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

Don't Panic


  1. Introduction
  2. Space
  3. Time
  4. Mass
  5. Energy
  6. E=mc**2
  7. Forces
  8. Bound Systems
  9. Gravity
  10. Gravity Near the Earth's Surface
  11. Circular Orbits
  12. Elliptical Orbits, Escape Orbits, and Orbital Pinball
  13. Thermodynamics
  14. The 2nd Law of Thermodynamics
  15. Universal Evolution
  16. Tides

  1. Introduction

    1. The Introduction of the Introduction:

      To say the least, it's hard to sum up all the physics that one needs to know to understand all astronomy and physical cosmology---which is the science of the universe in broad outline.

        By the way, in one sense, cosmology is a subfield of astronomy---in another sense, it's the other way around.

      Partially this is because there is a whole lot of such physics and partially becasue we don't know all of the physics we need to know for complete understanding.

      As discussed earlier in IAL 0: A Philosophical and Historical Introduction to Astronomy and the figure below (local link / general link: cosmos_history.html), we don't have the final, eternal, fundamental theory of physics: Theory of Everything or TOE.

      But we're NOT just sitting around
      Waiting for the TOE.

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

    2. No Completely Logical Presentation of Physics:

      There is NO completely logical presentation of physics---at least without infinite tediousness.

      One just has to dive in and swim to a degree.

      One obvious point is there is a lot of circularity in the definitions---but it's NOT a viscious circle---like in the figure below (local link / general link: ouroboros.html).

      It's hard to pull the concepts apart and define them without referencing other concepts.

      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.

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

      By the way---in case you didn't know---physics is very mathematical, but we will skip math almost entirely. We do sometimes show formulae for contemplating them, but almost never for calculating with them or analyzing them in detail.

    3. What is Physics?

      What is physics?

      The short conventional answer is that physics is the science of matter and motion. For motion, see the figure below (local link / general link: muybridge_horse.html)

      Light is usually NOT considered matter, but is considered in physics. But to be brief, we can include light under matter for the nonce. One could say "stuff and motion," but that sounds weird and pedantic.

      For motion illustrated, see the figure below (local link / general link: muybridge_horse.html).

      What do we want to do with

      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. For the inner Solar System, see the figure below (local link / general link: solar_system_inner.html).

      Everything else in the
      universe is the environment.

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

      But in our course, we restrict ourselves to systems whose behavior is closely dependent on physical laws and NOT so dependent on emergent principles outside of physics---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 we avoid like the plague.

      So we just tell stories---but physicists tell stories all the time to themselves---it's how we understand things up to a point---then the math kicks in. For storytelling, see the figure below (local link / general link: walter_raleigh.html).

      So to start those stories what about "matter and motion"?

      But even saying "matter and motion" implies a lot of understood concepts that actually need some definitions---like space and time.

  2. Space

  3. Space is such a basic item of our existence that it's to explain or define in brief or at length.

    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.

    1. Flat Space:

      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.

      See the figure of 2-dimensional Euclidean geometry below.

      For most purposes, FLAT SPACE is observationally verified both terrestrially and in 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 Λ-CDM model---the overall geometry of physical space is very nearly flat: i.e., the space of 3-dimensional Euclidean geometry.

      From the Λ-CDM model, we obtain a mass-energy distribution of the observable universe. See the figure below (local link / general link: cosmos_energy_pie_chart_images.html).

      space may NOT be exactly FLAT---there are good reasons for thinking NOT---and near dense acccumulations of mass significant space curvature is expected: e.g., 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 NOT violated.

    2. Inertial Frames Redux:

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

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

        Recall a FRAME OF REFERENCE is just a set of coordinates covering space that you use to describe the locations and motions of objects. It can just be an arbitrary set of coordinates in space or attached to some physical structure. See the examples in the figure below.

      See the insert The Basics of Inertial Frames below (local link / general link: frame_reference_inertial_frame_basics.html).

      the rest of this subsection is UNDER RECONSTRUCTION. Don't read

      Inertial frames were discussed at length in IAL 1: Scientific Notation, Units, Math, Angles, Plots, Motion, Orbits: Physics for Orbits We will only do a partial recapitulation of that discussion here.

