Including...
Introduction
Early Astronomical Thought
The Development of "Modern" Astronomy
Newton and the Classical Laws of Motion
Relativity and Space-time
Angular Momentum and Gravity
Orbital Mechanics
This is where some of the heavy-duty laws of nature come into effect
Lots of math and physics
This should be the toughest two weeks of the course
Survive this and you'll probably make it!
In large part first clearly defined by Sir Issac Newton (1642-1727)
"Principia" in 1686
We'll get to him soon enough
But first some background...
Matter: The stuff of reality
Mass: How much stuff there is in an object
Does not change with a change of location
Volume: how much space a mass occupies
DIGRESS TO: Nature loves spheres
Density: a very important concept (so pay attention)
In my opinion: one of the fundamental driving forces of nature
Defined as: Density = mass / volume (units: g/cm3)
EXAMPLES: See table 3:1 pg. 50
Panning for gold: gold in a placer deposit
Oil, water, antifreeze, and mercury
Hot air vs. cold air
DEMONSTRATIONS:
Pepsi cans
Candle in the wind
Some extremes:
Comet's tail: 10-16 g/cm3
Neutron star: 1015 g/cm3
Density differences are responsible for internal structure of the earth
To sum it up:
Mass = How much
Volume = How big
Density = how tightly packed at atomic level
Some basic definitions:
Star vs. planet vs. moon (flashlights vs. mirrors)
Click here for a summary of some other physics and chemistry concepts
The Ancients - far more advanced than Europe before the Renaissance
The Chinese - for 5000 years or more...
Europe - Stonehenge (pg. 12) in England
Where did this come from?
The Original Americans (Maya, Aztec, Inca)
These cultures clearly understood part of the reality of celestial motions
They had great calendars
Polynesia (Michenor's "Hawaii")
Driven out for religeous reasons
Sail north - navigation always a problem
Polaris (fig. 1.2, pg. 13)
The Greeks (a.k.a. the Ionians)
Very sharp culture
First postulated "atoms"
Root for the term "ion"
Pythagoras - we still use formulas which bear his name
Aristotle (384 - 322 B.C.)
Earth and Moon both spheres
Orbits in perfect, uniform circles (fig. 1.13, pg. 22)
Needed "epicycles" to explain subtle variations
Phases of the moon
Aristarchus (310 - 230 B.C.)
Credited with first heliocentric model (sun in the center)
Hipparchus (worked from 160 - 127 B.C.)
Excellent and subtle observations
Stellar magnitudes - we still use his original scale
Identified the precession of the earth's axis (approx. 22,000 year cycle)
DEMO: gyroscope
Ptolemy (140 A.D.)
Supported geocentric model
Published "Almagest" - accepted in Europe for over 1000 years
Also began formal study of Astrology
Not much more happened during the Dark Ages
If anything, European cultures retreated into ignorance
But there were some who kept a thread of knowledge concerning the sky
Belief in Astrology definitely survived
Requires some rudimentary understanding of celestial events
Magicians & eclipses ("Listen up, King...")
Copernicus (1473-1543)
Agreed with Aristotle - uniform circular motion (with epicycles)
Also agreed with Aristarchus and resurrected the heliocentric model
Said that earth (and the other planets) were in orbit around sun
Described basic layout of solar system (fig. 2.3, pg. 31)
Superior vs. inferior planet
Opposition vs. conjunction
Quadrature
Elongation
Calculated relative distances for the planets
Was remarkably accurate (table 2.1, pg. 32)
Redshift - Tours ("Solar System" 5/20)
Tycho Brahe (1546-1601)
Was the court mathematician in Prague
"Arrogant and extravagant"
Did not accept heliocentric model
Was, however, and excellent observer and took great notes
Proof of the value of note taking: you can be a bozo and still get a crater on the moon named after you if you take good notes
His work was later used as support of the Copernican heliocentric model
Johannes Kepler (1571-1630)
Succeeded Tycho as the court mathematician in Prague
Used Tycho's observations to come up with the 3 fundamental "laws" of planetary motion that are named after him
Published the first two of his laws in 1609 and the third law nearly a decade later, in 1618.
