The planets move in ellipses with the Sun at one focus.

Conic section orbits are a natural outcome of the 1/d2 nature of the gravitational force, in fact the only force law that gives stable orbits.

Kepler’s 1st law

Discussion

A ball held on a string is coasting around in a large horizontal circle. The string is then pulled so the ball coasts in a smaller circle. When coasting the smaller circle its speed is

a) Greaterb) Lessc) Unchanged

A line drawn from the planet to the Sun sweeps out equal areas in equal intervals of time.

Just another way of saying angular momentum is conserved which comes from Newton’s 2nd law of motion.

Kepler’s 2nd law

Newton’s form of Kepler’s 3rd law

22 3

1 2

4

( )P a

G m m

Discussion

Notice that we can only determine the sum of the masses using Newton’s from of Kepler’s 3rd law. In the case of the solar system this sum is dominated by the Sun. Why can’t we figure out the mass of an object by observing its orbit?

All objects fall in a gravitation field with the same acceleration regardless of mass.

Because being in orbit is just falling, all objects will orbit the same regardless of their mass as long as the mass of the orbiting object is much less than that of the object it is orbiting.

Discussion

The Moon’s mass (consider it all at the center of the Moon) attracts every atom on the Earth. If every atom has exactly the same mass, is the gravitational attraction of the Moon the same on each atom on the Earth? Explain.

Tidal Forces

Different distances from a mass will experience different forces and therefore different accelerations.

Discussion

Consider yourself sitting on the center ball, number 2 in the previous diagram. How will you perceive the motion of the other two balls relative to you?

Spring Tides and Neap Tides

The Sun also contributes to the Earth’s tides. When the Sun and Moon line up to produce higher tides, this is called spring tides. Neap tides occur when the Moon and Sun Partially cancel each other.

What phases of the Moon do spring and neap tides occur?

Tidal Forces

Tidal forces act to stretch things out along the direction of a gravitating source and squeeze them in the middle.

Discussion

Does it matter that all the atoms on the earth have the same mass? Or that all three billiard balls have the same mass? Why or why not?

The Scientific method at work

• Use the simplest model to explain the observations

• Refine the model, make it more complicated, only if new observations require

• Explain why the model works

Explanation vs. usefulness

Kepler’s laws were adopted because they were useful for predicting planetary motions.

Newton’s laws explained why Kepler’s laws worked in a broader context.

Discovery of Neptune

Saturn and Uranus did not follow Kepler’s laws exactly

Le Verrier and Adams use these deviations to predict the existence and position of Neptune which was observed in 1846

Light

The primary source of information we have about the universe comes from the light received from space.

Does light travel instantaneously for one place to another?

Galileo – tried to measure the speed of light using the mountains in Italy and some lanterns.

Speed of Light from astronomy

Olaus Romer – in 1676 was the first to measure the speed of light using the moons of Jupiter.

The moons of Jupiter disappear behind the planet at regular intervals, based on their orbital period around Jupiter.

Discussion

Romer noticed that the eclipses of Jupiter’s moons happened about 13 minutes later when Jupiter was near conjunction than it did when Jupiter was near opposition. Why is that?

Romer’s Speed of Light Determination

Fizeau-Foulcoult Apparatus

Maxwell’s equations

Moving charges (changing electric fields) produce magnetic fields.

Example: an electromagnet

Changing magnetic fields produce electric fields.

Example: the dynamo

And let there be Maxwell!

Maxwell found that by combining the equations for oscillating electric and magnetic fields he could get the equation for a wave with a velocity of

83.00 10 m/sc

Electric and Magnetic Waves

Water Waves

Electric Field Waves

Frequency Wavelength Relation

light of speed

frequency

Wavelength

c

f

cf

We see variations in wavelength or frequency as color

White light contains all colors of the rainbow

The Electromagnetic Spectrum

The energy of electromagnet waves.

E = h f = h c/

The higher the frequency, or the smaller the wavelength, the higher the energy.

h is a constant, f is the frequency is the wavelength, and c is the speed of light

Discussion

How can I make electromagnetic waves with a magnet?

Discussion

How can I make electromagnetic waves with a with some charged particles?

Light interacts with matter in four general ways

1. Emission2. Absorption3. Transmission 4. Reflection

Come up with an example of each type of interaction.

Three types of spectra

Continuous – emits all frequencies of colors of light

Emission line – only specific frequencies are emitted.

Absorption line – mostly a continuous spectrum with specific frequencies missing

Continuous, Absorption and Emission Spectra

There are three main types of emission

• Blackbody or thermal emission which produces a continuous spectrum, i.e. all colors of the rainbow.

• Line emission which produces only certain wavelengths of light.

• Emission from free electrons which produces all wavelengths but has properties different from thermal emission.

Discussion

All hot objects emit radiation, called thermal or blackbody radiation. Why do you think this is?

Atom

Temperature

Thermal Emission

The temperature of matter is a measure of how much the atoms or molecules that make up the substance are vibrating. All matter vibrates, even if it is just above absolute 0 K.

Atoms are made up of negatively charged electrons and positively charged protons. Vibrating charges produce oscillating electric fields and thus electromagnetic waves.

Discussion

Do you think people emit thermal radiation?

Infrared Image

Blackbody radiation

In general the spectrum emitted by a hot object depends on the composition of the object. But there is a class of objects, called blackbodies because they appear black, that are perfect absorbers and perfect emitters. The spectrum of a blackbody depends only on its temperature.

Discussion

It is fairly easy to see that a perfectly black object is a perfect absorber of light. But why is a perfect absorber also a perfect emitter? What would happen if a perfect absorber was not a perfect emitter?

Properties of thermal radiation

1) Blackbodies emit radiation at all frequencies.

Thus, they emit a continuous spectrum, all the colors of the rainbow.

Blackbody emission

Discussion

How does a filament light bulb work?

Discussion

Why do you think thermal or blackbody radiation is a continuous spectrum?

Properties of thermal radiation

2) Wien’s law – the temperature of the object is directly proportional to the the frequency of maximum emission.

We perceive the frequency of maximum emission as the color of the object.

Discussion

Why do you think that the color red is often associated with hot while blue is associated with things that are cool?

Discussion

Is it warmer or cooler in the shade on a hot summer day?

If you have a perfectly opaque object what color is its shadow on a clear day?

Discussion

Why do you think the frequency of maximum emission increases with the temperature of the object?

Properties of thermal radiation

3) Stefan-Boltzmann law – the intensity of the emission is proportional to the 4th power of the temperature.

Discussion

If we doubled the surface temperature of the Sun, how much more intense would the light emitted by it be?

Thermal Spectra

The color of a star indicates that star’s surface temperature.

Red stars are cooler stars.

Yellow stars are intermediate in temperature.

Blue stars are hotter.

Sunspots are cooler regions of the Sun’s photosphere

Photons

Electromagnetic radiation is emitted or absorbed by matter only in discrete quanta called photons. A photon is a packet of electromagnetic energy.

Light acts as both an electromagnetic wave and as a particle.

Continuous, Absorption and Emission Spectra

Ionized Hydrogen gas

Line emission

Discussion

An excited electron will drop rapidly back down to ground state, emitting a photon. If the photon absorbed is the same wavelength as the photon that is emitted, why do we see dark absorption line features in the spectrum?