---Isaac Newton circa 1684 in De Motu, quoted from Cohen & Whitman's Newton's Principia (CW-18).
Sections
Thus, some appreciation of physics is needed to understand much of astronomy.
In this lecture and the next two lectures ( IAWL Lecture 6: Light and Electromagnetic Radiation and IAWL Lecture 7: Spectra) we aim mainly at a qualitative appreciation of some of the physics that turns up in astronomy: in particular gravity, orbital motion, energy, thermodynamics, electromagnetic radiation, and spectra.
There are a few numbers and formulae and one or two DERIVATIONS. But our approach is mainly qualitative.
Some of the topics are just good for folks to know in general apart from any astronomical application, but we keep the astronomical applications in mind and some of those applications turn up: e.g., tides in the section Tides.
Lagrange (I think) said of him something like he was the greatest mathematician and the luckiest---for there is only one system of the world to discover.
The 2nd statement isn't completely true, but it is certainly true that Newton was lucky to be alive at the right time when the groundwork had be laid for a surpassing genius (i.e., himself) to the discover the classical laws of motion (i.e., the Newton's laws of motion) and the universal law of gravitation.
Newton was also a bit of an eccentric---no surprise there.
The Principia (1687) (long title: Mathematical Principles of Natural Philosophy) was the book in which what we called Newtonian physics was presented.
This physics is still correct for most of everyday life and much of astrophysics too.
Newton's 3 laws of motion are:
Newton's 1st law.
Alternatively, one could say a body is unaccelerated unless acted on by a NET FORCE.
F_net = ma , where F_net is the net force,
m is the mass,
and a is the acceleration.
Frequently, one just says ``F=ma'' when one means the 2nd law.
Force and acceleration are in fact VECTORS: they are quantities with both magnitude and direction.
Force is a physical relation between bodies or between a body and field of a force (e.g., a gravity or electric field) that can cause an acceleration or can balance (i.e., cancel) other forces.
Acceleration is a kinematic quantity evaluated using distances and times.
Mass is a scalar (i.e., it only has a magnitude) and is a measure of the resistance of a body to acceleration. It is sometimes defined as the quantity of matter, and that is OK, but it means nothing more than the first definition.
Acceleration.
Newton's 2nd law (F=ma) illustrated.
Note if net force is zero, then the 2nd law case reduces to the 1st law situation.
Net force zero does NOT mean there are no forces. There may be forces, but they must cancel out.
It's answer 1.
Newton's 3rd law illustrated.
Newton's laws are very simple to write down, but to understand them and use them as a student in a physics class should takes MANY qualifications and additions.
We won't do so much---we'll just do a FEW qualifications and additions below.
Our use for Newton's laws is to help understand the force of GRAVITY in causing ORBITS and TIDES.
Just think, did you ever rediscover Newton's laws by yourself.
It's answer 2 in my opinion.
For example walking is an immensely complex motion and we do it very well without using Newton's laws. Experience and evolution have overcome the difficulties. In fact, analysing walking in terms of Newton's laws would be very difficult.
Newton's laws show up clearly only in very simple motions.
So simple we seldom encounter them mainly because we always have to deal with complex resistive media: air, water, surface friction.
Humankind build the pyramids, the cathedrals, and sailed the oceans all without Newtonian physics.
The Giza Pyramids.
Khufu, c. 2520-2494 BC pyramid (Great Pyramid; Cheops' Pyramid); Khafre, c. 2520-2494 BC pyramid; Menkaure c. 2490-2472.
Credit: Digital Imaging Project of Mary Ann Sullivan, Bluffton College; download site Digital Imaging Project's Pyramid Gallery. The download site gives more information.
But you couldn't build a suspension bridge or a Moon rocket without Newtonian physics.
At some point in scientific and technological development you must give up on the purely empirical approach and look for fundamental laws or at least very general, basic laws.
You can then build up complex systems by understanding them in terms of these general, basic laws---plus a lot of empirical knowledge too.
Also Newtonian physics is truth---well approximate truth about the basics of motion---and truth is good to know.
Fundamental means that it cannot be further explained---it is JUST SO.
Nowadays, Newtonian physics known to be NOT fundamental, but as approximation to more fundamental physics---fundamental is a moving target in physics---so far anyway.
The physical theories of quantum mechanics, special relativity, and general relativity are more fundamental than Newtonian physics.
But Newtonian physics is BELIEVED to be the correct limiting form of these more fundamental physical theories.
Newtonian physics and more fundamental physics.