Kepler's first law
A planet describes an ellipse in its orbit around the Sun, with the Sun at one focus
Some appropriate terms:
Ellipse: basically a flattened circle (fig. 2.9, pg. 35)
Major axis - the maximum diameter of the ellipse (through the foci)
Semimajor axis -half the major axis
Commonly used as the "distance from the planet to the sun"
Eccentricity - the shape of the ellipse (fig. 2.10, pg. 36)
A circle has an eccentricity of zero (0)
Kepler's second law (law of equal areas)
A ray directed from the Sun to a planet sweeps out equal areas in equal times
See fig. 2.11, pg. 36
This means that a planet's speed changes as it moves around the sun
Faster as it gets closer, slower as it moves away
Kepler's third law (the Harmony of the Worlds)
Keppler tried to come up with an underlying harmony to nature which could be defined mathematically
He published The Harmony of the Worlds in 1619
The square of the period of a planet's orbit is proportional to the cube of its semimajor axis (p2 = a3)
This proportionality is the same for all planets (table 2.2, pg. 37)
How about artificial satellites?
Galileo Galilei (1564-1642)
Experimental physics and astronomy
Physics
Inertia
The property of matter which resists any change in motion - either while moving or at rest
The lack of motion is no more natural than motion
Acceleration
Different sized bodies fall at the same rate (fig. 2.14, pg. 38)
Astronomy
Supported heliocentric model
Cost him dearly later in life
In 1616 the church stated the heliocentric model was "false and absurd"
Galileo was forced to recant on pain of torture and excommunication
Invented the telescope
Defined the Milky Way
Discovered lots of other new stuff
Four of Jupiter's moons
The phases of Venus
The "seas" of the moon
Sunspots (and evidence of the sun's rotation)
Sir Issac Newton (1642-1727)
VIDEO: Inertia video clip
Newton's 1st Law of Motion: Inertia
"A body will continue in a state of rest, or in uniform motion in a straight line, unless it is acted upon by a net external force"
Inertia: a property of matter which requires a force to cause acceleration
NOTE: acceleration is a vector: both magnitude and direction
Can you hold an inertia in your hand?
Momentum: a measure of the inertia or state of motion of a body
Momentum = mass X velocity
Examples:
Changing mass: hit by a VW vs. a dump truck
Changing velocity: speed up the VW
Both together: bullet vs. a medicine ball
DIGRESS TO: a sniper uses small caliber rounds
Low mass and resistance, but very high velocity
Newton's 2nd Law of Motion: changes in momentum
"When an unbalanced force acts upon a body, the body will be accelerated in the direction of the greater force"
EXAMPLE: Tug of war (use vector addition)
Defines force: Force = mass X acceleration
Refer back to video clip
Newton's 3rd Law of Motion: Law of action and reaction
"For every action there is an equal and opposite reaction"
A single force cannot exist or there would never be balance
Every force MUST be accompanied by an equal and opposite force
EXAMPLES:
When I push on the wall, the wall has to be pushing back
Recoil of a rifle: the shooter's mass is far greater than the bullet
Rockets: work best in a vacuum
Therefore, it is clear that the force need not be pushing against something
The classical laws of physics work well for most of what we have to deal with
Start to break down when we get too big or small
Or overcome inertia and start moving fast
DIGRESS TO: Relativistic speeds
With respects to Professors Einstein and Hawking...
I'm not qualified to discuss their work, but I'll give it a shot
Albert Einstein: Early 1900's
Spatial reality and time - we think we handle them pretty well
We define our reality relative to what is around us
All points in space defined relative to another point
EXPAND TO: Where is the fixed reference point?
How about time?
The concepts of past, present, and future are all relative
Is there a fixed reference point for time?
For most of what we do, this doesn't matter at all
In our daily lives we don't notice anything weird
But there are some weirdities...
