Lecture 5: Physics, Gravity, Orbits, Thermodynamics, Tides

Don't Panic

``Unless I am much mistaken, it would exceed the force of human wit to consider so many causes of the motion at the same time, and to define the motions by exact laws which would allow of easy calculation.''

---Isaac Newton circa 1684 in De Motu, quoted from Cohen & Whitman's Newton's Principia (CW-18).

Sections

Introduction
Space
Time
Mass
Energy
E=mc**2
Forces
Bound Systems
Gravity
Gravity Near the Earth's Surface
Circular Orbits
Elliptical Orbits, Escape Orbits, and Orbital Pinball
Thermodynamics
The 2nd Law of Thermodynamics
Universal Evolution
Tides

Introduction

To say the least, it's hard to sum up all the

Caption: "Astronaut Bruce McCandless II, mission specialist, participates in a extra-vehicular activity (EVA), a few meters away from the cabin of the shuttle Challenger." 1984feb11.

Credit: NASA

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Astronaut-EVA.jpg.

Permission: Public domain at least in USA.

physics

As discussed earlier, we don't have the final, eternal, fundamental theory of physics: Theory of Everything or TOE

Caption: Timeline of the observable universe.

Credit: NASA

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:CMB_Timeline75.jpg.

Permission: Public domain at least in USA.

Waiting for da TOE

The physics we do have explains a lot and one hopes that this physics will be explained fully by TOE.

Before we begin rambling about the concepts needed in physics be warned, there is a lot of circularity in the definitions---but it's not a viscious circle.

Caption: "Drawing by Theodoros Pelecanos, in alchemical tract titled Synosius (1478)."

The snake or dragon eating its own tail is the Ouroboros (tail-devourer) which is ancient symbol probably invented independently in several cultures such as ancient China, ancient Egypt, and Aztec Mesoamerica.

Not a viscious circle---maybe.

Credit: Theodoros Pelecanos (circa 1478). Uploaded by User:Carlos adnero.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Serpiente_alquimica.jpg.

Permission: Public domain at least in USA.

To a large degree, one has to accept physics as a package: the parts make most sense as parts of the whole.

So to start describing one concept inevitably means describing others and an orderly one concept at time description is nearly impossible---you just have to have patience that everything will make some coherent sense after awhile.

By the way---in case you didn't know---physics is very mathematical, but we will skip math almost entirely---maybe one or two equations---that wouldn't be so bad.

What is physics?

The short conventional answer is that physics is the science of matter and motion.

http://upload.wikimedia.org/wikipedia/commons/d/dd/Muybridge_race_horse_animated.gif

Caption: "Animated sequence of a race horse galloping. Photos taken by Eadweard Muybridge (1830--1904), first published in 1887 at Philadelphia (Animal Locomotion)."

Maybe the first sports film.

Before early motion pictures like this, it was not clear when a galloping horse has all his feet of the ground at once. It's when they are close together.

Credit: Eadweard Muybridge (1830--1904) who is probably the best candidate for the inventor of the motion picture if not film.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Muybridge_race_horse_animated.gif.

Permission: Public domain at least in USA.

physics

Many things.

Probably, the key one is to predict---and thereby understand---the future and past evolution of systems.

A system is any set of objects we are interested in---for example the Solar System.

Caption: The inner Solar System out to Jupiter. The Asteroid Belt is shown. The diagram is to scale.

This is a view from the North Pole side of the Earth's orbital plane which, in astro-jargon, is the ecliptic plane. This is the customary way to view the Solar System face-on.

The planets and asteroids orbit counterclockwise from this perspective.

Credit: NASA

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:InnerSolarSystem-en.png.

Permission: Public domain at least in USA.

universe

environment

A system could be anything including the universe as a whole.

Well not quite anything if we are discussing physics---as discussed in Lecture 0: A Philosophical and Historical Introduction to Astronomy, physics restricts itself to systems whose behavior is closely dependent on physical laws and not so dependent on emergent principles---but there are no hard lines.

To make predictions we need those physical laws AND boundary and initial conditions for the system.

Physical laws are what are generally true---or at least very general true---and boundary and initial conditions are what are peculiar to the system.

To do the predictions in general takes a lot of math---which avoid like the plague.

So we just tell stories---but physicists tell stories all the time to themselves---it's how we understand things in part.

Caption: "The Boyhood of Raleigh, 1871".

Credit: John Millais (1829--1896).

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Millais_Boyhood_of_Raleigh.jpg.

Permission: Public domain at least in USA.

space

time

Space

But we understand a lot about space anyway: it has extent, it's where we find things, things can be near or far---and this nearness and farness is quantified as displacment or more loosely distance.

Historically, space was assumed to the the space of 3-dimensional Euclidean geometry that we learn in high school.

Space with Euclidean geometry is customarily described as FLAT SPACE.

Caption: "Small portion of the Cartesian coordinate system, showing the origin, axes, and the four quadrants, with illustrative points and grid."

Cartesian coordinates are used to map Euclidean space.

Credit: User:Kbolino.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Cartesian-coordinate-system.svg.

Permission: Public domain at least in USA.

FLAT SPACE

outer space

But different space geometries are possible.

The geometry of the curved surface of a sphere is not the same as that of flat 2-dimensional surface.

Curved 3-dimensional geometries can exist mathematically. They are NOT easy to picture.

In general relativity, curved 3-dimensional geometries do exist in the physical world.

Accumulations of mass actually cause curved 3-dimensional regions of space.

You will be happy to know that in the current standard model of the observable universe---which is called Lamda-CDM model---the overall geometry of physical space is very nearly flat: i.e., the space of 3-dimensional Euclidean geometry.

http://upload.wikimedia.org/wikipedia/commons/b/b9/Cosmological_composition.jpg

Caption: Dark energy and dark matter percentages.

In the Lamda-CDM model, we have values for most of the energy and matter in the observable universe.

The model may be wrong, but in the model this is what we get.

Credit: NASA.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Cosmological_composition.jpg.

Permission: Public domain at least in USA.

space

FLAT

mass

black holes

But the ordinary geometry of space, we can think of most purposes as flat---which is good because our ordinary intuition about space is violated.

An important point about (phsical) space is that it has active properties in several respects.

A key one property is that of having inertial frames of reference.

FRAME OF REFERENCE

Inertial frames

Actually, everyone knows about inertial frames even if they don't know the name inertial frame.

acceleration

http://en.wikipedia.org/wiki/Image:2nd-Toyota-Prius.jpg

Caption: "2004-2007 Toyota Prius photographed in USA."

The Prius: nothing special to look at, but it gets about 45 miles per gallon which makes it the most fuel-efficient car currently sold in the US.

Of course, in 1991, the standard GM Geo Metro got 60 miles per gallon at least according to the specifications.

Credit: IFCAR

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:2nd-Toyota-Prius.jpg.

Public domain.

acceleration

In both cases, there is a relative acceleration between the other car and you---but only in one case is do you experience a sense of acceleration.

That sense of acceleration is the car exerting a force on your body

Why is a force needed in one case and not the other?

Well forces are needed to accelerate relative to an inertial frame and NOT NECESSARILY relative to NON-INERTIAL FRAMES.

An everyday observation really, but profound.

Now what is an acceleration actually?
Now what is force?
What is an inertial frame?

Special relativity and general relativity are, of course, theories developed by Albert Einstein (1879--1955).

Discussion of that modification is mostly beyond our scope.

But some points of special relativity and general relativity are going to keep turning up continually.

Time

If you thought

space

time

An object can occupy different positions in space and NOT simultaneously.

In fact, there are a continuum of positions as it moves from one place to another.

Time passes while things move.

Immediately, one sees that our notion of time is linked to our notion of space---time without space is hard to define.

This linkage or coupling becomes complex in modern physics as we'll discuss below---but not in detail.

In physics, there is this parameter time in fact.

This parameter time increases as things move about.

There are certain systems that do repeat motions in equal periods of the parameter time.

We can call these systems clocks.

Caption: "Astronomical Clock, Cathedral Notre-Dame de Strasbourg, France."