But we don't think the advanced modern theories are absolutely fundamental.
We are still looking for the absolutely fundamental theory of physics: sometimes, but inappropriately, called the theory of everything: TOE.
But Newtonian physics is a true approximate theory.
Within in domain of applicability, there are no doubts that it holds.
And its domain of applicability is very broad: most of everyday life and macroscopic engineering and the motions of celestial bodies up to the scales of clusters of galaxies.
We use it in its domain of applicability because it is a lot simpler to use in this domain than the more fundamental theories---we only use them when we have to.
Inertial frames are a special kind of frame.
They are NOT hard to understand and everyone really knows something about them---they know when they are NOT in one for example: e.g., a car making too sharp a turn and you feel that you are being thrown sideways: really you are just moving in a straight line.
The primary inertial frames are probably the frames that participate in the MEAN EXPANSION OF THE UNIVERSE.
The CMB pervades space is quite measurable especially above the atmosphere.
The CMB is discussed in IAWL Lecture 31: Cosmology.]
Probably almost NO FRAME attached to a physical body with rest mass is truly inertial. Almost every body with rest mass is being accelerated by gravity and/or some other force.
To be explicit almost every large material body is rotating: clusters of galaxies, galaxies, stars, planets in orbit and on their axes, all things on planets.
Rotating frames are always NON-INERTIAL strictly speaking.
The frame of reference attached a merry-go-round is non-inertial.
The Earth is spinning, and so the ground is a non-inertial frame too.
But some non-inertial frames are more non-inertial than others---to paraphrase George Orwell.
If a merry-go-round rotates once in 10 seconds, it is more non-inertial than if it went around in 20 seconds.
The Earth goes around once in 24 hours = 86400 seconds.
Although radius counts too as we'll see below, the much longer period of Earth's rotation suggests it is more inertial than merry-go-rounds.
And the Earth is more INERTIAL---but we won't do the calculation.
That we've not done this above is for pedagogical, not logical, reasons.
Newton's laws are just as valid in NON-INERTIAL FRAMES, but they are NOT referenced to them.
The merry-go-round as a non-inertial frame.
Objects thrown in merry-go-round frame do NOT travel in straight lines.
Thus, they are accelerated relative to the non-inertial merry-go-round frame with NO force acting.
But they travel in straight lines in the relatively inertial ground frame, and so are unaccelerated in that frame and obey Newton's laws.
It may seem odd that Newton's laws are specified for inertial frames when we have difficulty finding a truly inertial frame.
But this is part of the procedure of formal science particularly physics.
Envision the ideal case and then add on the complications as perturbations.
In fact we can find approximately inertial frames adequate for most purposes.
The Earth is sufficiently INERTIAL for many purposes.
To understand those effects, you have to effectively consider the Earth in the closer-to-inertial frame of the Earth's orbital position.
There are clever ways of doing this.
In discussing weather systems later on we will consider a NON-INERTIAL FRAME EFFECT called the Coriolis force.]
We will take the Earth and other planet and moon frames as being sufficiently INERTIAL for things on their surfaces---except when we need to invoke the Coriolis force later on.
For the planets and moons in orbit, the FIXED STARS defines a sufficiently inertial frame most of the time.
The more physicsy definition offered was given above:
Now in physics we want to calculate MOTIONS from CAUSES: forces are the causes.
At least, I can't see any way it can't be.
There must be force laws or force formulae that exist independently of Newton's laws of motion.
It takes more laws than Newton's laws of motion to make up Newtonian physics.
Of course, force laws do exist.
There are only 4 fundamental forces:
Einstein famously tried to find a UNIFIED FIELD THEORY that would show that gravity and the electromagnetic force are really one force---but he failed at least in finding a useful theory.
Still he set the agenda for physics: i.e., to find a UNIFIED FIELD THEORY---but for all the forces.
In some sense the last 3 forces have been united in a very abstract way, but gravity has resisted unification---but there are speculative theories that may do the trick.
NUCLEAR FORCES
The strong and weak nuclear forces are intrinsically quantum mechanical and can't be treated by Newton's laws.
Here we will just say that the strong nuclear force binds nuclei together.
When we discuss the energy source of the SUN and stars in, respectively, IAWL Lecture 8: The Sun and IAWL Lecture 22: The Main Sequence Life of Stars we will refer to nuclear forces again.
ELECTROMAGNETIC FORCE
The electromagnetic force is an immensely complex force.
It has many complex manifestations which are often given their own special names.