      Definition of Inertial Frames: In modern understanding based on general relativity (GR) and in particular its axiom the strong equivalence principle, an inertial frame is a frame of reference that is unaccelerated in a free-fall frame in a uniform gravitational field.

      In an inertial frame accelerations are caused only by forces: i.e., physical relationships between bodies.

      Two key points about the inertial frame definition:

      1. An exact external uniform gravitational field is an ideal limit that can sometimes be approached very closely. When it CANNOT, you can often correct for the non-uniformity by considering tidal forces: i.e., the stretching force. on non-uniform gravity.

      2. If the acceleration of your frame of reference relative to an inertial frame is small enough it can be neglected and if NOT small enough you can still treat your frame of reference as an inertial frame if you introduce inertial forces which are NOT real force, but are the effects of using a non-inertial frame.

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

      In everyday life, an inertial frame is just a frame of reference in which motions behave as you ordinarily expect them too.

      For example, the frame of reference of the Earth's surface.

      But you say that's NOT a free-fall frame and the external gravitational field due to astronomical objects beyond the Earth is NOT uniform. No, but the center of mass of the Earth defines a free-fall frame since it is free falling in space and the non-uniformity of the external gravitational field is relatively small. So for most purposes, but NOT all, the Earth's surface adequately approximates an inertial frame.

      Another everyday life example of an adequately approximate inertial frame is that of an unaccelerated car (see the figure below).


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

        The Prius: nothing special to look at, but it gets about 45 miles per gallon which made it the most fuel-efficient car sold in the US circa 2007.

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

        Credit/Permision: User:IFCAR, 2007 / Public domain.
        Image link: Wikipedia: File:2nd-Toyota-Prius.jpg.

      Everything is normal throwing balls, etc., around in unaccelerates cars. But if a car accelerates, you know that motions are affected: e.g., you get thrown forward relative to the car if you decelerate to fast---and arn't wearing your seat belt.

    3. Physics Terms:

      Before proceeding, we should try to define our physics terms---but admitting some inescapable circularity at the start.

      1. Now what is an acceleration actually?

        It is a change in velocity relative to a frame of refence.

        In physics, velocity is a quantity with both magnitude and direction---it's a vector.

        Velocity is vector.

        A change in MAGNITDE and/or DIRECTION is an acceleration---which is also a vector.

        Note that velocity is FRAME-DEPENDENT quantity.

        What velocity you have depends on what frame of refence you measure that velocity in.

      2. Now what is force?

        A force is a physical interaction on a object that can cause acceleration relative to an inertial frame.

        See the examples of forces in the figure below (local link / general link: free_body_diagram_object_wedge.html).

        Actually, a NET
        force is needed for an acceleration.

        Balanced forces give no acceleration.

        In order for the force concept to be of any use or significance, one must have laws of force which are independent of an object's acceleration.

        And, of course, we do have such laws.

        And by the way force is vector.

      the rest of this section is UNDER RECONSTRUCTION. Don't read

    4. More on Inertial Frames:

      We have reviewed the modern definition inertial frames pretty thoroughly above in subsection Inertial Frames Redux.

      Here we will only expand a bit on fine points about inertial frames.

      1. Absolute Space:

        Isaac Newton (1643--1727) when developing what we call Newtonian physics postulated that there was a fundamental inertial frame which he called absolute space.

        The fixed stars (illustrated in the figure below) are at rest (at least on average) in absolute space. Nowadays, we know the fixed stars are NOT truly fixed. They are just the nearby stars (within a kiloparsec (kpc) or so) which before sometime in the 19th century seemed unmoving.

        All reference frames NOT accelerated relative to absolute space are secondary inertial frames and low-acceleration reference frames (like the Earth's surface) are approximate inertial frames.