An astronomical clock is used to track astronomical motion and not keep daily time only.

Credit: User:Sam67fr.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Cathedrale_de_Strasbourg_-_Horloge_Astronomique.jpg.

Permission: Licensed under the Creative Commons Attribution ShareAlike 2.5.

time

Of course, we didn't need a mathematical physical theory to be aware of time---changes in position---and make use of clocks---repeating systems.

We---humankind---good old homo sapiens---have always had clocks---and so probably has all of life.

The clocks were all repeating systems (periodic systems) of some kind.

For most of human history, astro-body clocks had precedence: the Sun and Moon.

The Sun and Moon were unique and massive and their period could easily be counted.

It was probably assumed that were exactly regular and measured time itself.

solar days

solar years

lunar months

http://upload.wikimedia.org/wikipedia/commons/8/86/Lunar_libration_with_phase_Oct_2007.gif

Caption: Lunar libration and lunar phases.

The apparent growing and shrinking of the Moon is due to the 11 % difference between distance to perigee and distance to apogee.

The libration is the apparent rocking which is explained as follows.

The Moon is tidally locked to the Earth which means that the Moon always turns the one side to the Earth: this is the near side.

So from we never see the far side of the Moon from the Earth.

But the tidal locking isn't perfect: various small effects cause the lunar libration which is bit rotational oscillation from the perspective of the Earth.

So we do see a 59 % of the Moon's surface Wikipedia: Tidal locking: Occurrence: Earth's Moon, but only 50 % at one time.

Credit: User:Tomruen.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/File:Lunar_libration_with_phase_Oct_2007.gif.

Permission: Public domain at least in USA.

They didn't keep time with the regularly with astro-body clocks or each other and frequently had obvious non-repeating features. These irregular clocks include:

The climatic seasons. They stay pretty close to the Sun clock, but not perfectly.
The chonobiologic rhythms---flowers blooming in the spring, etc.---that in many cases evolved in response to the astronomical cycles of the Sun: the solar day and solar year and their effect on the physical environment on Earth.
And---in probably much more limited way---to the lunar month through it's relation to tides.
Maybe many animals are probably conscious of the passing of time mainly through the solar day.
The pulse---usually measured from the radial artery---can be used for short-time time measurements. It tracks the beating of the heart.
The life cycles of animals and especially our own life cycle has also been conspicuous and can be used to keep time---to this day we talk about human lifetimes and generations.
But as aforesaid, the astro-body clocks---Sun and Moon---had precedence.
For short time measurements during a day, the astro-body clocks were not fully satisfying.
They were sometimes hard to read precisely or at all if the sky were cloudy.
So artificial clocks were invented: sundials (which can't be read when it's cloudy either or a night) and water clocks in prehistory and mechanical clocks sometime in 13th century.
Early water clocks and mechanical clocks didn't keep time all that well as judged by intercomparisons between different examples and by comparisons to the astro-body clocks.
The theoretical position of measuring time changed considerably with the advent of Newtonian physics in the 17th century.
Newtonian physics gave a physical explanation in terms of basic laws as to why periodic systems should count the parameter time discussed above.
There was no "Shock of the New" in that ideal mechanical clocks were shown to count the same time as the astro-body clocks.
But there was one shock: the astro-body clocks couldn't keep time perfectly either.
Small perturbations would always cause them not to repeat in exactly equal periods.
In the modern age, to measure time to high accuracy, we use atomic clocks.
According to quantum mechanics (our modern theory of small systems), an atomic clock should keep time exactly regularly---if there are no PERTURBATIONS.
But there are always are PERTURBATIONS.
Nevertheless, the best atomic clocks measure time more accurately than anything we know of.
But there is a big complication arising in modern physics that was shown by special relativity and general relativity.
Time in general flows at the different rates in different frames of reference that are in relative motion and in frames in different gravitational fields.
This effect is given the general name time dilation.
For example, two frames in relative motion or in different gravitational fields will have different time flow rates.
If you initially synchronized two clocks in these two frames, as time passed---as measured in either frame---the two clocks would increasingly give different times when measured simultaneously by any observer---according to her determination of simultaneity.
It doesn't matter what the clocks are.
Time dilation is well understood and we can calculate the time discrepancies that arise.
We don't perceive time dilation in everyday life because the time discrepancies in everyday life are minute.
But time dilation is experimentally verified.
One example, is gravitational time dilation of general relativity:
Time dilation is of profound importance in astronomy and cosmology, of course.
It's also important in technology. For example, for keeping modern standard times, such a Coordinated Universal Time (UCT) used for civil purposes, must account for time dilation to keep the standard times exactly the same for everyone.
For another example, the Global Positioning system (GPS) would not work at all as accurately as it does if time dilation were simply neglected.
The coupling of space and time in special relativity and general relativity is so much a part of those theories that a joint word was needed.
So in relativity-speak, one speaks of spacetime.
In a very general sense, spacetime is the realm of physics.

Mass

Mass can be described as the stuff of existence.
Mass is the property is the property of bodies to resist acceleration.
Sometimes it's called the quantity of matter and that's sort of helpful---but if you ask what it means, one can has to we quantify matter by its resistance to acceleration.
Mass has another important physical property that in Newtonian physics is completely independent of its role in resisting acceleration.
Mass is the source of the gravitational field that is the cause of the gravitational force and the gravitational force on an object is proportional to its mass.
We'll discuss gravity in some detail below in section Gravity.
The point at the moment is that mass has two important aspects: resistance to acceleration and its role in gravity.
In Newtonian physics, that mass has these two aspects is just a coincidence.
In general relativity, the two aspects are fundamentally related---but we won't go into that in our discussion.