Although there are long-range manifestations of the electromagnetic force (the macroscopic Coulomb [i.e., electrostatic] and magnetic forces), the forces important for giving structure to solids are primarily SHORT-RANGE.
SHORT-RANGE here means that on the macroscopic level there has to be actual touching: e.g.,
If cut a board in half you just break (ideally) one layer of bonds, but that is enough: the two halves don't stick together.
Jump off the floor and the forces between feet and floor vanish.
The SHORT-RANGE nature of the most manifestations of the electromagnetic force are a consequence of the TWO SOURCES of the Coulomb force (electrostatic force).
Answer 1.
Actually, Ben Franklin assigned the names positive and negative to charge (HRW-507).
Answer 2.
And neutral matter will NOT exhibit a strong, long-range (macroscopic) Coulomb force.
The positive and negative charges cancel macroscopically.
But at the microscopic level, positive and negative patches are everywhere.
At the microscopic level quantum mechanical laws prevent exact cancellation.
But why is it a good thing that the electromagnetic force has complex manifestations?
Answer 1, I'd say. But you argue for answer 3.
It has only one ``charge'': MASS.
This double function is just a coincidence in Newtonian physics.
general relativity the coincidence is explained---but we will never go into that esoteric point.
Now gravity on Earth was always known. Newton didn't discover that.
Isaac Alien discovers gravity.
What Newton discovered was that gravity is universal: both on Earth and in the astronomical realm there was gravity obeying the same law.
The UNIVERSAL LAW OF GRAVITY.
The gravity force law (or Newton's law of gravity) which holds between ideal point masses is:
G M_1 M_2
F_12 = -------------------
R_12**2
where G = 6.6742*10**(-11) in MKS units (circa 2002)
is the universal constant of gravity.
M_1 is the mass of point mass 1.
M_2 is the mass of point mass 2.
R_12 is the distance between the masses.
Notice this distance comes in as an inverse-square.
We say that the formula is an inverse-square law
and gravity is an inverse-square law force.
F_12 is the force that 1 exerts on 2
and the force that 2 exerts on 1.
The forces are directly on the line between the
two objects and point in opposite directions.
The gravitational forces are attractive always.
No anti-gravity exists in the ordinary realm of physics, but
there may be a cosmological anti-gravity that is discussed in
IAWL Lecture 31: Cosmology.
By the way, the MKS unit of force is the newton: N=kg*m/s**2:
1 N = about 1/5 lb.
The gravity force law gives force in newtons when MKS units
are used consistently.
Now POINT MASSES are one of those idealizations that physicists love.
They may not exist in any sense---but then again they may: i.e., black hole singularities, but black holes can't be treated by Newtonian physics in any case.
But the gravity force law is actually of the greatest use.
Firstly:
Gravity between objects of general shape.
Secondly:
Gravity between objects with simplifying conditions.
What is the gravitational force between two, 1 kilogram spherically symmetric masses held 1 meter apart?
Gravity is a very weak force.
The last figure illustrates that the gravitational force between human size and even much larger objects is usually unnoticeable.
Now recall
G M_1 M_2
F_12 = -------------------
R_12**2
In a sense, gravity drops off rapidly with distance because of the 1/R**2 factor which makes it an INVERSE-SQUARE LAW FORCE.
This behavior is shown in cartoon in the figure below.
Some simple function behaviors.
But it is still called a long-range 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:
Answer 2 is right.
Question: If we double both masses, the force:
Answer 3 is right.
Recall all masses attract.
Question: Why don't we in this room feel mutually attracted?
Answer 3 is right.
Gravity can actually be measured for human-sized objects, but it takes very sensitive apparatus.
Gravitation force per unit mass on Earth's surface.
The acceleration g due to gravity on the Earth's surface.
Accelerating downward under the force of gravity alone.
In fact the whole kinematics of falling objects should be the same regardless of mass---if you can neglect air resistance.
Drop a chalk brush and a coin: air resistance relatively small.
Then drop a brush and a sheet of paper: air resistance not relatively small for the sheet of paper.
Air resistance causes falling to reach a terminal velocity.
Examples of terminal velocities.
In free fall you feel weightless, but this is not because gravity has turned off.
Gravity is just pulling you down atom by atom and you arn't resisting, and so there is no internal stress or pressure to resistance.
Standing up and resisting gravity is a different matter.
Standing up and resisting gravity.
Now not only you, but the atmosphere, the oceans, and the solid Earth must stand up under gravity pulling it down.
