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9/12/2010
1
The Four Fundamental Forces of Nature
1. Gravity
2. Electromagnetism
3. The Strong Nuclear Force
4. The Weak Nuclear Force
The Universe is made of matter
Gravity – the force of attraction between matter
Most important force in Astronomy!
Operates over large distances!
The five naked eye planets
1. Mercury
2. Venus
3. Mars
4. Jupiter
5. Saturn
Direct and Retrograde Motion
Planets are brightest during retrograde motion
The Geocentric Cosmology of
Ptolemy (100-170 AD)
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Epicycles and Deferents The Ptolemaic explanation for retrograde motion
Occam’s Razor
The simplest ideas are usually the best
The simplest ideas are those with the fewest assumptions
Assumptions are things which are assumed to be true but which have not been confirmed
experimentally
Nicolai Copernicus(1473-1543)
The Heliocentric Cosmology
Inferior and Superior planets
Inferior Planets (Mercury, Venus)• always seen close to the Sun in the sky• must be closer to the Sun than the Earth• since they have a shorter distance to travel they should take less time to orbit the Sun
Superior Planets (Mars, Jupiter, Saturn)• can be seen far from the Sun in the sky (high in the sky at midnight)• must be further from the Sun than the Earth• since they have a longer distance to travel they should take more time to orbit the Sun
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The Copernican explanation for retrograde motion
Tycho Brahe(1546-1601)
Made detailed observations of
planetary motion
Johannes Kepler (1571-1630)
Used the empirical method to determine the optimum shapes of planetary orbits
The Empirical Method: An Example Planetary Orbits are Ellipses!
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Eccentricity – measuring the shape of ellipses
Zero Low High
1st Law: the orbit of a planet is an ellipse with the Sun at one focus
2nd Law: an imaginary line joining the Sun and a planet sweeps out equal areas in equal times
Planets move faster when they are closer to the Sun!
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3rd Law: the Harmonic Law
P2 = a3
where:
P = orbital period (Earth years)
a = semi-major axis (AU)
3rd Law: the Harmonic Law
P2 = a3
where:
P = orbital period (Earth years)
a = semi-major axis (AU)
a is also equal to the average distance of the planet from the Sun!
What does this mean?
Mathematical Equations
Describe the relationship between things (called variables)
More concise than using words
Allow calculations to be made
Example: in P2 = a3, P and a are the variables
Analyzing Equations
1. Ignore any powers (and constants)
2. Make sure the two variables to be analyzed are on opposite sides of the = sign
3. Are the variables on the same level i.e. if you were to draw a line under the equation both
variables would be above it?
4. If so, we have what is called a direct relationship where variables increase and decrease in the
same direction
Example
P2 = a3
1. Ignore powers: P = a
2. P and a are on opposite sides of =
3. P and a are on the same level: P = a
4. We have a direct relationship: a ↑ P ↑
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P = how long a planet takes to go around the Sun
a = average distance of planet from Sun
The further a planet is from the Sun, the longer it takes to orbit!
Galileo Galilei(1564-1642)
Galileo didn’t invent the telescope but was one of the first people to study
the sky with it
He saw four objects surrounding Jupiter
And found that their positions
shifted with time in a regular
pattern
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This could only be explained if they were in orbit about the planet!
Observed motions consistent with heliocentric theory!
Today they are called the Galilean moons of Jupiter!
The Phases of Venus
Can only be explained if Venus orbits the Sun! If Venus moved about the Earth, we would not see the observed cycle of phases!
The Inquisition of Galileo (1616)
Placed under house arrest “for vehement suspicion of heresy”
Isaac Newton(1642-1727)
The Analytical Method
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Newton’s Laws of Motion
1st Law
An object will remain at rest or move in a straight line at constant speed unless a
force acts
In their elliptical orbits around the Sun, are the planets at rest or moving in
straight lines?
No!
So what does this mean?
A force must be acting!
This force is called gravity!
speed (m/s) = how fast
velocity, v (m/s) = speed + direction
acceleration, a (m/s2) = changing velocity
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There are three different kinds of acceleration!
Changing Speed, Constant Direction
Changing Direction, Constant Speed
Planet in a circular orbit
Changing Speed and Direction
Planet in an elliptical orbit
Gravity exerts a force which causes the planets to accelerate around the Sun!
2nd Law
F = ma
where:
F = force applieda = resultant acceleration
m = mass
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F = ma
Relationship between F and a?
Direct!
F ↑ a ↑
Mass = measure of total amount of matter
Weight = force exerted by mass due to gravity
Mass same everywhere
Weight varies with location
Location Weight
Earth 165 lbs
Moon 28 lbs
Space ≈ 0 lbs
Example
Mass is constant!
Relationship between a and m?
F = ma
F/m = ma/m (divide both sides by m)
a = F/m
Assume F is constant
Inverse relationship!
m ↑ a ↓
3rd Law
Action and reaction are equal and opposite!
Only applies to forces that are in equilibrium (balance)
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Force of Sun on planets
=
Force of planets on Sun
Why do the planets then orbit the Sun?
Why can’t the Sun orbit the Earth?
Newton’s 2nd Law
a = F/m
Masses:
mSun >> mplanet
Planets are much less massive than the Sun so accelerate much more!
This is why they orbit the Sun!
Newton’s Universal Law of Gravitation
G is a constant (does not change)Can be ignored during analysis
Relationship between F and M?
Direct!
M ↑ F ↑
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Relationship between F and d?Inverse squared!
d x 2 F x 1/22 = 1/4
d x 3 F x 1/32 = 1/9
Applications
Proof of Kepler’s 3rd LawNewton’s modified form:
P2 = a3/(M1+M2)
where:
P = orbital period (Earth years)
a = average distance from the Sun (AU)
M1+M2 = combined mass (solar masses)
Application to Solar System
MSun = 1
Mplanet = 0.001
MSun + Mplanet = 1.001 ≈ 1
P2 = a3/1
P2 = a3 !
Kepler only deduced an approximation!
For any two masses in orbit about each other, if we know their average separation, a and their orbital period, P it is possible to use this formula to
calculate their combined masses:
M1 + M2 = a3 / P2
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Sir Edmund Halley (1656-1742)
Historical records showed that a comet appeared in the sky at regular
intervals of 76 years!
Adoration of the Magi – Giotto (1304-6)
Inspired by Halley return in 1302?
The Bayeux Tapestry
Depicts the Norman conquest at the Battle of Hastings (1066)
He used Newton’s theory predict when it would return!
Calculations suggested it should return in 1758
Indeed, it was first sighted at end of 1757 in agreement with theory!
Halley’s Comet!
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