Energy

Now what about energy.
It's actually rather hard to define---all textbooks seem to admit this.
No short definition is adequate. But a common one-sentence definition that is useful is:
Another one-sentence definition that yours truly made up is:
Both one-sentence definitions are illuminated in the rest of this section.
We think of energy as being in things.
As the above discussion suggests, the everyday qualitative use of the term energy is actually pretty much correct as far as it goes.
Of course, energy is quantified and that requires units.
In fact, you are all used to thinking about energy, but probably not in the Metric System unit of energy which is the joule with symbol J.
But you are used to thinking about watts (with symbol W) which is the Metric System unit of power and power is energy transferred or transformed per unit time.
So a watt is a joule per second.
Rather than joules, you probably more used to hearing about energy measured in weird units that bedevil all civil discourse about energy.
Here's a table of energy unit conversions just to clue you in.
```
     -----------------------------------------------------------------------------------
     Energy Unit Conversions
     -----------------------------------------------------------------------------------
     Weird unit            In convenient    Comment
                           metric units
     -----------------------------------------------------------------------------------

     1 food calorie        4.1868 kJ        Typical human food needs are
                                            in the range 2000--3000 food calories.
     1000 food calories    4.1868 MJ        per day.  That turns into 8--12 MJ.
                                            So the megajoule is a perfectly
                                            convenient unit for food energy.
                                            It's better than food calories.

     1 calorie             4.1868 J         A food calorie is really a kilocalorie.
                                            The real calorie is the amount of
                                            energy needed to raise the temperature
                                            of one gram of water by 1 degree Celsius.
                                            Various versions exist because the
                                            amount of energy needed varies
                                            with conditions.  The shown one
                                            is the International Steam calorie
                                            (See Wikipedia:  Calorie).

     1 kilowatt-hour       3.6 MJ           The kilowatt-hour is hybrid unit
                                            that is (kilojoule/second)*hour.
                                            The MJ is good-sized replacement.
                                            Electric companies should bill in MJs.

     1 Btu                 1.0545 kJ        British thermal units of slightly
                                            different size still linger around.
                                            Kilojoules can obviously replace them.

     1 kg of gasoline      44--45 MJ        About 5.5 times daily human
                                            food needs.  You could live
                                            on a about 0.2 kg of gasoline.

     1 kg of oil           41.868 MJ        This is standard definition
                                            since the chemical energy content
                                            of oil varies.  It looks like the
                                            calorie digits.

     barrel (bl) of oil    6.12 GJ          This is approximate.  The oil
     equivalent                             industry insists are reporting
                                            oil in barrels---though no one
                                            has put oil in barrels in a
                                            jillion years (to be precise).
                                            Why not just report oil quantities
                                            in energy equivalent since energy
                                            content is the key issue.

     1 Mbl of oil          6.12 PJ          World daily consumption is often
                                            given in mbls.

     1 Gbl of oil          6.12 EJ          World yearly consumption is often
                                            given in Gbls.

     -----------------------------------------------------------------------------------
     Source:   Wikipedia:  Energy unit conversions.
     -----------------------------------------------------------------------------------

     
```
An important aspect of energy is that it obeys the principle of the conservation of energy which says that energy can never be created or destroyed.
Energy can change forms though. All forms are convertible to other forms---but not necessarily easily.
There, in fact, many forms of energy, but the sum of all these kinds for a closed system (one isolated form everything else in the universe) stays constant no matter transformations the closed system undergoes.
Energy has many forms.
In fact, it's almost impossible to have definitive list because there are different ways of defining the forms of energy and the form categories overlap.
But there is no such thing as PURE ENERGY: energy is always in some form: it also has some calculational value from measurable characteristics of a physical system.
So energy is a somewhat abstract thing---but we're used to abstract things like money.
Here's a limited list of the forms, we often use:
1. Kinetic energy (KE): The energy of motion. It has a simple formula for an object:
```
                      E=(1/2)mv**2 ,

                      where m is the object mass

                      and v is the magnitude of velocity of the 

                         center of mass

                          of the object.
         
```
2. Potential energy (PE): The energy of position in a field of force.
  A field of force is just a region of space where a particular force can be exerted.
  Examples are the graviational field and the electric field.
  So there is gravitational potential energy and electrical potential energy.
  There are other forms of potential energy too.
3. Heat energy: It's the energies associated with microscopic motions and structures.
  The most obvious of these energies is the kinetic energy of atoms and molecules in the frame of reference of a material.
  Heat energy sums up to MACROSCOPIC amounts.
  And humans are quite sensitive when the amount of it per unit mass is too high or too low: the material is hot or cold.
  The proper name is internal energy rather than heat energy or heat.
  But, in fact, many people just say heat for internal energy even if they never do in writing.
4. Chemical energy It's the energy of chemical bonds.
  This means it's actually the electrical potential energy and kinetic energy of chemical bonds.
5. Nuclear energy It's the energy of nuclear bonds.
  This means it's actually the nuclear potential energy and kinetic energy of the atomic nucleus.
6. Electromagnetic field energy The energy of electromagnetic field. Often we can partition this energy into the energy of the electric field and the energy of magnetic field.
7. Electromagnetic radiation energy The energy of electromagnetic radiation or light.
  Actually, electromagnetic radiation is just a traveling electromagnetic field, and so Electromagnetic radiation energy is really just electromagnetic field energy---different contexts demand different words, however.
  Electromagnetic radiation energy is a key means by which energy and information are transferred.
  The transferrals are both over short distances and times as from the lights in this room and long ones like across the observable universe and everything in between.
  A universe without electromagnetic radiation would rather limited to say the least.
8. Rest mass energy Let's wait to discuss this in section E=mc**2.
9. Etc.
The list of forms of energy goes on and on.
Where did all these forms come from.
Historically, kinetic energy was the first form of energy to be recognized in in the early 19th century (see Wikipedia: Energy: History).
The other forms were mostly recognized/discovered in the course of 19th century.
In a sense, folks invented new forms of energy in order to maintain the principle of conservation of energy.
So one might ask is conservation of energy a sort of an accounting trick.
I think the answer is no.
The new forms of energy were always there to be discovered which I think means energy is a real thing and so is conservation of energy.
The whole question of existence of energy was transformed by the discovery of special relativity in 1905.
We discuss this just below in section E=mc**2.