Only PRESSURE FORCES can withstand the self-gravity of dense, massive bodies like planets and stars.
In normal gases (but not degenerate gases) they are caused by atoms and molecules bouncing off of one and another: the electromagnetic force is the actual interaction.
In liquids and solids the atoms and molecules are pressed into contact.
The electromagnetic forces which give atoms their structure strongly resist compression of atoms from their unbound size.]
The pressure force will not provide strength for complex structures.
For example, water has a strong pressure force: you CANNOT compress it easily.
But water cannot resist shearing forces very well: drops can hold a shape, but nothing much bigger.
Liquids and pressure forces.
Even solids will not resist a shearing force if their mass is too big for a shape to be sustained by inter-atomic bonds: i.e., they will act like fluids.
Inter-atomic bonds make a boulder keep its shape under planet-size gravity.
But a boulder as big as a mountain on a planet is flattened into a mountain: i.e., a small protuberance on the face of a planet.
The pressure force can hold up the super-big boulder's mass, but it will push sideways causing the boulder to ``flow'' sideways and slump done to being a mountain.
A boulder as big as a planet in space would be pulled into spherical shape.
The solid pressure resists collapse, but not shearing that leads to spherical symmetry.
Why massive astrobodies tend to be round.
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.
There are TWO QUALIFICATIONS:
The centrifugal force is not a real 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.
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 ,
where R_equatorial is the equatorial radius and
R_polar is the polar radius.
(Cox-295).
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 ( sidereal rotation period) is 0.44401 days or 10.656 hours (Cox-295).
Credit: NASA.
Earth atmosphere, ocean, crust, mantle, core in a column.
Pressures at various depths in the Earth.
Besides pressure, MOTION can withstand strong gravity. 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.
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.
Answer 2 is right.
Velocity is a vector: a quantity with both magnitude and direction.
If either changes, the object accelerates.
Acceleration is toward the center in uniform circular motion.
Consider a slingshot demonstration.
Answer 2 is right.
A non-ideal rope can be pushed on a little, of course.
Centripetal acceleration a=v**2/r.
The gravitational orbital speed of uniform circular motion.
Let us now apply our circular orbital speed result to the case of a satellite in LOW-EARTH ORBIT.
Answer 1 is right.
Answer 1 is right.
But it is a question that makes me ponder.
I guess the Earth constitutes a sufficient approximation to an inertial frame for close, fast orbiting objects.
Low-Earth orbit velocity and period.
Low-Earth orbit satellites orbit really very fast: 8 km/s and this is independent of their mass, shape, color, etc.
And note rockets don't need any rocket thrust to do this.
The rocket thrust was needed to give the satellite kinetic energy (energy of motion) to lift it up from the ground and get it moving at about 8 km/s.
Once in orbit the satellite is in a perpetual falling motion.
Quite literally the satellite and all its contents are falling toward the Earth under gravity---but they keep missing.
Newton's mountain-orbit diagram.
Answer 1 is right.
The longest-answer-is-right rule triumphs again.
Free falling in orbit.
Answer 2 is right.
Nothing accelerates (or decelerates) the astronaut drastically when he/she goes EVA.
Tethering though is essential since small pushes and pulls could sending him/her floating off into slightly different orbits.
We discuss energy and its various forms below, but you already understand energy in the everyday life sense which is pretty close to the physics sense.]
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!
Ever since the original Star Trek, we have known to call space junk space debris.
But an encounter with a satellite or space debris on another orbit is potentially deadly.
Of what order is the relative speed between objects moving on randomly related orbits on collision trajectories?
Answer 2 is right.
Zero is right if the objects are moving in the same direction which is unlikely for randomly related objects.
8+8 = 16 km/s would be right for a head-on collision.
But if the orbits are random, the relative speed will somewhere between 0 and 16 km/s and on average something like 8 km/s.
Of order:
Answer 3 is right. See Alaska Science Forum:
How Fast Can a Bullet Go?.
8000 m/s = 8 km/s the low-Earth orbital speed.
There are thousands of pieces of junk left over from broken-up satellites or that have escaped from space missions.
These pieces pose a real threat to space operations. NASA can track pieces down to melon size (made of metal anyway???), but not smaller ones.
Below is a schematic picture of the haze of space junk in low-Earth orbit.
Space debris in low-Earth orbit.
Answer 1 is right.
All kinds of orbits have been used for satellites and spacecraft, and so you can find junk in almost any orbital vicinity.
Also collisions between space debris can send the fragments off into random orbits.