FOR EXAMPLE: How do we measure speed, distance, and time
We all think that these can be defined as absolute and specific quantities
We even have formulas (with equal signs) to relate them to each other
Rate = Distance / Time (re-arrange and solve for each)
They are all inter-related and inter-dependent
If any of these 3 are not absolute, then none can be absolute
Let's start with distance and shoot some free throws in the gym
(or play catch, or kick a soccer goal, or throw a touchdown pass, or toss a pom-pom into the air and catch it)
We know the exact distance to the basket, and if we can control the trajectory of the ball we can make them all day
But what if Shaq's nightmare comes true and the NBA introduces the "moving basket" in 2003
Suddenly our "absolute distance" is gone and we've got a problem
How about on a ship at sea
Isn't the basket in motion now?
Yes, but so are we
So, we are motionless relative to each other
And, thanks to inertia, can still make the shot
But is the basket in the gym motionless?
The gym is attached to the earth, and the earth is in motion
(REFER BACK TO: "How fast are we moving" discussion)
So, if distance is measured between 2 points, and both are in motion...
How can we obtain an absolute value for distance
There can't be any absolute distances
The important thing is the relative motion of the 2 points
We can only define relative distances between two points (which are in motion)
The distance constant only if they are in uniform motion
Therefore motionless relative to each other
How about time?
VIDEO: "Back to the Future" scene with 2 synchronized clocks
They did this with accurate clocks and jet planes
Time changes as you speed up! (oops)
So if distance and time are both variable, so must be rate
How can we attempt to define absolute spatial reality?
We can only define a relative sense of mechanical position and motion
How about electro-magnetics? Does relativity also apply here?
Radios and computers both work at high rates of speed
So the principle of relativity must also work for electromagnetic waves
Speed of light: here's where it gets seriously weird
We like the speed of light
We base quite a bit of scientific "truth" on how fast it goes
And that it is a constant (absolute) value (2.998 X 108 meters per second)
But relativity states that it, too, must be dependent upon the motion of the observer
But, here comes the weird part...
Speed of light / bullet train example (DESCRIBE)
East-west across Kansas at sunrise and sunset
No measurable change in the speed of light
If speed of light is an absolute value then how can this be?
It must be different for each observer
Or the train changes in length and messes up our measurement
Time and distance are both relative and change as you speed up! (oops)2
So how can we successfully define our reality?
Everything we see is only what it is relative to everything else
And if everything we see is relative to everything we see, we are probably relative, too
I'm getting a headache (but it's only relative)
Clearly there are things here that we still don't fully understand
Einstein also said that at sufficient speed matter and energy are interchangeable (E = MC2)
See Sec. 8.3g; pg. 137
Stephen Hawking: severely handicapped (physically) but still alive and working
Hopes to unify classical mechanics, relativity, and quantum mechanics
Way too many formulas
Very confusing for modern astrophysicists
Not to mention us normal mortals
Remember Kepler and The Harmony of the Worlds?
Hawking is convinced that there is a GUT
Combines everything into a single mathematical expression
Angular Momentum
A measure of the momentum of a body as it rotates around a fixed point
Angular Momentum = mass X velocity X radius
Angular momentum is conserved
EXAMPLE: a spinning ice skater
DEMONSTRATION: swivel chair, a student, and 2 books
This is an important concept which we will refer to later
For example: formation of the solar system
As nebulas condense they must speed up their rotation to conserve angular momentum
Causes them to flatten and bulge out in the center
Leads to planetary formation
Newton's "Universal" Law of Gravitation: G=M1M2/D2
There has to be something which attracts two bodies
Several observations indicate this
1) The orbits of the planets:
1st law says they will go in a straight line unless acted upon by a net external force
EXAMPLE: ball on a string
Spin it around your head and let go
Flies off in a straight line
Ask Goliath about this one!
Since the planets are not orbiting in a straight line, there has to be an external force which "attaches" them to the star
2) Back to definition of mass: does not change with a change of location
Astronauts on moon: bounced around like Roger Rabbit
Why: mass is same, what was different
Weight: mass under the influence of some external (and invisible) force
This one gets even weirder
Astronauts in space: weightless
It seems as though an object only has "weight" if it is associated with a second object
We now know that there is a force of mutual attraction between all objects
Newton's "Universal" Law of Gravitation
Defined as: Fg = G X M1 X M2 / D2
Where:
M1 = mass of an object (in kilograms)
M2 = mass of an object (in kilograms)
D = distance between the objects (in meters)
G = gravitational constant (6.67 X 10-11 N m2/kg2 on earth)
Give some examples:
Any 2 people are bound by this force
Even people you don't like!