E=mc**2

The discovery of special relativity in 1905 by Albert Einstein (1879--1955) radically transformed some of our ideas about energy---and mass---and physical space---and time.
Actually, it was in Einstein's 2nd paper on special relativity in 1905 that he derived his famous equation E=mc**2 (Be-97--98).
Many people just call this equation E=mc**2, but one can also call the Einstein equation or the mass-energy equivalence.
Note E is energy, m is mass, and c**2 is the vacuum light speed squared.
But what does E=mc**2 mean?
It's primary meaning is that mass and energy are really the same thing.
The properties we associate with mass and the properties we associate with energy are both the properties of the thing we can call either mass or energy.
In relativity jargon, one frequently says mass-energy to emphasize the identity.
So an amount of mass is an amount of energy and an change in energy is a change mass.
I know this all seems a bit mysterious given the properties of mass and energy, we've discussed.
But we can clarify things by a few more considerations.
1. Rest Mass in General
  Rest mass is just the mass of a physical system observed in an inertial frame of reference in which the physical system is at rest.
  You can imagine enclosing the physical system in black box so as NOT to see any moving parts inside.
  If the physical system is moving relative to the inertial frame of observation because kinetic energy has mass.
  Now if you look inside the system you may see that there are moving parts.
  So some of the rest mass of the system can be the mass of the kinetic energy of the parts.
  The higher the velocity of those parts, the higher the kinetic energy of the system and the higher it's mass.
  The kinetic energy adds
```
         kinetic energy / c**2 to the rest mass.
         
```
  Rest mass by E=mc**2 is the same as rest mass energy.
2. Rest Mass of Ordinary-Matter Particles
  The ordinary-matter particles of physics are protons, neutrons, and electrons.
```
  ---------------------------------------------------------------------------------------
  Ordinary-Matter Particle Properties
  --------------------------------------------------------------------------------------- 
  Particle       mass (kg)           mass (AMU)       E (MeV)       electric charge
  --------------------------------------------------------------------------------------- 
  proton         1.6726*10**(-27)    1.0073           938.27        +e  
  neutron        1.6749*10**(-27)    1.0087           939.57         0 
  electron       9.1094*10**(-31)    5.4858*10*(-4)     0.51100     -e
  --------------------------------------------------------------------------------------- 

  The values have been rounded-off to 5 digits.

  The atomic mass unit (AMU) is 1.660538782(83)*10**(-27) kg
  and is by definition the 1/12 of the mass of an unperturbed 
  Carbon-12 atom.

  e is the
  elementary charge
  which is 1.602176487(40)*10**(-19) coulombs.
 
  The coulomb is the macroscopic unit of charge.
  A coulomb per second is the ampere, the familiar unit of current.

  
```
  All ordinary matter throughout the observable universe is constructed of the ordinary-matter particles.
  And the ordinary-matter particles are rather stable.
  They can be created and destroyed---and those processes go on all the time---but in ordinary conditions throughout the observable universe at relatively low rates.
  The ordinary-matter particles have most of the mass and therefore the most of the energy of the luminous observable universe ---it's in the form of their rest mass energy.
  Since the ordinary-matter particles are rather stable, the mass and energy associated with them is rather fixed and undergoes relatively little transformation.
  This fact is what gave rise to the historical conservation of mass for physical systems where heat, electromagnetic radiation, and/or mechanical work (which a macroscopic energy transfer process) was emitted or absorbed, but no MACROSCOPIC flows of matter were observed.
  Actually, there is no conservation of mass for such physical systems---if their energy content changed, their mass changed---to be exact, if their energy changed by Delta E, then there mass changed by Delta m=Delta E/c**2.
  But before 1905 or so, such changes in mass were undetectably small.
  For example, say a chemical reaction caused a physical system to emit 1 gigajoule of heat---this amount of energy is what a human need for about 100 days.
  How much does the mass of the physical system change by?
```
   E/c**2 = 10**9 J /((3*10**8)**2) = 10**(-8) kilograms. 

   
```
  Until modern times such mass changes were too small to detect.
  Note that if that heat did not get out of the system, the mass of the system would NOT change.
  There would just be change in the form of some of the energy from chemical energy to heat.
  People were able to observe and measure the transformations of energy using the known formulae for the various known forms of energy, but they didn't notice the accompanying mass changes since they were too small.
  So up until 1905, the principles of conservation of mass and conservation of energy were thought to be distinct.
  Since 1905, mass and energy have been recognized as the same thing, and the principles of conservation of mass and conservation of energy are recognized as the same principle.
  Mass and energy only appeared to be different things since different properties were associated with them and since most ``mass-energy'' is in the rather stable form of the ordinary-matter particles, and so doesn't undergo transformations at a high rate in ordinary circumstances.
  Now what if you could make a large transformations of the rest mass energy of ordinary-matter particles.
  For example, say we could convert 1 kg of iron into kinetic energy.
```
    The energy amount is

    E=mc**2 = 1 * (3*10**8)**2 = 10**17 J 

     =  10**17 J  *  (1 Mt/(4.184*10*15 J))

     = 25 Mt   , 

     where 1 megaton (Mt) is the chemical energy released by 
     1 megaton of TNT
     (Wikipedia:  TNT equivalent.

    
```
  Of course, TNT equivalent is used to measure the energy released by nuclear bombs.
  Here's a graph illustrating cloud height---the clouds being the famous mushroom clouds of nuclear explosions, but also occur in other systems such volcanic erruptions.
  The Little Boy nuclear bomb used at Hiroshima was 15 kt.
  Castle Bravo test at Bikini Atoll in 1954 was the biggest test US nuclear bomb at 15 Mt---earlier tests at Bikini inadvertantly gave a name to innocent form of beach wear.
  The Soviet Tsar Bomba had a yield of 50 Mt.
  So conversion of an isolated clump of 1 kg of ordinary-matter particles into explosion energy yields really big explosions.
  But fortunately such conversions are hard to do.
  In principle, they can be done, but in practice on nuclear bomb scale they are impossible---which in our bombing time is a good thing.
  In nuclear bombs you do NOT simply convert a clump of ordinary-matter particles into explosion energy.
  You change nuclear bonds either breaking up nuclei ( nuclear fission) or building them up (nuclear fusion).
  The process is analogous to changing chemical bonds to absorb or emit chemical energy.
  But the energy of nuclear bonds is of order 10**6 times that of chemical bonds.
  That factor of million in energy scale has mesmerized people since nearly the discovery of radioactivity in 1896.
  So much energy from so little fuel.
  Well nuclear power has developed a place in the modern world---it produced about 14 % of the world's electrical energy in 2007 (Wikipedia: Nuclear power)---but it is far from dominant and it may never be dominant.
  By the way, Einstein's disovery of E=mc**2 is NOT the singular important invent in the development of nuclear energy---it is one of other important ingredients.
3. Mass without Rest Mass
  Certain particles are said to be massless particles.
  They photon (the particle of light), gluon (a particle that causes the strong nuclear force), and other hypothetical particles.
  These particles actually have mass since they have energy, but they have NO rest mass.
  Saying REST MASSLESS is just too longwinded I guess though more accurate.
  How can massless particles have no rest mass?
  They are never observed at rest.
  They always move at the vacuum light speed relative to any local observer???.
  Another aspect of special relativity is that all observers in inertial frames see these massless particles as propagating at the vacuum light speed.
  Our ordinary ideas of relative motion get upset by this.
  In special relativity and general relativity, this upset manifests itself by having time and length become frame-dependent quantities.
  Actually, massless particles can contribute to the rest mass of physical system if they are included in system.
  For example, electromagnetic radiation contained in internally reflecting box contributes its energy to the box system viewed as a whole, and so contributes to its rest mass.
  The mass of massless particles acts just like other massless particles, of course.
  It resists acceleration and it is the source of gravitational field and is the object of the gravitational force.
  Note also that particles with rest mass can NEVER move at or above the vacuum light speed.
  They would have to have infinite kinetic energy to do so in special relativity and general relativity.
4. The Energy of Space
  In discussing inertial frames, we argued that physical space has properties and this is what made inertial frames inertial frames.
  Physical space has other properties.
  One of which may be to have an average energy content.
  In inflation cosmology, transformations between different states of space energy can release energy that creates pocket universes.
  Universe as we know it would be one of these pocket universes.
  The pocket universes are embeded in a much larger background universe.
  There is also the dark energy whose nature is pretty much unknown, but seems to be necessary to drive the acceleration of the expansion of the universe which has been observed since about 1997.
To sum up this section, we've been argued that E=mc**2 shows that mass and energy are the same thing.
For me this is a strong proof that energy is a real thing, not just an accounting trick---it measures resistance to acceleration and it gravitates.
How much more real can it be?
In section Mass, we said mass can be described as the stuff of existence.
So energy can be described as the stuff of existence too.
In fact, because the word energy is more associated with changes in the physics, I think that saying energy is the the stuff of existence is the best locution.
Energy is also very much the stuff of physics too since all physical effects can be discussed in terms of energy and long with a lot of other concepts.
A series of events can often be described as a series of energy transformations.
Forces

As noted in section Space, a force is a physical interaction on a object that can cause acceleration relative to an inertial frame.
Acceleration.
So forces can push things apart or pull them together.
Force also mediate the change of energy forms.
For example, if an object is accelerated by a force, its speed might (but not necessarily will) increase and that means its kinetic energy will increase.
We will skirt the details of energy transformations.
If forces are balanced, then you can create structures or, in other words, BOUND SYSTEMS.
Usually by BOUND SYSTEM, you mean a STABLE BOUND SYSTEM.
A ball a the bottom of curved pocket---which in physics jargon would be a gravitational well---is in a stable BOUND SYSTEMS: small perturbations will make it oscillate about, but it can't get out of the pocket.
On the other hand, a ball balanced on top of hill is an unstable structure.
It will stay there if there are no perturbations, but any perturbation causes it to role away and not come back.
Another example of a stable system and an unstable system is given below.
So BOUND SYSTEMS are stable structures.
But not perfectly stable, any BOUND SYSTEM can be disrupted by a big enough perturbation.
A typical BOUND SYSTEM would be when attractive forces pull objects together, but repulsive forces prevent the objects from just collapsing into a point---which in theory is what's at the center of black hole which is NOT a typical BOUND SYSTEM---at least in everyday terms.
But there is another way to prevent collapse to a point besides repulsive forces.
That's by MOTION as measured using kinetic energy, momentum, and angular momentum.
Kinetic energy is a directionless measure of motion.
Momentum for straight-line motion and angular momentum for rotational motion are directional measures of motion.
To see how MOTION can prevent collapse, we can consider for example of straight-line motion the simple harmonic oscillator which could be as simple as oscillating object attached to a spring.
There are four fundamental forces in the traditional physics jargon:
1. The strong nuclear force.
2. The weak nuclear force.
3. The electromagnetic force.
4. Gravity or the gravitational force.
The first three of the four forces have been unified as a single force and we expect/hope that gravity will join the party, we still talk say four foundamental forces as a matter convention/tradition/convenience.
All other forces are actually manifestations of the four foundamental forces.
The electromagnetic force for example, manifests itself as the Coulomb's law force (i.e., electrostatic force), magnetic force, chemical bonding force, pressure force, elastic force, tension force, and so on quasi-endlessly.
In fact, all forces in everyday life, except gravity, are manifestations of the electromagnetic force.
The complexity of the electromagnetic force makes it difficult to deal with actually.
Now what about structures or BOUND SYSTEMS.
Typically when you form from particles or subsystems that are brought in from infinity, you get energy out that typically we don't count as part of the BOUND SYSTEM because often it propagates away somehow.
The subsystems had more energy apart than together.
The energy you get out is often in the form of electromagnetic radiation, heat, and/or kinetic energy.
Since the subsystems had more energy apart than together, they had mass apart than together.
So forming BOUND SYSTEMS from initially far apart subsystems is typically exothermic usuing the the jargon of thermodynamics (heat physics) loosely.
If you transform from kinds of BOUND SYSTEMS, you may get energy more energy out (i.e. have an exothermic transformation) or you may need to put energy in (i.e., have an endothermic transformation).
SYSTEMS become more tightly bound if you get energy out and less tightly bound if you put energy in.
But note exothermic transformations don't necessarily happen spontaneously.
Often you have to overcome an energy threshold before exothermic transformations
For example, fire.
It's an exothermic chemical reaction.
But fires in everyday life don't start spontaneously.
There has to be an initial heat energy input to overcome a threshold and then the heat energy output from the first reactions propagates the reactions.
Fire is a chain reaction actually, but usually not described that way.
When one says chain reaction, one usually thinks a nuclear chain reaction.
We will briefly consider the hierarchy of BOUND SYSTEMS.