The International Space Station (ISS) has I believe already had to take evasive maneuvers to avoid known space debris I believe.
For more information see NASA Orbital Debris Program Office.
Recall if there is vast mass disparity, the smaller body orbits the larger body in an ellipse with the larger body at one focus.
A Sun-planet orbital system.
The eccentricity e is a measure of the non-circularity of an orbit:
e = 0 for a circular orbit
0 < e < 1 for a closed eccentric orbit
e = 1 for a line orbit
or, depending on initial conditions, an parabolic escape orbit.
e > 1 for a hyperbolic escape orbit.
See Go3-94. The escape orbits are unclosed or OPEN ORBITS. The body travels off to infinity on such an orbit.
What sets the orbit?
Newtonian physics, of course, but that is general and applies to all orbits.
The thing that is particular to individual orbits is INITIAL CONDITIONS.
One way is start the orbit with a small mass a distance R from a large mass.
The large mass becomes the orbit focus or center of force.
The initial speed is v and is perpendicular the radial direction.
The INITIAL CONDITIONS for this setup are R and v.
Elliptical orbit parameters.
Orbits for increasing initial velocity v.
The INITIAL CONDITIONS of the planets were set by the formation process of the solar system.
But the orbits have since evolved due complex perturbations and collisions.
Space probes have their orbits set by their initial launch and subsequent rocket firings.
That is just a taste of celestial mechanics.
But we can mention the orbital pinball game that space agencies often play.
NASA (or whomever) can use planetary encounters to change probe orbits in useful ways.
But since the Earth is moving at 30 km/s relative to the fixed stars, the launch speed must be 30 km/s opposite to the Earth. No existing launch vehicle can achieve such a speed.
Instead, the probe can be launched the direction of motion of the Earth.
This gives it a higher orbital speed than the Earth's and sends it on a orbit to the outer solar system.
A carefully controlled slingshot encounter with Jupiter, then slows the probe to zero velocity relative to the fixed stars.
The probe then just falls under gravity toward the Sun.
A slingshot maneuver.
This procedure, of course, takes years to complete. It takes a long time for the probe to reach Jupiter and return to the inner solar system.
For example, the Ulysses probe was sent into a polar orbit about the Sun after a slingshot maneuver about Jupiter ( NASA/JPL Ulysses Site).
In this case the slingshot maneuver wasn't used to stop the probe, but to put it in an orbit that was well out of the ecliptic plane.
It took more than 4 years from launch on 1990oct06 to make its first pass over the Sun's south pole (Ulysses Milestones).
NASA is very clever at slingshot maneuvers and other orbital pinball actions.
But the ENERGY CONCEPT was implicit in his laws. Galileo already had a some idea of energy.
In the centuries after Newton, the ENERGY CONCEPT was introduced in Newtonian mechanics and then extended into all other branches of physics.
The ENERGY CONCEPT is one of the most fruitful of all physical conceptions.
ENERGY is, in fact, hard to define. There is NO satisfactory one-line definition. I think one has to explain energy rather than define it.
But here's a couple of stabs at a ``definition'':
This is an aphorism, of course, but it suggests the ubiquity of energy in physics and in everyday speech.
Energy in everyday life.
ENERGY is sort of the primal stuff of the universe---Urstoff for those who know German.
ENERGY has many forms any of which can converted to any other form which is why it is all energy.
All forms have the same unit: the joule (J)
By following the transformations of ENERGY, one can follow how a system evolves or how it is maintained in a steady-state.
This is useful both at the elementary level and at the advanced level in qualitatively understanding what is happening without worrying about complicated processes.
``Not missing the forest, because of the trees.''
Also energy analysis frequently gives you partial quantitative information very easily: total information may require much, much more work.
These are main reasons that energy analysis is so ubiquitous in physics and in everyday life really.
But it is not the only limit.
By the way, historically physicists have had to invent new kinds of energy with different prescriptions for evaluating it in order to maintain conservation of energy.
So is energy an artificial construct?
That we always have been able to find new energy forms, I think, proves it is real stuff. Special relativity gives more evidence: see below.
The conversions of ENERGY are often very useful to us---but useful or not, they are everywhere.
Sometimes the conversions happen readily, but sometimes not.
The conversions of ENERGY are determined by physical laws: e.g., Newton's laws, but other laws too like the laws of thermodynamics.
But the conversions are also determined by INITIAL CONDITIONS.
If the setup for a conversion is not present, then the conversion won't happen.
Having enough ENERGY for a particular conversion is a NECESSARY, but NOT a SUFFICIENT condition for that conversion.