        These ideas were superceded by the explanation of inertial frames from general relativity (GR) given in the aforesaid subsection Inertial Frames Redux. But they held sway for a long time between Newton and the advent of GR.

      2. The Comoving Frames of the Expanding Universe:

        Our modern definition of inertial frames shows that inertial frames and approximate inertial frames are everywhere in the observable universe.

        Wherever you have free-fall frame, or a reference frame unaccelerated with respect to a free-fall frame, there you have an inertial frame. For approximate inertial frames, the same words mutatis mutandis.

        But are there any basic inertial frames?

        Yes. Reference frames that participate in the mean expansion of the universe (see figure in the next subsection below). We can call these comoving frames of the expanding universe or just comoving frames.

        Note comoving frames is a term just invented by yours truly, but some term for these reference frames is badly needed.

      3. How Do We Find the Comoving Frames of the Expanding Universe?

        Cosmological theory (which we can trust this far we think) tells us the centers of mass (CMs) of field galaxies and galaxy clusters (which we can identify pretty well) define approximate comoving frames. See the figure below for field galaxies and galaxy clusters participating in the mean expansion of the universe.

        One can identify comoving frames more and more exactly with more and more data and modeling.

        Of course, actually almost all material
        astronomical objects have some rotation, and so none of them define exact inertial frames in themselves. But like the Earth's surface many do to some approximation.

        For a specific example, consider the Local Group of galaxies (AKA Local Group): all the component galaxies are in some irregular orbits about the center of mass. See the figure below.

      4. Our Local Comoving Frame:

        It is easy to measure our rotation relative to our local comoving frame to very high accuracy/precision.

        Cosmological theory (which we can trust this far we think) tells us our rotation relative to cosmologically remote astronomical objects (i.e., remote galaxies and quasars) which we can measure easily is the rotation relative to our local comoving frame.

        How do we determine our translational motion relative to our local comoving frames?

        Cosmological theory (which we can trust this far we think) tells we can measure this using cosmic microwave background radiation (CMB).

        The figure below shows how we determine
        translational motions relative to our local comoving frame and nearby local comoving frames using the CMB and the Doppler effect.

  4. Time

  5. If you thought space was tricky, time is probably even worse.

    1. A Start on 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.

    2. Clocks:

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

      We can call these systems clocks.

      For an astronomical clock, see the figure below (local link / general link: strasbourg_cathedral_astronomical_clock.html).

      We count repeats of their motions and call that a measure of

      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, astronomical cycle clocks had precedence: i.e., the astronomical cycles of the Sun and Moon.

      The Sun and Moon were unique and massive and their periodic motions (i.e., astronomical cycles) could easily be counted.

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

      So we counted solar days, solar years, and lunar months.

      The days of the lunar month could be correlated with the lunar phases which are illustrated in the figure below (local link / general link: moon_lunar_phases_animation.html).

    3. Non-Astronomical-Cycle Clocks:

      All other repeating motions were obviously irregular and NOT eternal compared to the astronomical cycle clocks of the Sun and Moon

      These irregular clocks include:

      1. The climatic seasons. They stay pretty close to the Sun clock, but NOT perfectly.

      2. 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.

      3. The pulse---usually measured from the radial artery---can be used for short-time time measurements. It tracks the beating of the heart.

      4. 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.

        We've always been conscious that our days if NOT numbered are distinctly finite---it causes a certain anxiety. We ponder our monuments. See the figure below (local link / general link: giza_pyramids.html).

      But as aforesaid, the astronomical cycle clocks of the Sun and Moon. had precedence.

      But they had problems too:

      1. Their periods are NOT commensurable which led to a lot of difficulties in trying to keep time with all of them simultaneously.

        The mean lunar month is 29.53059 DAYS and the solar year is about 365.2421897 DAYS

        Trying to keep a lunisolar calendar was tricky as discussed in IAL 3: The Moon: Orbit, Phases, Eclipses, and More.

        Even just keeping a solar calendar calls for leap years and a somewhat tricky rule for keeping official years consisting of integer number of days.

        But that's all another story. In the modern age, we do it with the Gregorian calendar.