Bound Systems

Nowadays in standard model of particle physics, one thinks of the fundamental particles has being quarks and leptons and the force carrier particles.
We won't try to cover the whole particle zoo here.
We'll just sketch how one builds up the world from the fundamental particles.
Quarks in threes make up the protons and neutrons.
Quarks may be truly point-like---or maybe not.
Free quarks are apparently impossible in most environments.
They can exist in a superdense state called quark-gluon plasma which can be briefly formed in large particle accelerators and exist in some astrophysical environments probably.
Protons and neutrons are BOUND SYSTEMS.
The strong nuclear force binds them.
Protons and neutrons are about 10**(-15) meters in size scale.
The strong nuclear force also binds the protons and neutrons into the atomic nuclei of which there are a large variety.
Atomic nuclei typically have size scales of 10**(-14) meters.
Because of the protons, atomic nuclei have positive electrical charge.
Those, negatively charged electrons can be bound to the atomic nuclei by the electromagnetic force.
Electrons are the most important kind of leptons.
The bound systems of atomic nuclei and electrons are the atoms.
The periodic table below shows the known atoms and atomic nuclei that go with them.
If the electrons equal the number of protons, the atom is electrically neutral.
Otherwise it has a positive or negative charge and is called an ion.
Atoms can be bound together to make molecules.
The binding force is again the electromagnetic force, but in a complex manifestation.
Molecules can be immensely complex, but even simple ones can have very complex behavior---like the water molecule---good old H2O.
Atomic nuclei, atoms, and molecules are NOT static structures.
The constituents are partially held up from collapse by kinetic energy and angular momentum.
We talk of the constituents as being in orbitals---which are in some respects similar to gravitational orbits---but in others very different.
Atoms arn't really like little solar systems---although in older science fiction that idea sometimes turned up.
Free atoms and molecules form gases. Bound atoms and molecules form liquids or solids.
In liquids the atoms and molecules though bound freely slide over each other.
In solids, they don't. The atoms and molecules are fairly rigidly bonded.
The binding of liquids or solids is done by the electromagnetic force.
But what does gravity do for the structures we've discussed so far?
Well self-gravity does very little for structures of human-size or even mountain-size or smaller.
All particles of mass---which means all particles of energy---attract all others gravitationally.
There is no anti-gravity so far as we know.
But gravity in a sense is a rather weak force.
It a takes mountain-size object or more for self-gravity to have a significant effect on structure.
Everyone in this room is attracted to everyone else---but so weakly you never notice---good thing to or we could be just a mass of arms and legs.
Now the self-gravity of big objects like the Earth does have an obviously important effect on the Earth's structure as a whole.
And on the little objects on the Earth like us.
The self-gravity doesn't cause the Earth to collapse---to black hole because the pressure force of the atoms
Support by kinetic energy and and angular momentum is not very important for the Earth.
There's a small bit of support because the Earth is rotating.
On the other hand, the Solar System, the planetary systems (i.e., other solar systems), the galaxies and the galaxy cluster are supported from collapse by kinetic energy and and angular momentum.
Let's turn our attention to gravity now in a bit of detail.

Gravity

Gravityis some ways much simpler than the electromagnetic force.
It has only one ``charge'': MASS.
And mass always attracts mass: gravity is never canceled by having two flavors of mass.
Now gravity on Earth was always known. Newton didn't discover that.
Isaac Alien discovers gravity.
What Newton discovered was that gravity is universal: both on Earth and in the astronomical realm, there was gravity obeying the same law.
The UNIVERSAL LAW OF GRAVITY.
The gravity force law (or Newton's law of gravity) which holds between ideal point masses is:
```
                G M_1 M_2
 F_12 =     -------------------
                 R_12**2

   where G = 6.6742*10**(-11) in MKS units (circa 2002)

      is the universal constant of gravity.

   M_1 is the mass of point mass 1.

   M_2 is the mass of point mass 2.

   R_12 is the distance between the masses.

   Notice this distance comes in as an inverse-square.

      We say that the formula is an inverse-square law
      and gravity is an inverse-square law force.

   F_12 is the force that 1 exerts on 2

     and the force that 2 exerts on 1.

   The forces are directly on the line between the
      two objects and point in opposite directions.

   The gravitational forces are attractive always.

   No anti-gravity exists in the ordinary realm of physics, but
      there may be a cosmological anti-gravity that is discussed in
      Lecture 31: Cosmology. 

   By the way, the MKS unit of force is the newton:  N=kg*m/s**2:

          1 N = about 1/5 lb.

   The gravity force law gives force in newtons when MKS units
      are used consistently.

 
```
Now POINT MASSES are one of those idealizations that physicists love.
In classical physics they don't exist. They may exist in quantum mechanics. We are not sure. In any case, we really don't know how gravity behaves close to quantum mechanical particle. No established quantum theory of gravity exists. The quantum theory of gravity should be part of Theory of Everything or TOE.
But the gravity force law is actually of the greatest use.
Firstly:
Gravity between objects of general shape.
Secondly:
Gravity between objects with simplifying conditions.
What is the gravitational force between two, 1 kilogram spherically symmetric masses held 1 meter apart?
Gravity is a very weak force.
The last figure illustrates that the gravitational force between human size and even much larger objects is usually unnoticeable.
Now recall
```
                G M_1 M_2
 F_12 =     -------------------
                 R_12**2

 
```
Gravity Near the Earth's Surface

In an absolute sense, gravity near the Earth's surface is a very parochial affair, but it's our parish: i.e., where we live.

Gravitation force per unit mass on Earth's surface.

The acceleration g due to gravity on the Earth's surface.

Accelerating downward under the force of gravity alone.
In fact the whole kinematics of falling objects should be the same regardless of mass---if you can neglect air resistance.
Drop a chalk brush and a coin: air resistance relatively small.
Then drop a brush and a sheet of paper: air resistance not relatively small for the sheet of paper.

Air resistance causes falling to reach a terminal velocity.

Examples of terminal velocities.

In free fall you feel weightless, but this is not because gravity has turned off.
Gravity is just pulling you down atom by atom and you arn't resisting, and so there is no internal stress or pressure to resistance.
Standing up and resisting gravity is a different matter.
Standing up and resisting gravity.
Now not only you, but the atmosphere, the oceans, and the solid Earth must stand up under gravity pulling it down.
Only PRESSURE FORCES can withstand the self-gravity of dense, massive bodies like planets and stars.
And the pressure force only acts against compression of a material.
The pressure force will not provide strength for very complex structures.
For example, water has a strong pressure force: you CANNOT compress it easily.
But water cannot resist shearing forces very well: drops can hold a shape, but nothing much bigger.
Liquids and pressure forces.
Even solids will not resist a shearing force if their mass is too big for a shape to be sustained by inter-atomic bonds: i.e., they will act like fluids.
Inter-atomic bonds make a boulder keep its shape under planet-size gravity.
But a boulder as big as a mountain on a planet is flattened into a mountain: i.e., a small protuberance on the face of a planet.
The pressure force can hold up the super-big boulder's mass, but it will push sideways causing the boulder to ``flow'' sideways and slump done to being a mountain.
A boulder as big as a planet in space would be pulled into spherical shape.
Let us consider how the EARTH is sustained.

Earth atmosphere, ocean, crust, mantle, core in a column.
Actually, the columm should be a wedge that narrows to a point at the Earth's center.