FORMS OF ENERGY
The list is not exhaustive nor are the different forms completely distinct.
And we are not deriving them or showing how they were established.
Gravitational potential energy on Earth.
Gravitational potential energy in space.
KE and PE in space.
The orbital oscillation of energy between KE and PE forms is analogous to that with a pendulum: e.g., a swinging meter stick. At maximum height, KE is zero and PE is maximum; at minimum height, KE is maximum and PE is minimum. If there were no resistive forces, the pendulum would oscillate perpetually.
It is the energy you get out of a wall socket. Voltage is electrical potential energy per unit charge.
Much of interesting solar phenomena like PROMINENCES are caused by energy conversions to and from magnetic field energy.
Because all energy has mass is a good reason for believing that it is a kind of stuff, and not just an artificial construct of physicists.
The Einstein equation gives the extremely simple relation between an amount of energy and its mass (or alternatively the energy associated with a given mass).
E = mc**2 ,
where E is some amount of energy,
m is the mass of the energy,
and c is the speed of light.
Rest mass
is the mass of objects measured in a frame
in which they are at rest.
Atoms and nuclei and things build up out of them have rest mass.
Rest mass is what we usually mean when we say ``mass'' when there is no ambiguity.
From the Einstein equation, we know that rest mass is a particular form of energy.
Once people thought that rest mass was not a form energy---very silly of them---they thought it was a different kind of physical thing.
Since rest mass is a form of energy, it can be converted to other forms.
Example: What if we could transform 1 kg of ordinary terrestrial
matter into explosion heat, kinetic, and light energies?
E = mc**2 = 1 * (3*10**8)**2 = 9*10**16 J
equivalent to about 20 megatons of TNT.
See WP-A-20.
On a large scale this kind of transformation isn't easy---which
is a good thing for us, I think.
The Sun does it: that is the Sun's energy source, in fact, as is discussed in IAWL Lecture 8: The Sun.
More exactly, the Sun's energy comes from changing nuclear bond energies, but that changes the rest mass of the nuclei because of E=mc**2.
As I mentioned, the energy categories are not completely distinct.
Well we arn't going to cover thermodynamics at all really.
But there are a few features of thermodynamics that we will cover since we will refer to continually.
Answer 2 is right.
This is one of the simplest of all everyday observations. In a physics sense it follows from the 2nd law of THERMODYNAMICS---which we won't discuss here.
One can, of course, make heat flow the other way by doing work---Las Vegas would not exist without air conditioning.
TEMPERATURE is a measure of the THERMODYNAMIC EQUILIBRIUM STATE among other things.
Answer 2 is right.
Stars are very hot and space if very cold. The interior temperature of stars is millions of degrees Kelvin.
The temperature of the electromagnetic radiation field that permeates space is 2.726 K (Ze2002-469).
Systems in THERMODYNAMIC EQUILIBRIUM to not change thermally anyway.
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 Earth) with steady inflow and outflow of energy across a temperature gradient.
Energy for life.
Almost all our energy ultimately comes from the Sun.
The unhappy consequences for plants of photosynthesis.
Herbivores are just plant predators you know.
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.
Let's see how many landlubbers we have.
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).
Tidal zone at low tide.
The parallel ripples form perpendicular to the tide flow.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line1725, America's Coastlines Collection; Photographer: Mr. David Sinson, NOAA, Office of Coast Survey.
Wetlands with tidal streams in South Carolina, 1991.
I'd guess this is closer to high tide than to low tide. But I know nothing.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line0095, America's Coastlines Collection; Photographer: Richard B. Mieremet, Senior Advisor, NOAA OSDIA.
Lower Patuxent River, Maryland during an extreme high tide.
You can see the tide is running up a country lane of some kind. This is just off Chesapeake Bay where there is considerable land subsidence.
Part of the problem is that if you pump fresh water out of the ground you lower the water table and the Earth subsides. This is a problem not unknown in Las Vegas.
Flooding like this could become very common if the sea level rises with global warming.
Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line0647, America's Coastlines Collection; Photographer: Mary Hollinger, NODC biologist, NOAA.
A tidal map of East Friesland from the late 19th/early 20th centuries.
This is Map B in The Riddle of the Sands (1903), a classic nautical spy-thriller by Erskine Childers (1870-1922). Childer was English, but joined the Irish in their rebellion. He was later executed by the Irish government for the illegal possession of a small hand-gun given to him by Michael Collins.