      2. For short time measurements during a day, the astronomical cycle 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.

      See an early mechanical clocks or facsimile in the figure below.

      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 astronomical cycle 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 astronomical cycle clocks.

      But there was one shock: the astronomical cycle clocks could NOT 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.

    4. 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 atomic clocks have a problem. They are delicate things and if NOT maintained, they stop. The astronomical cycle clocks of Sun and Moon do NOT keep time so accurately, but will NOT stop for gigayears.

    5. Time Dilation:

      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.

        Interestingly, Newton himself wondered if time flowed the same everywhere and everywhen.

        He admitted the possibility that maybe NOT.

        But that time did flow the same always was the simplest hypothesis and no observation contradicted it in his time and until about 1900.

      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 general relativity:

        The deeper one is in gravitational field (a gravitational potential to be a bit more precise), the slower time passes relative to to infinity (where there is vanishing gravitational field).

        atomic clocks.

        The time discrepancies for terrestrial experiments are of order nanoseconds: i.e., of order 10**(-9) seconds.

      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) (see the figure below: (local link / general link: gps_global_positioning_system.html) 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.

    6. Cosmic Time:


      cosmic time

      We can never know it so precisely as atomic clocks, but it is the fundamental time for the observable universe.

      age of the observable universe = 13.797(23) Gyr (Planck 2018)

      Cosmic time is illustrated in the figure below (local link / general link: cosmos_history.html), we don't have the final, eternal, fundamental theory of physics: Theory of Everything or TOE.

  6. Mass

  7. 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. It 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.

    The gravitational force on mass is what we measure by weighing. For an example of weighing, see the figure below (local link / general link: anubis.html).

    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.

  8. Energy

  9. 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. For general reference, the figure below gives the Link: Energy explication which gives a fullish explication of energy. That figure and the discription below need to be conflated sometime sine die---but maybe on the Greek kalends.

    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) which was named for James Joule (1818-1889)---see the figure below (local link / general link: james_joule.html).

    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.

        MICROSCOPIC in physics jargon means molecular size or smaller usually: i.e., size scales of 1 nanometer = 1**(-9) meters.

        But the word is used loosely MICROSCOPIC. All fields need flexible jargon.

      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.

      The electromagnetic spectrum and its conventional wavelength bands are illustrated in the figure below (local link / general link: electromagnetic_spectrum.html).

      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.

  10. E=mc**2

  11. 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 it 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. E=mc**2 Explicated:

      E=mc**2 is explicated in the figure below (local link / general link: e_mc2.html).


    2. 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.

    3. The Rest Mass of Baryonic-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.

        Note I don't use the word fundamental particle---which means a particle with no known constituents.

        The electron is considered a fundamental particle.

        But nowadays, protons and neutrons are believed to be made of quarks---which we discuss below in section Bound Systems.

      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.

        You can make these particles by supplying the the energy to make up their rest mass energy and recover that energy back by destroying them.

        In practice the supplied and recovered energy is often that of photons (i.e., the particles of light).

        Creation and destruction, of course, require other conditions than just ones of energy.

      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.

        The ton of kilotons (kt) and megatons (Mt) are actually metric tonnes of 1000 kg (i.e., 1 megagram).

      Below is a figure illustrating cloud height---the clouds being the famous mushroom clouds of nuclear explosions, but also occur in other systems such volcanic erruptions.

      Little Boy nuclear bomb used at Hiroshima was 15 kt.

      Castle Bravo test at Bikini Atoll in 1954 (see figure below) 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.

        For example, the rest mass of a particle can all be converted into electromagnetic radiation by interacting the particle with its antiparticle.

        For example, the antiparticle of the electron is the positron which is seemingly nearly the same as the electron, except that it has charge +e.

        Antiparticles exist both in nature and in the laboratory, but they never accumulate into MACROSCOPIC amounts as far as we know.

        For good reason---they annihilate with their corresponding particles before this can happen.

        So if you had a kilogram of antimatter, you maybe could cause a big explosion by bringing it into contact with a kilogram of matter.