Pressures at various depths in the Earth.
Besides pressure, MOTION can withstand strong gravity as we have discussed above. This is what holds up planetary and galactic systems.
The strong self-gravity of these systems is countered by motion.
Usually rotational motion quantified as ANGULAR MOMENTUM or KINETIC ENERGY (i.e., energy of motion which we discuss this below).
ANGULAR MOMENTUM is, loosely speaking, the tendency of rotating bodies to keep rotating.
Let us now move on to gravity in space.

Circular Orbits

One thing to emphasize at the beginning about circular and other orbits due to gravity is that they are quasi-eternal.
They do not need extra energy input to keep going. It turns out (and we will not prove this) that gravity in pure TWO-BODY SYSTEMS cannot cause the orbit to change. Gravitational and other perturbations can to this, but to 1st order the orbit is perpetual.
Let us first consider a circular orbit with the speed constant: i.e., uniform circular motion.
Acceleration is toward the center in uniform circular motion.
Consider a slingshot demonstration.
If you accept Newton's 2nd law, then the acceleration in the slingshot demonstration must be toward the center ideally.
Actually, one has to keep drawing the object along a little to compensate for air resistance and friction at the central pivot.

Centripetal acceleration a=v**2/r.

The gravitational orbital speed of uniform circular motion.

Let us now apply our circular orbital speed result to the case of a satellite in LOW-EARTH ORBIT.
Low-Earth orbit velocity and period.
Low-Earth orbit satellites orbit really very fast: 8 km/s and this is independent of their mass, shape, color, etc.
And note rockets don't need any rocket thrust to do this.
The rocket thrust was needed to give the satellite kinetic energy (energy of motion) to lift it up from the ground and get it moving at about 8 km/s.
Once in orbit the satellite is in a perpetual falling motion.
Quite literally, the satellite and all its contents are falling toward the Earth under gravity---but they keep missing.
Newton's mountain-orbit diagram.
Free falling in orbit.
Low-Earth orbits are only quasi-perpetual because in fact there is still some ATMOSPHERE in low-Earth orbit and this gives a weak air resistance that eventually transforms the kinetic energy of the satellite into heat energy and the satellite orbit decays.
A decaying orbit is one that is spiraling into the Earth.
The decay accelerates because the lower the orbit, the more the atmospheric resistance.
Most satellites would burn up in the atmosphere: their kinetic energy changing partially into heat energy due to air resistance.
Very large satellites can make it to the ground.
NASA is very concerned about large satellites hitting the ground in an uncontrolled manner.
Usually, they command large satellites to ditch in the ocean.
This may be the fate of the HUBBLE SPACE TELESCOPE!

Elliptical Orbits, Escape Orbits, and Orbital Pinball

Elliptical orbits are non-circular orbits.
Recall if there is vast mass disparity, the smaller body orbits the larger body in an ellipse with the larger body at one focus.
A Sun-planet orbital system.
The eccentricity e is a measure of the non-circularity of an orbit:
```
 
   e = 0 for a circular orbit

   0 < e < 1 for a closed eccentric orbit

   e = 1 for a line orbit
           
     or, depending on initial conditions, an parabolic escape orbit. 

   e > 1 for a hyperbolic escape orbit.

   See Go3-94.

     
```
The escape orbits are unclosed or OPEN ORBITS. The body travels off to infinity on such an orbit.
What sets the orbit?
Newtonian physics, of course, but that is general and applies to all orbits.
The thing that is particular to individual orbits is INITIAL CONDITIONS.
One way is start the orbit with a small mass a distance R from a large mass.
The large mass becomes the orbit focus or center of force.
The initial speed is v and is perpendicular the radial direction.
The INITIAL CONDITIONS for this setup are R and v.
Elliptical orbit parameters.
Orbits for increasing initial velocity v.
The INITIAL CONDITIONS of the planets were set by the formation process of the solar system.
But the orbits have since evolved due complex perturbations and collisions.
Space probes have their orbits set by their initial launch and subsequent rocket firings.
That is just a taste of celestial mechanics.
But we can mention the orbital pinball game that space agencies often play.
NASA (or whomever) can use planetary encounters to change probe orbits in useful ways.

For example, to launch a probe straight at the Sun, requires launching it at zero velocity in the frame of the fixed stars (Ni-61--62).
But since the Earth is moving at 30 km/s relative to the fixed stars, the launch speed must be 30 km/s opposite to the Earth. No existing launch vehicle can achieve such a speed.
Instead, the probe can be launched the direction of motion of the Earth.
This gives it a higher orbital speed than the Earth's and sends it on a orbit to the outer solar system.
A carefully controlled slingshot encounter with Jupiter, then slows the probe to zero velocity relative to the fixed stars.
The probe then just falls under gravity toward the Sun.
A slingshot maneuver.
This procedure, of course, takes years to complete. It takes a long time for the probe to reach Jupiter and return to the inner solar system.
For example, the Ulysses probe was sent into a polar orbit about the Sun after a slingshot maneuver about Jupiter (NASA/JPL Ulysses Site).
In this case the slingshot maneuver wasn't used to stop the probe, but to put it in an orbit that was well out of the ecliptic plane.
It took more than 4 years from launch on 1990oct06 to make its first pass over the Sun's south pole (Ulysses Milestones).
NASA is very clever at slingshot maneuvers---the boys and girls at NASA consider themselves the real pinball wizards.

Thermodynamics

Thermodynamics, like energy, is hard to define in one-sentence.
1. One can say that thermodynamics is the science of heat---which properly should be called internal energy---but which in speaking, one seldom does.
  Essentially, heat (or internal energy) is the sum of all microscopic forms of energy.
  Let's not list them. The list is complicated by overlapping categories.
  But the key one for thermodynamics is the microscopic kinetic energy: the translational, rotational, and vibrational kinetic energy of microscopic particles.
  This kinetic energy is NOT macroscopically correlated---you don't see a macroscopic system moving because of this kinetic energy.
  It's the kinetic energy of the random or semi-random microscopic motion of atoms, molecules, electrons, nuclei, photons, and other stuff we won't go into.
  The macroscopic manifestations of changes in internal energy are changes in pressure, volume, temperature, and phase of a system---and other things too.
2. Temperature is a bit hard to define too.
  A rather general definition is that it is a measure of the average energy per degree of freedom of the particles in a system.
  More intelligibly, it's a measure of average microscopic kinetic energy of particles.
  The higher the temperature, the more the particles are jostling.
  This increases pressure in gases which may cause the gas to increase in volume depending on how it is contained.
  Pressure is force per unit area on any surface in a medium. In a gas faster the particles, the harder the particles hit, the more pressure.
  In solids and liquids, higher temperature usually---but not always---causes bonds to to lengthen which means there is a macroscopic increase in volume and decrease in density. This is called thermal expansion.
  In fact, we typically measure temperature by measuring pressure or volume of some substance and having a correlation table of those quantities with temperature: e.g., the scale on a temperature.
  There are other ways to measure temperature.
  And, of course, we humans are sensitive to temperature and can measure semi-quantitatively just by feel.
3. There is an absolute zero.
  It occurs when all the microscopic kinetic energy that can be removed from a system has been removed.
  There is actually zero-point energy that cannot be removed from particles as dictated by quantum mechanics
  On the Kelvin scale, absolute zero is 0 K.
  On the Celsius scale, it's -273.15 degrees C.
  On the Fahrenheit scale, no one cares.
  Practically speaking, it seems impossible for macrscopic system to reach absolute zero, but microscopic systems can easily---but some folks say that doesn't count since temperature is defined to be a macroscopic average.
4. Heat can flow between macroscopic systems. The main mechanisms at our level are:
  1. Conduction: This is one particle colliding with or shaking another neighboring one resulting in a transfer of microscopic kinetic energy.
    We don't see conduction with our eyes, but you can sure feel it happening when you touch something hot or cold.
  2. Convection: This is actually, a macroscopic process.
    Macroscopic clumps of fluid (gas or liquid) transport heat energy from where the clump formed to where it breaks up.
    Convection happens in gravitational fields.
    A heated clump expands, becomes less dense, and buoyancy causes it to rise.
    Buoyancy is essentially the pressure force.
    If a clump's density goes down, net pressure force on the clump increases (because it has more surface area), but its mass and weight don't, and so the gravity force is no longer balanced.
    The clump is pushed opposite to the gravity force direction.
    Cold clumps sink to fill the space left by the rising hot clumps.
    Convection goes on everywhere on all kinds of scales.
    You see it in a boiling pot of water.
    It's major flow in the Earth's atmosphere, but it's not usually visible since air is invisible.
    Even the solid Earth flows on long time scales.
    This is the convection in the Earth's mantle that drives plate tectonics.
  3. Radiative Transfer: All bodies above absolute zero radiate electromagnetic radiation.
    We won't go into why.
    But this is not reflected electromagnetic radiation.
    It comes at the expense of the internal energy and has a special distribution with wavelength, that we'll discuss in a later lecture.
5. If two systems are at the same temperature heat will not flow between them when they are in thermal contact.
  Thermal contact means the heat transfer processes can operate.
  The two systems are said to be thermodynamic equilibrium if heat won't flow during thermal contact---so they are in thermodynamic equilibrium if they are at the same temperature.
  Here's a question for the class.
6. Systems in thermodynamic equilibrium to not change thermally or macroscopically.
  Thermodynamic equilibrium is, in fact, a timeless and lifeless state.
  Timeless at the macroscopic level: at the microscopic level atoms are always moving about and changing their microscopic state.
  Life as we know it could not live in a universe in thermodynamic equilibrium
  We need to live in an open system (which is the biosphere of the Earth) with steady inflow and outflow of energy across a temperature gradient.
7. Almost all our energy ultimately comes from the Sun.
  Energy for life.
  1. Food energy and wood fuel from photosynthesis.
    The unhappy consequences for plants of photosynthesis. Herbivores are just plant predators you know.
  2. Hydroelectricity is comes from the hydrological cycle which is driven by solar heat.
  3. Fossil fuels (i.e., coal, oil, and natural gas) are derived from plant material laid down in the geological past.
  4. Direct solar power, of course, from photovoltaic cells.
  Only nuclear power and geothermal power are from non-solar sources.
  The nuclear bond energy in atomic nuclei created either in other stars or in the Big Bang.
  Geothermal power is based on residual/radioactive heat from the Earth's interior. It drives much of geology (e.g., plate tectonics, earthquakes, and volcanoes), but as a direct energy source for society is very minor and unlikely to increase much in importance.
The 2nd Law of Thermodynamics