The Riddle of the Sands is one of those great old stories where men were men and women stayed as the romantic interest and didn't try to take over the plot.
Credit: The original publishers of the map were Walker and Cockerell sc.: their copyright is long expired I'd guess. Download site: Wolfram Fassbender's The Riddle of the Sands site.
EARTH TIDES
The Earth tides are caused by the gravitational effects of the MOON and to a lesser degree the SUN.
Let's just consider the MOON alone first and worry about adding the effect of the SUN later.
The gravitational force of the Moon on the Earth.
But Moon's varying gravitational force is only part of the story.
There is another part.
The Earth revolves around the center of mass of the Earth-Moon system.
Although the Earth is approximately an inertial frame for many purposes, the tides can't be understood without invoking the NON-INERTIAL FRAMENESS of the Earth.
The Earth is a rotating (i.e., non-inertial) frame.
In a rotating frame there is an effect that is called the centrifugal force.
It is NOT a real force.
But it sure feels like a real force that is trying to throw you out of a rotating frame.
Really you are just trying to move in a straight line as required by Newton's 1st law.
But relative to the rotating frame, centrifugal force acts, as outward radial force that is exactly equal to the inward radial centripetal force needed to maintain the circular motion.
If there is insufficient to maintain the body in uniform circular motion, then centrifugal force will accelerate the body outward relative to the rotating frame.
The centrifugal force acts like a body force, not a contact force.
It ``pulls'' on you atom by atom, like gravity.
It is only when you resist it that you feel forces in action.
The centrifugal force on a carnival centrifuge.
Answer 3 is right.
In order to move in a circle there must be a centripetal force.
The wall of the bottle provides this only for the fluid touching the wall.
In the interior this force must be provided by pressure. So pressure must increase with radius from the center of the circular motion.
But this variation in pressure with radius forces a variation in the vertical colummn height with radius.
Low pressures at small radius can only support a low level of water; high pressures at large radius support a high level of water.
One can view the situation from the ROTATING FRAME treated as an inertial frame with the centrifugal force treated as a real force.
In this picture, the water just seeks a hydrostatic equilibrium configuration with centrifugal force, pressure force, and gravity canceling at every point.
If one just as a rotating glass of water a similar analysis holds.
A rotating glass of water.
The shape of the surface for hydrostatic equilibrium in the rotating frame is, in fact, parabolic (Fre-550).
The TIDAL FORCE is a combination of the variation in the Moon's gravitational force from its MEAN VALUE and the centrifugal force.
The tidal force of the Moon on the Earth.
The force per unit mass due to the Earth's own gravity is 9.8 N/kg.
The tidal force is about 10**(-7) times smaller (Fre-532).
So humans never notice the tidal force directly: you just do NOT notice small variations in the effective force of gravity you are subject to.
On the other hand, the OCEANS notice it minutely.
But a minute effect on the big ocean is big by human scale: a small ripple becomes a tsunami.
Thousands of kilometers across and several kilometers deep, a change in sea level by a meter or so to adjust for the tidal forces is NOT very big relatively speaking.
The adjustment allows the Earth's gravity and water pressure to partially balance the tidal force.
Tidal bulges and hydrostatic equilibrium.
If the oceans were allowed to come into HYDROSTATIC EQUILIBRIUM in the rotating frame of the Earth around the Earth-Moon center of mass, there would be permanent bulges.
This is just the adjustment of gravitational, tidal, and water pressure forces so the net force at every point is ZERO.
The the reality is that HYDROSTATIC EQUILIBRIUM can never be established because of the Earth's rotation on its axis.
In the diagram below we take a north pole view and for simplicity assume the Moon's orbits in the Earth's equatorial plane.
Actually, the Moon's orbit is tilted from the equatorial plane by an amount varying between 18.5 degrees and 28.5 degrees????: the variation is caused by that pesky rotation of the notes we discussed in IAWL Lecture 3: The Moon: Orbit, Phases, and Eclipses
The dynamic tidal situation.
Note an individual water particle doesn't go very far before the tidal current reverses.
Typically a water particle might go of order 20 km relative to the solid Earth---but the particle is not alone.
The whole ocean is sloshing back and forth.
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.
So the full tidal cycle of two high tides takes about 24 hours, 50 minutes.
So on average there are fewer than than two high tides a day: most days there will be two, but sometimes there will only be one.
The 24 hours, 50 minutes tidal period, also means that tides will cycle through the whole day: e.g.,
In the open ocean the tidal range (i.e., high to low tide) is typically about 0.5 meters.