        But you can't accumulate a kilogram of antimatter.

        There are people working making larger amounts of antimatter: for example antihydrogen has been made since 1995, but only in MICROSCOPIC quantities.

      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.

        The spent fuel does have less mass than the initial fueld because emitted energy of the transformations is emitted as heat.

      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.

    4. 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???. See vacuum light speed illustrated in the igure below (local link / general link: light_speed_earth_moon.html).

      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 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.

    5. 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.

  12. Forces

    1. What is Force?

      As noted in section Space, a force is a physical interaction on a object that can cause acceleration relative to an inertial frame.

      This interaction is illustrated in the figure below.

      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.

        An acceleration can be just a change in direction without a change in speed. In that case, kinetic energy does NOT change.

      We will skirt the details of energy transformations.

    2. Bound Systems: A First Look:

      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 at 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.

      The ball example is illustrated in the cartoon in the figure below (local link / general link: stability_mechanical.html).

      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 as illustrated in the figure below (local link / general link: simple_harmonic_oscillator.html).

      In the astrophysical realm,
      kinetic energy and angular momentum prevent the collapse of gravitationally-bound systems: e.g., moon systems, planetary systems, star clusters, galaxies, galaxy groups and clusters.

      It is also true in the astrophysical realm, kinetic energy also prevents the collapse of unbound systems too: e.g., galaxy superclusters and the observable universe.

      An example of a gravitationally-bound system is illustrated in the figure below (local link / general link: orbit_elliptical_equal_mass.html).

    3. The 4 Fundamental Forces:

      There are 4 fundamental forces (illustrated in the figure below) 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.

      The figure below illustrates some of the manifestations of the electromagnetic force.

      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.

  13. Bound Systems

  14. Nowadays in standard model of particle physics, one thinks of the fundamental particles has being quarks and leptons and the force carrier particles. See figure below for some insight.

    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. See figure below for the proton structure of 3 quarks.

    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 (see figure 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.

  15. Gravity

  16. Gravity is 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. Isaac Newton (1643--1727) did NOT discover that.

    What Newton discovered was that gravity is universal: both on Earth and in the astronomical realm, there was gravity obeying the same law. See figure below for Newton's discovery.

    Let's expand a bit on

    1. Newton's Law of Universal Gravitation:

      The Newton's law of universal gravitation which holds between ideal point masses is:

                      G M_1 M_2
       F_12 =     -------------------
         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
            IAL 30: 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 great use as we describe in the subsection below.

    2. Newton's Law of Universal Gravitation is of Great Use:

      Newton's law of universal gravitation is actually of the great use.



        Caption: Gravity between objects of general shape.

        Credit/Permission: © David Jeffery, 2004 / Own work.
        Image link: Itself.



        Caption: Gravity between objects with simplifying conditions.

        Credit/Permission: © David Jeffery, 2004 / Own work.
        Image link: Itself.

    3. Some Gravity Questions:

      What is the gravitational force between two 1-kilogram spherically symmetric masses held 1 meter apart?


        Caption: Gravity is a very weak force as shown by the gravity between two 1-kilogram spherically symmetric masses held 1 meter apart

        Credit/Permission: © David Jeffery, 2003 / Own work.
        Image link: Itself.

      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 =     -------------------

        Question: If we double the distance between two masses, the force:

        1. drops by a factor of 2.
        2. increases by a factor of 2.
        3. drops by a factor of 4.

        Answer 3 is right.

      Gravity drops off rapidly with distance (in certain sense rapidly) because of the 1/R**2 factor which makes it an INVERSE-SQUARE LAW FORCE.

      This behavior is shown in a cartoon in the figure below (local link / general link: function_behaviors_plot.html).

      gravity's fall off with distance is actually slow compared to many other forces. So it is considered a long-range force. We also call it a field force or a BODY FORCE because it interacts with the whole body NOT just the surface as CONTACT FORCES do.

      Gravity is much more long range than any contact force.