Close to earth, its greater mass results in sufficient force to mask the others forces of attraction
In space, however...
Powerful implications in this
Pulls planets out of their straight-line trajectory and into orbit
Called Centripetal Force and results in Centripetal Acceleration
The gravitational force is proportional to the amount of mass
With a larger mass exerting more gravitational force
Therefore, since the moon has less mass than the earth, we can all play Roger Rabbit there
Also, the world's quickest diet
The gravitational force is inversely proportion to the square of the distance between the bodies
As they get farther apart, the force lessens by the square of the distance
DIGRESS TO: What is the net result of the gravitational constant
This makes gravity a VERY weak force
Even the smallest and weakest baby can defeat gravity
The problem is that gravity never stops
How to apply this to a spherical object (such as the sun or a planet)
Pretty complex math - Newton invented calculus to solve it
Beyond the scope of this class (fortunately!)
What Newton found (see fig. 3.6; pg. 52)
"A spherical mass acts gravitationally as though all its mass were concentrated at a point at its center"
Called the "Center of Mass"
Allows us to consider all celestial bodies as "points" with regard to their gravitational forces
Therefore, the weight of an object is defined as the gravitational force between the object and the earth
Weight of an object on earth = G X M1 X M2 / r2 where
r = radius of the earth in meters (6.4 X 106 meters)
M1 = mass of the earth in kilograms (6 X 1024 kg)
M2 = mass of any object (like an apple, or me)
Let's try one: the attraction between the earth and a 65 kg ball of toe jam
g = 6.67 X 10-11 N m2/kg2 X ((6 X 1024 kg) X 65 kg) / (6.4 X 106 meters)2
= 635 Newtons
One step farther...
From this we can calculate the gravitational acceleration
On earth this is 9.8 m/s2
An object will fall towards the earth at this rate
Section 3.2(d) pg. 52 details the mathematical proof of this
The ancients thought that the natural path of an object was a perfect circle
Newton's 1st law says it's a straight line
Laws of motion allow us to predict the motions of 2 bodies under the influence of their mutual gravitational attraction
Review center of mass
Newton says "A spherical mass acts gravitationally as though all its mass were concentrated at a point at its center"
How about 2 spherical bodies?
They also have a common center of mass
Called the "barycenter" (the true center of mass in a two body system)
Must lie on the plane between the centers of mass of the 2 bodies
The distance of each body from the barycenter will be inversely proportional to its mass.
Means that the barycenter will be closer to the more massive object
Like 2 kids on a seesaw
How does this impact the orbits of planets?
Both objects move about the barycenter
EXAMPLE: earth and moon
Does the moon orbit the earth?
Yes, but the center of the earth is not the center of the orbit
Both actually orbit each other about the barycenter
VIDEODISC: Earth-Moon System (Barycenter clip)
Putting all this together, we can explain the orbit of the moon
See 3.4 pg. 54 and figure 3.9 pg. 55
An object dropped on the earth will fall at 9.8 m/s2
Average speed during first second is 4.9 m/s, so it drops that far
How about the orbit of the moon
In 1 second the moon travels 1 km horizontally, and wants to continue in a straight line (Law of Inertia)
Which would carry it out into space and away from the earth
However, the earth exerts a gravitational attraction on the moon
But the moon is 400,000 km from the earth, so the force is less
The earth's attraction on the moon is 1/3600 as strong, so it "falls" only 1.4mm in the same 1 second (not 4.9 meters)
Fortunately, due to the curvature of the earth, the ground drops away from the moon at the same rate, so it doesn't get any closer
The moon actually "falls" around the earth without ever getting any closer
The orbits of the planets around the sun can be explained in the same way
Also explains any satellite in orbit around any space body