The tidal current is 1 to 2 m/s or 4 to 7 km/hr which is not too different from walking speed.
Open ocean tides were very hard to measure before satellites with radar ranging.
If you didn't have that you'd have to measure with respect to the bottom of the ocean which can be several kilometers down. Not easy to do very often.
The kind of satellite mapping that can be done to study tides.
This is not a tidal map. It shows sea height relative to mean sea height with tidal variation averaged away.
The sea height changes are dependent on the temperature of the water, and thus on the heat energy stored in the water.
Water is a rather complicated liquid in that it contracts going from 0 degrees C to about 4 degrees C and then expands as temperature increases above 4 degrees C (HRW-432).
Of course, melting ice caps are the big danger.]
The height measurements are done by radar from the TOPEX/Poseidon satellite. This satellite is in a near polar orbit, and so almost all of the Earth is below it at some time or other.
Credit: NASA: Visible Earth.
Now above we studied an idealized case where just the MOON has a tidal effect.
The SUN also has tidal effect that is a bit less than half the strength of the Moon's.
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.
There are two times when the Moon and Sun tidal effects add up and two times when they partially cancel.
Spring tides and neap tides.
Spring tides are the strongest tides and neap tides the weakest tides.
And there are other complications for the Earth tides:
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:
Weather can lead to severe problems.
If you have an on-shore storm coinciding with a spring tide, then you can have severe flooding---a TIDAL SURGE.
This is when unstable islands and coastal homes can be washed away.
SMALL BODIES OF WATER
Small bodies of water (small seas and lakes), in fact, have measurable tides, but they are usually too minute for humans to notice.
Everything scales down from the oceans.
Even the Mediterranean (which is fairly large) only has noticeable tides in a few places: e.g., Venice.
TIDAL SLOWING AND LOCKING
The Earth drags the oceans that are trying to form tidal bulges.
But by Newton's 3rd law, this means the oceans drag on the Earth too.
The dynamic tidal situation.
The drag is slowing down the Earth's rotation and increasing the length of the day.
The rate measured over some millennia is about 0.0014 seconds/century (USNO site).
The standard time day is set to be exactly 86400 seconds, where the second is now defined by an atomic clock measurement---and has no connection to astronomical cycles any more.
The mean solar day (i.e., the actual day relative to the Sun) is currently about 86400.002 seconds.
Every 500 or so days a leap second is introduced in standard time to keep standard time and mean solar time consistent.
The international time people in charge of leap seconds (International Earth Rotation Service) usually ordain leap seconds at the beginning of January or July without making much noise about. See the US Naval Observatory's leap second site and past leap second catalog.
Another way of viewing the slowing down of the Earth's rotation is to say that the Earth's rotational kinetic energy is being dissipated to heat---recall friction leads to heating.
Dissipation of tidal energy.
The tidal friction with the solid Earth and internally via viscosity dissipates energy that ultimately mostly comes from the rotational energy of the Earth.
The dissipation is complex and may have profound current and climate implications.
The removal of Earth rotational energy is increasing the length of the Earth's day by about 0.0014 seconds per century.
The figure illustrates the tidal dissipation in the ocean in milliwatts per square meter. It isn't clear to me what the zero on the scale represents.
Credit: NASA: Visible Earth.
The tidal bulges also have the effect of causing the Moon to spiral away from the Earth to larger orbits with longer periods.
The tidal bulges and the outward spiraling of the Moon.
The Moon's mean distance increases by about 3 cm/year as we know from bouncing laser beams off reflectors left on the Moon by the Apollo missions (Se-38).
400 million years ago---BEFORE dinosaurs ruled the Earth---the Earth's day was only 22 hours long (Se-38, Cox-250) and the Moon was probably significantly closer than today.
When dinosaurs ruled the Earth.
This can be deduced from the fossil record.
Long in the future---if the Earth lasts that long---the day will
be the same length as the lunar month---then maybe 50 days
(FMW-75).
The Moon then will be farther away.
The Earth will always turn the same face to the Moon---this is
just what the Moon does now to the Earth.
This situation is called SYNCHRONOUS TIDAL LOCKING.
In fact, almost all
the significant moons in the solar system are already
synchronously tidally locked to their planets
(Cox-307).
Planet tidal forces on their moons, are much larger than the reverse.
Answer 2 is right.
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.
Question: Why does no one ever talk about land tides or
atmosphere tides.
Over long enough distances the solid Earth is flexible and there
are land tides of a few centimeters.