      Question: If we double one mass, the force:

      1. drops by a factor of 2.
      2. increases by a factor of 2.
      3. drops by a factor of 4.

      Answer 2 is right.

      Question: If we double both masses, the force:

      1. drops by a factor of 2.
      2. increases by a factor of 2.
      3. increases by a factor of 4.

      Answer 3 is right.

      Recall all masses attract.

      Question: Why don't we in this room feel mutually attracted?

      1. Gravity repels for small masses.
      2. Gravity turns off for small masses.
      3. Gravity is very small for small masses and thus we arn't pulled into a big cluster of arms and legs in the center of the room.

      Answer 3 is right.

      Gravity can actually be measured for human-sized objects, but it takes very sensitive apparatus.

  17. Gravity Near the Earth's Surface

  18. 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.

    For some elucidation, see the three figures below.

    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.

    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. See figure below.

    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.

      Shear is the sliding of one layer of matter with respect to another. A shearing force causes shears.

    Pressure force and shear are illustrated in the figure below.

    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.

    We see the combined effect of self-gravity and pressure is to produce a body with nearly exact spherical symmetry.

    There will be a few low protuberances (i.e., mountains, continents, etc.) and relatively small interior asymmetries due inter-atomic bonds strong enough to resist the relatively low pressures at the base of the protuberances.


    1. The centrifugal force due to their axial rotation will make planets and stars oblate (i.e., bulge at the equator).

      The centrifugal force is NOT an ordinary force, but the tendency of bodies to move in a straight line. It is the thing that tends to throw you off playground merry-go-rounds. It increases with rotation rate.

      This is just one manifestation of rotation helping to hold and determine structure.


        Caption: Saturn ♄, the ringed world. Real color? Two moons are visible.

        You note that Saturn is obviously oblate with equatorial diameter (which is parallel to the bands and rings) is about 10 % larger than the polar axial diameter.

        The defined oblateness is

             (R_equator-R_polar)/R_polar=0.0979624 = approximately 10 % ,
               where R_equatorial is the equatorial radius and 
               R_polar is the polar radius.

        The oblateness is caused by the centrifugal force which is high for Saturn because of its fast rotation.

        Saturn's deep interior rotation period relative to the fixed stars (i.e., sidereal rotation period) is 0.44401 days or 10.656 hours (Cox-295).

        Credit/Permission: NASA, before or circa 2003 / Public domain.
        Image link: Itself.

    2. The TIDAL FORCE (as we show below) can perturb the overall shape from an exact sphere into a slightly stretched shape.

    Let us consider how the EARTH is sustained.

    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.

  19. Circular Orbits

  20. 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.

    The figure below explicates 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 pulling the object along a little to compensate for air resistance and friction at the central pivot.

    The figure below (local link / general link: orbit_002_centripetal.png) illustrates centripetal acceleration.

    The figure below (local link / general link: ial/ial_005/orbit_003_speed.png) illustrates how to derive the orbital velocity formula from the entripetal acceleration formula a=v**2/r and Newton's law of universal gravitation.

    Let us now apply our circular orbital speed result to the case of a satellite in LOW-EARTH ORBIT.

    What is the low-Earth orbital speed and low Earth orbit orbital period. See the figure below.

    A fiducial-value formula for the low Earth orbit orbital period is given in the figure below.

    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. This fact is illusrated by Newton's cannonball. See the figure below (local link / general link: newton_cannonball.html).

    Free-fall in orbit is illustrated in the figure below.

    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!

  21. Elliptical Orbits, Escape Orbits, and Orbital Pinball

  22. Elliptical orbits are non-circular orbits.

    Elliptical orbits are illustrated in the animation below.

    Recall if there is vast mass disparity, the smaller body orbits the larger body in an ellipse with the larger body at one focus as illustrated in the figure below.

    The eccentricity e is a measure of the non-circularity of an orbit:

    1. e = 0 for a circular orbit.
    2. 0 < e < 1 for a closed eccentric orbit.
    3. e = 1 for a line orbit or, depending on initial conditions, an parabolic escape orbit.
    4. e > 1 for a hyperbolic escape orbit.
    5. 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.