Why does heat flow spontaneously from hot (i.e., high temperature systems) to cold (i.e., low temperature systems)?
We now understand this universal observation as a consequence of the 2nd law of thermodynamics.
Entropy is a measure of microscopic disorder.
So the 2nd law of thermodynamics just says that left to themselves things go to heck.
There are an enormous number of microstates in which a closed system can find itself consistent with conservation of energy.
An axiom of thermodynamics is that they are all equally likely.
The random microscopic interactions lead to this axiom.
The number of macrostates are much fewer.
There is a many-to-one correspondance of microstates to each macrostate.
The macrostate with the most corresponding microstates is the one most likely to be observed: i.e., it is the most probably macrostate.
So one sees the most probable macrostate or something very close to it.
There are more ways for a system to be disordered than ordered, and so the macrostates that are maximally disordered are favored: i.e., the maximum entropy macrostates.
Just think of your living room.
It's ordered because you've ordered it---one hopes---you're not living squalor, right?
If a tornado came through it could order things too, but it's a randomizing process and is more likely to disorder then than order them.
In fact you never see a tornado order a living room even though it's got all the energy in the world to do that.
It could but it's just so unlikely.
Heat flowing from cold to hot spontaneously has some miniscule probability of happening in principle, but you never ever see it in reality.
It's just so unlikely that random processes will result in ordering the energy in that way.
So the 2nd law of thermodynamics gives a direction to thermal processes---it's sometimes called the arrow of time---like on a one-way street.
So the 2nd law of thermodynamics tends to disorder things.
But there are ordering processes too.
Gravity by trying to clump matter gives an apparent ordering on a big scale.
And yes it does increase order---but only in some places.
You create ordered clumps of matter, but energy is emitted as heat or light and spreads throughout space. Overall disorder increases.
So even gravity seems to bow to the 2nd law of thermodynamics.
In fact, the richness of physical law allows order to grow in some places at the expense of increasing disorder elsewhere. Overall disorder increases.
Evolution too results some pretty high states of order---life. Overall disorder increases.

Universal Evolution

If you have a physical system at some instant in time and specify all it's conditions, physics dictates how the physical system will evolve.
One billard ball hits another or one gas molecule hits another and everything plays out.
Now if the universe were in complete stable macroscopic equilibrium and thermodynamic equilibrium, nothing would ever change.
At the microscopic level, microscopic systems would fluctuate randomly, but thermodynamic equilibrium ensures that nothing changes.
We obviously don't live in such a universe.
As discussed in the section Thermodynamics, the universe is profoundly not in thermodynamic equilibrium.
It's not in macroscopic equilibrium either as we'll discuss in Lecture 31: Cosmology.
It's an evolving universe.
In Big Bang theory, the Big Bang was itself the initial condition of the universe and everything evolves from that.
The tendency of macroscopic energy forms to dissipate as waste heat and of physical systems to evolve to thermodynamic equilibrium suggests that thermodynamic equilibrium will be the fate of the universe will.
A lifeless state of thermodynamic equilibrium.
This happy state of affairs is called the heat death of the universe.
But it may not happen.
We don't understand the universe as whole.
And anyway, it's predicted to be of order 10**100 years off.

Tides

The Earth tides are an important application of the physics we've been learning.
Let's see how many landlubbers we have.
Tidal zone at low tide.
The parallel ripples form perpendicular to the tide flow.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line1725, America's Coastlines Collection; Photographer: Mr. David Sinson, NOAA, Office of Coast Survey.
Wetlands with tidal streams in South Carolina, 1991.
I'd guess this is closer to high tide than to low tide. But I know nothing.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line0095, America's Coastlines Collection; Photographer: Richard B. Mieremet, Senior Advisor, NOAA OSDIA.
Lower Patuxent River, Maryland during an extreme high tide.
You can see the tide is running up a country lane of some kind. This is just off Chesapeake Bay where there is considerable land subsidence.
Part of the problem is that if you pump fresh water out of the ground you lower the water table and the Earth subsides. This is a problem not unknown in Las Vegas.
Flooding like this could become very common if the sea level rises with global warming.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line0647, America's Coastlines Collection; Photographer: Mary Hollinger, NODC biologist, NOAA.
A tidal map of East Friesland from the late 19th/early 20th centuries.
This is Map B in The Riddle of the Sands (1903), a classic nautical spy-thriller by Erskine Childers (1870-1922). Childer was English, but joined the Irish in their rebellion. He was later executed by the Irish government for the illegal possession of a small hand-gun given to him by Michael Collins.
The Riddle of the Sands is one of those great old stories where men were men and women stayed as the romantic interest and didn't try to take over the plot.
Credit: The original publishers of the map were Walker and Cockerell sc.: their copyright is long expired I'd guess. Download site: Wolfram Fassbender's The Riddle of the Sands site.

