a particle structure is releasing photon energies. Consequently many earth particles turn toward the sun, drawing the other energy linked particles with them. Energies collected and distributed are soon in excess of particle needs and many of earth particles want away from photon excesses.
There is no uniformity of action throughout the earth, no perfect energy scene for all particles within the earth. Those at the surface are more free and responsive. Those under pressure at earth’s centre are more inhibited in their motions yet vibrate at higher frequencies. There is a sum total response that the earth exhibits by either moving toward or away from the sun and thereby following an orbit around it. The earth is also highly influenced by the photon energies exchanged with the moon, as seen through earth’s tides and to a lesser extent by the planets.
Looking back at our cyclist diagram the pushing up normal force is in opposition to the desire for earth energies whilst the lateral centripetal force provides the particle thrust that enables the structure to deviate fro its would be straight line path.
It would not be unreasonable for you to ask at this stage why it is that some particle structures will combine or break apart to form other structures whilst others will want to stay independent and resist the approach of other structures. I will try to answer that in a blog on chemical and nuclear energies.
The story of evolution on earth goes back over 4 billion years and starts with the appearance of tiny single cells whose evolved forms we know today as bacteria and archaea. Such single cells are called prokaryotes. Those early cells, regarded as the first forms of life, would have just a few of the present day prokaryote abilities.
I can only imagine that some particle structures in a highly fluid environment developed membrane like surrounds. They attracted into their more settled interiors suitable particle energies from their surround and grew in size and shape. Larger flexing cells split naturally in that active environment. Doing so produced two cells each with better energy gathering surface to cell volume ratios. Over time cells evolved a way of splitting, using their internal energies. It was a step on the evolutionary ladder that has always been about particles coming together in ever better and more efficient structures and for the purpose of satisfying their energy needs.
Much later we have evidence of the first eukaryote cells. The current eukaryote cells are the basis of all plant and animal life. They may have evolved when larger prokaryote cells engulfed smaller ones and the arrangement was found to be to their mutual benefit. Those engulfed cells may well have evolved to be early forms of mitochondria energy processors storing energy in their surround cell. Certainly present day eukaryote cells have in them a number of membrane surrounded organelles that deliver specialist services for the cell.
The evolution of all eukaryotic organisms was at first only in the fluids of seas and lakes. Not until plants colonised the land was it possible for creatures to leave the sea and feed on their energies, evolving over time into the land animals we know and into us. Plants made this possible because their chloroplasts gave them the ability to take in sun energy, carbon dioxide and water and grow the source of energy that is their carbohydrate structure
Go back to the time of those first cells and ask how could the supposedly “pushed around” inanimate particles of those early structures become the energy desiring, living, pro active cellular particle structures that we encounter today. The answer must surely be that particle energies were never inanimate; they were always seeking to satisfy their desires and that all evolution has been about their desires.
It means we humans evolved for the purpose of satisfying our particle desires and if we want a continued existence we should be mindful of that.
Trigonometry may be the branch of mathematics that considers the relationships between lengths of sides and angles but its mathematics is almost entirely about the equality or otherwise of numerical values.
In a right angle triangle the Sine of an angle is the ratio between the side Opposite the angle and its Hypotenuse and the Cosine of that angle is the ratio of the side Adjacent to the angle and the Hypotenuse. Remember SOH CAH, your chinese friend who lives at TOA where Tangents are the ratio of Opposites and Adjacents.
In our diagram, cosθ = x/r, sinθ = y/r, tanθ = y/x All are the ratios of lengths and therefore numbers so when you encounter sin, cos and tan in pure maths you are handling numbers not angles or lengths.
x and y are numerical lengths that lead to coordinate points on our circle. They are always at right angles and Pythagoras applies so x2 + y2 = r2 . It is the equation of a circle of radius r which could of course be written as x2/r2 + y2/r2 = 1 and therefore as cos2θ + sin2θ = 1 Get your calculator out and put this to the test. It is purely a numerical equality.
The following are trig equalities sin(A ± B) = sinAcosB ± cosAsinB cos( A + B) = cosAcosB – sinAsinB cos( A – B) = cosAcosB + sinAsinB
Here is just one proof The blue length value issin a The red length value iscos a Together the yellow and green length values aresin(a + b)
But in the top triangle cos b = yellow/blue and in the lowest triangle sin b = green/red
which makes yellow = cos b sin a(as blue = sin a) and green = sin b cos a ( as red = cos a)
So sin (a + b)(yellow + green )= cos b sin a + sin b cos a Again try it on your calculator. It is an identity and always true.
In any triangle like that shown the cosine rule says c2 = a2 + b2 – 2abcosC. Lets prove it using pythagoras c2= (b – acosC)2 + (asinC)2 = b 2 + a 2 (cos 2 C + sin 2 C) – 2abcosC
As proved above cos 2 C + sin 2 C = 1 So c 2 = a 2 + b 2 – 2abcosC The cosine rule