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)

9/12/2010

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(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

9/12/2010

3

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!

9/12/2010

4

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!

9/12/2010

5

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 ↑

9/12/2010

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(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

9/12/2010

7

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

9/12/2010

8

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

9/12/2010

9

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

9/12/2010

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

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)

9/12/2010

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 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 ↑

9/12/2010

12

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

9/12/2010

13

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!

9/12/2010

14

The Planet Uranus – discovered telescopically in 1781

The planet Neptune – discovered by gravitational calculations in 1846