EARTH TIDES
The Earth tides are caused by the gravitational effects of the MOON and to a lesser degree the SUN.
Let's just consider the MOON alone first and worry about adding the effect of the SUN later.
The gravitational force of the Moon on the Earth.
But Moon's varying gravitational force is only part of the story.
There is another part.
The Earth revolves around the center of mass of the Earth-Moon system.
Although the Earth is approximately an inertial frame for many purposes, the tides can't be understood without invoking the NON-INERTIAL FRAMENESS of the Earth.
The Earth is a rotating (i.e., non-inertial) frame.
In a rotating frame there is an effect that is called the centrifugal force.
It is NOT a real force.
But it sure feels like a real force that is trying to throw you out of a rotating frame.
Really you are just trying to move in a straight line as required by Newton's 1st law of motion.
But relative to the rotating frame, centrifugal force acts, as outward radial force that is exactly equal to the inward radial centripetal force needed to maintain the circular motion.
If there is insufficient to maintain the body in uniform circular motion, then centrifugal force will accelerate the body outward relative to the rotating frame.
The centrifugal force acts like a body force, not a contact force.
It ``pulls'' on you atom by atom, like gravity.
It is only when you resist it that you feel forces in action.
The centrifugal force on a carnival centrifuge.
The TIDAL FORCE is a combination of the variation in the Moon's gravitational force from its MEAN VALUE and the centrifugal force.
The tidal force of the Moon on the Earth.
The force per unit mass due to the Earth's own gravity is 9.8 N/kg.
The tidal force is about 10**(-7) times smaller (Fre-532).
So humans never notice the tidal force directly: you just do NOT notice small variations in the effective force of gravity you are subject to.
On the other hand, the OCEANS notice it minutely.
But a minute effect on the big ocean is big by human scale: a small ripple becomes a tsunami.
Thousands of kilometers across and several kilometers deep, a change in sea level by a meter or so to adjust for the tidal forces is NOT very big relatively speaking.
The adjustment allows the Earth's gravity and water pressure to partially balance the tidal force.
Tidal bulges and hydrostatic equilibrium.
If the oceans were allowed to come into HYDROSTATIC EQUILIBRIUM in the rotating frame of the Earth around the Earth-Moon center of mass, there would be permanent bulges.
This is just the adjustment of gravitational, tidal, and water pressure forces so the net force at every point is ZERO.
The the reality is that HYDROSTATIC EQUILIBRIUM can never be established because of the Earth's rotation on its axis.

In the diagram below we take a north pole view and for simplicity assume the Moon's orbits in the Earth's equatorial plane.
Actually, the Moon's orbit is tilted from the equatorial plane by an amount varying between 18.5 degrees and 28.5 degrees????: the variation is caused by that pesky rotation of the notes we discussed in Lecture 3: The Moon: Orbit, Phases, and Eclipses
The dynamic tidal situation.
Note an individual water particle doesn't go very far before the tidal current reverses.
Typically a water particle might go of order 20 km relative to the solid Earth---but the particle is not alone.
The whole ocean is sloshing back and forth.
Likewise because the Moon moves eastward continually, it takes the Earth about 24 hours, 50 minutes to make a complete rotation relative to the Moon.
So the full tidal cycle of two high tides takes about 24 hours, 50 minutes.
So on average there are fewer than than two high tides a day: most days there will be two, but sometimes there will only be one.
The 24 hours, 50 minutes tidal period, also means that tides will cycle through the whole day: e.g.,
In the open ocean the tidal range (i.e., high to low tide) is typically about 0.5 meters.
The tidal current is 1 to 2 m/s or 4 to 7 km/hr which is not too different from walking speed.
Open ocean tides were very hard to measure before satellites with radar ranging.
If you didn't have that you'd have to measure with respect to the bottom of the ocean which can be several kilometers down. Not easy to do very often.

The kind of satellite mapping that can be done to study tides.
This is not a tidal map. It shows sea height relative to mean sea height with tidal variation averaged away.
The sea height changes are dependent on the temperature of the water, and thus on the heat energy stored in the water.
Water is a rather complicated liquid in that it contracts going from 0 degrees C to about 4 degrees C and then expands as temperature increases above 4 degrees C (HRW-432).
Maps of this kind can be done to study tidal changes in detail.
The height measurements are done by radar from the TOPEX/Poseidon satellite. This satellite is in a near polar orbit, and so almost all of the Earth is below it at some time or other.
Credit: NASA: Visible Earth.

Now above we studied an idealized case where just the MOON has a tidal effect.
The SUN also has tidal effect that is a bit less than half the strength of the Moon's.
The solar tidal effect leads to a lunar month cycle (i.e., a 29.531 day cycle) for the tides.
There are two times when the Moon and Sun tidal effects add up and two times when they partially cancel.
Spring tides and neap tides.
Spring tides are the strongest tides and neap tides the weakest tides.
And there are other complications for the Earth tides:
1. The varying tilt of the Moon's orbit relative to the Earth's equatorial plane. This is caused by the rotation of the line of nodes.
2. The varying distance of the Moon due to the elliptical nature of the Moon and Earth orbits.
3. Continents, continental shelfs, coasts, and shallows.
4. Permanent ocean currents.
5. Seasonal changes.
6. Weather.
All these things go on at once, of course, and lead to some very strange effects.
Complicated coast-lines can lead to funny sloshing around. For example:
1. The tidal range in the Bay of Fundy in Nova Scotia gives a tidal range of 12 meters or more and tidal currents of up to 8 m/s (i.e., about 28 km/hr).
2. On the other hand, the Gulf of Mexico tidal range is only about 0.3 meters and there is only one noticeable high tide per day.
3. In the English Channel, there is a place (Southampton) that has 4 high tides per day due to a backwash effect (CW-385).
Weather can lead to severe problems.
If you have an on-shore storm coinciding with a spring tide, then you can have severe flooding---a TIDAL SURGE.
This is when unstable islands and coastal homes can be washed away.

SMALL BODIES OF WATER
Small bodies of water (small seas and lakes), in fact, have measurable tides, but they are usually too minute for humans to notice.
Everything scales down from the oceans.
Even the Mediterranean (which is fairly large) only has noticeable tides in a few places: e.g., Venice.

TIDAL SLOWING AND LOCKING
The Earth drags the oceans that are trying to form tidal bulges.
But by Newton's 3rd law, this means the oceans drag on the Earth too.
The dynamic tidal situation.
The drag is slowing down the Earth's rotation and increasing the length of the day.
The rate measured over some millennia is about 0.0014 seconds/century (USNO site).
The standard time day is set to be exactly 86400 seconds, where the second is now defined by an atomic clock measurement---and has no connection to astronomical cycles any more.
The mean solar day (i.e., the actual day relative to the Sun) is currently about 86400.002 seconds.
Every 500 or so days a leap second is introduced in standard time to keep standard time and mean solar time consistent.
The international time people in charge of leap seconds (International Earth Rotation Service) usually ordain leap seconds at the beginning of January or July without making much noise about. See the US Naval Observatory's leap second site and past leap second catalog.
Another way of viewing the slowing down of the Earth's rotation is to say that the Earth's rotational kinetic energy is being dissipated to heat---recall friction leads to heating.

Dissipation of tidal energy.
The tidal friction with the solid Earth and internally via viscosity dissipates energy that ultimately mostly comes from the rotational energy of the Earth.
The dissipation is complex and may have profound current and climate implications.
The removal of Earth rotational energy is increasing the length of the Earth's day by about 0.0014 seconds per century.
The figure illustrates the tidal dissipation in the ocean in milliwatts per square meter. It isn't clear to me what the zero on the scale represents.
Credit: NASA: Visible Earth.

The tidal bulges also have the effect of causing the Moon to spiral away from the Earth to larger orbits with longer periods.
The tidal bulges and the outward spiraling of the Moon.
The Moon's mean distance increases by about 3 cm/year as we know from bouncing laser beams off reflectors left on the Moon by the Apollo missions (Se-38).
400 million years ago---BEFORE dinosaurs ruled the Earth---the Earth's day was only 22 hours long (Se-38, Cox-250) and the Moon was probably significantly closer than today.
When dinosaurs ruled the Earth.
This can be deduced from the fossil record.
Long in the future---if the Earth lasts that long---the day will be the same length as the lunar month---then maybe 50 days (FMW-75 ). The Moon then will be farther away.
The Earth will always turn the same face to the Moon---this is just what the Moon does now to the Earth.
This situation is called SYNCHRONOUS TIDAL LOCKING.
In fact, almost all the significant moons in the solar system are already synchronously tidally locked to their planets (Cox-307).
Planet tidal forces on their moons, are much larger than the reverse.
Over long enough distances the solid Earth is flexible and there are land tides of a few centimeters.
They arn't that geologically important on Earth, but they are elsewhere in the solar system.
The tidal force on Jupiter's moon Io makes that body the most geologically active body in the solar system.
Atmospheric tides exist too, but they seem much less important than daily heating and cooling effects of day and night.
Also since we are inside the atmosphere, there is no obvious interface to watch.