9/12/2010. The Four Fundamental Forces of Nature. 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force

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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 The Geocentric Cosmology of Ptolemy ( AD) Planets are brightest during retrograde motion 1

2 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 ( ) 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 2

3 The Copernican explanation for retrograde motion Tycho Brahe ( ) Johannes Kepler ( ) Made detailed observations of planetary motion Used the empirical method to determine the optimum shapes of planetary orbits The Empirical Method: An Example Planetary Orbits are Ellipses! 3

4 Eccentricity measuring the shape of ellipses 1 st Law: the orbit of a planet is an ellipse with the Sun at one focus Zero Low High 2 nd 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! 4

5 3 rd Law: the Harmonic Law P 2 = a 3 where: P = orbital period (Earth years) a = semi-major axis (AU) 3 rd Law: the Harmonic Law P 2 = a 3 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 P 2 = a 3, 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 P 2 = a 3 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 5

6 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 ( ) 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 6

7 This could only be explained if they were in orbit about the planet! The Phases of Venus Observed motions consistent with heliocentric theory! Today they are called the Galilean moons of Jupiter! 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) Isaac Newton ( ) Placed under house arrest for vehement suspicion of heresy The Analytical Method 7

8 Newton s Laws of Motion 1 st 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/s 2 ) = changing velocity 8

9 Changing Speed, Constant Direction There are three different kinds of acceleration! Changing Direction, Constant Speed Changing Speed and Direction Planet in a circular orbit Planet in an elliptical orbit Gravity exerts a force which causes the planets to accelerate around the Sun! 2 nd Law F = ma where: F = force applied a = resultant acceleration m = mass 9

10 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 Example Location Weight Earth 165 lbs Moon 28 lbs Space 0 lbs 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 3 rd Law Action and reaction are equal and opposite! Only applies to forces that are in equilibrium (balance) 10

11 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 2 nd Law a = F/m Masses: m Sun >> m planet 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 11

12 Relationship between F and d? Inverse squared! d x 2 F x 1/2 2 = 1/4 d x 3 F x 1/3 2 = 1/9 Applications Proof of Kepler s 3 rd Law Newton s modified form: P 2 = a 3 /(M 1 +M 2 ) where: P = orbital period (Earth years) a = average distance from the Sun (AU) M 1 +M 2 = combined mass (solar masses) Application to Solar System M Sun = 1 M planet = M Sun + M planet = P 2 = a 3 /1 P 2 = a 3! 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: M 1 + M 2 = a 3 / P 2 12

13 Sir Edmund Halley ( ) Historical records showed that a comet appeared in the sky at regular intervals of 76 years! Adoration of the Magi Giotto (1304-6) The Bayeux Tapestry Inspired by Halley return in 1302? Depicts the Norman conquest at the Battle of Hastings (1066) Indeed, it was first sighted at end of 1757 in agreement with theory! He used Newton s theory predict when it would return! Calculations suggested it should return in 1758 Halley s Comet! 13

14 The Planet Uranus discovered telescopically in 1781 The planet Neptune discovered by gravitational calculations in

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