    The two figures below (local link / general link: orbit_launch.html; local link / general link: newton_cannonball.html) illustrate the qualitatively distinct cases that follow from the initial conditions.

    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.

    The astro-jargon term is gravitational assist (AKA gravitational slingshot maneuver). See the figure below for an example of a gravitational assist.

  23. Thermodynamics

  24. 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. See the figure below for an illustraion of microscopic kinetic energy.

      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. See the figure below.

      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.

        Question: When objects of different temperature are in thermal contact (but CANNOT exchange particles), heat energy always flows spontaneously:

        1. from cold to hot objects.
        2. from hot to cold objects.
        3. never.

        Answer 2 is right.

        This is one of the simplest of all everyday observations.

        In a physics sense, it follows from 2nd law of thermodynamics---which we won't discuss here---we do just below in section The 2nd Law of Thermodynamics.

        One can, of course, make heat flow the other way by doing work---Las Vegas would NOT exist without air conditioning.

    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.

      1. Food energy and wood fuel from photosynthesis.

      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.

  25. The 2nd Law of Thermodynamics

  26. Why does heat flow spontaneously from hot (i.e., high temperature systems) to cold (i.e., low temperature systems) (at least as long as there are no particle flows)?

    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? See figure below for utter squalor.

    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. See tornado figure below.

    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.

  27. Universal Evolution

  28. 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 IAL 30: 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.

  29. Tides

  30. The tides (meaning ocean tides on Earth) are an important application of the physics we've been learning as well as being relevant in understanding the Earth as planet.

    They are due to the tidal forces of primarily the Moon and secondarily of the Sun.

    Before diving into the tides there two other terrestrial tidal behaviors due to the aforesaid tidal forces that we mention here only in brief:

    1. The solid Earth tide is the tidal behavior of the solid Earth (in contrast to the tidal behavior of the Earth's hydrosphere and Earth's atmosphere). It has an amplitude of order a meter with its dominant period being 12.421 h (Wikipedia: Earth tide: Tidal constituents). On the human scale, we never notice the solid Earth tide and it's relation to the ocean tide is complex (see Wikipedia: Earth tide: Other Earth tide contributors) and will NOT go into it.

    2. The atmospheric tide which is in many ways analogous to the ocean tide, but probably does NOT directly interact with it much.

    Now we dive into the tides.

    1. Question for Landlubbers:

      Let's see how many landlubbers we have.

        Question: Usually, but NOT invariably, there is/are:

        1. one high tide per day.
        2. two high tides per day.
        3. four high tides per day.

        Answer 2 is right.

        Tide behavior is pretty variable: 1 and 4 high tide situations do happen in confined inlets of oceans at certain times (CW-385).

    2. Illustrations of the Tides:

      The three figures below illustrate the tides in action.

      A nautical chart showing the intertidal zone of East Friesland is given in the figure below (local link / general link: riddle_of_sands_map_b.html).

    3. The Causes of the Tides on the Earth:

      The tides (i.e., the ocean tides) on Earth are caused by the tidal force of the MOON and secondarily to the SUN.

      Let's just consider the MOON alone first and worry about adding the effect of the SUN later.

        This the way (the tao) of physics and astronomy (and many other sciences too)---isolate the most important effect, understand it, and then add the other complications on as perturbations to end up back with messy reality.

      See the figure below for the tidal force of the Moon.

      The tidal force is rather fully explicated in the figure below (local link / general link: tidal_force.html).

      this subsection is UNDER RECONSTRUCTION below

      But the Moon's tidal force is only part of the story.

      There is another part.

      The Earth constitutes what yours truly calls a center-of-mass free-fall inertial frame (COMFFI frame): i.e., its center of mass is in free fall under the net external gravitational field of the rest of the observable universe---but the key components of that for determining its local motion are the gravitational fields of Sun and Moon.

      At the very local level, the Earth orbits the barycenter of the Earth-Moon system as illustrated in the figure below.

    4. The Explication of the Tides:

      The full explication of the tides in the ideal case is given in mechanics/tide_ideal.html, but this is mostly beyond the scope of IAL.

      Here we give the short, qualitative explication.

      First note that the force per unit mass due to the Earth's own gravity is the Earth's gravitational field strength g = 9.8 N/kg = 9.8 m/s**2 (fiducial value).

      The tidal force is about 10**(-7) times smaller than g = 9.8 N/kg (Fre-532).

      So humans never notice the tidal force directly: you just do NOT notice such small variations in the effective force of gravity you are subject to as Earth rotates in the course of a day.

      On the other hand, the oceans (or the World Ocean) notice it minutely.

      But a minute effect on the big oceans is big by human scale: e.g., a small ripple to it becomes a tsunami to us.

      Thousands of kilometers across and several kilometers deep, a change in sea level by a meter or so to adjust for the tidal force is NOT very big relatively speaking.

      The adjustment changes the Earth's gravity on the oceans and changes the water pressure in the oceans.

      The adjustment creates the tidal bulges which are illustrated in the figure below.

      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 reality is that HYDROSTATIC EQUILIBRIUM can never be established because of the Earth's rotation on its axis.

      In the figure 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 IAL 3: The Moon: Orbit, Phases, and Eclipses. See the figure below.

      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.

        Question: Why is the reversal of tidal flow about every 6 hours, 12 minutes and NOT just 6 hours which is a quarter of a day?

        1. Friction effects of the ocean floor.
        2. The Moon is continually moving westward around the Earth.
        3. The Moon is continually moving eastward around the Earth.

        Answer 3 is right.

        Because of the Moon's continual eastward motion, a water particle on average spends about 6 hours, 12 minutes in each quadrant of the diagram shown above.

      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.,

        If there is a high tide a 12:00 pm today,
        there will be one at 12:50 pm tomorrow,
        one at 1:40 pm the day after,
        and so on.
        Eventually a tide has occurred at every time of the day.

      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. See the figure below.

      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.


        Caption: 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).

          Global warming could cause sea levels to rise just because expansion of the water above about 4 degrees C even if there were no additions from the melting of the ice caps.

          Of course, melting ice caps are the big danger.

        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/Permission: NASA, before or circa 2003 / Public domain.
        Download site: NASA: Visible Earth: now dead link.
        Image link: Itself.

      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.

        Question: If there were no Moon, when would the solar high tides occur?

        1. At noon only.
        2. At midnight only.
        3. At noon and midnight only.

        Answer 3 is right.

        There would be tidal bulges peaking near the solar noon and midnight points on the Earth, but dragged somewhat eastward by the Earth's daily rotation.

      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. See the figure below.


        Caption: Spring tides and neap tides.

        Spring tides are the strongest tides and neap tides the weakest tides.

        "Spring" here is meant as in "spring up," NOT as in spring time. "Neap" is adjective that only describes a kind of tide.

        Credit/Permission: © David Jeffery, 2003 / Own work.
        Image link: Itself.

      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.

    5. Tides in 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.

    6. Tidal Slowing and Tidal 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 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. See the figure below.


        Caption: 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/Permission: NASA, before or circa 2003 / Public domain.
        Download site: NASA: Visible Earth: alas, a dead link.
        Image link: Itself.

      The tidal bulges also have the effect of causing the Moon to spiral away from the Earth to larger orbits with longer periods. See the figure below.


        Caption: The tidal bulges and the outward spiraling of the Moon.

        Credit/Permission: © David Jeffery, 2004 / Own work.
        Image link: Itself.

      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 (see figure below)---the Earth's day was only 22 hours long (Se-38, Cox-250) and the Moon was probably significantly closer than today.

      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.

        Question: Why does no one ever talk about land tides or atmosphere tides.

        1. There arn't any.
        2. They arn't that noticeable.

        Answer 2 is right.

      Over long enough distances the solid Earth is flexible and there are land tides of order a meter.

      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.