Units to cover: 55, 56, 59, 60

Homework 7

Unit 26. Problem 12, 18, 20

Unit 53. Problems 14, 18, 19, 20, 21, 22

If a new planet were found with a period of revolution of 6 years, what would be its average distance from

the Sun?

• a. About 1AU

• b. About 3.3 AU

• c. About 6 AU

• d. About 36 AU

In order of increasing wavelength the electro-magnetic spectrum is

• a. gamma rays, blue light, red light, radio waves;

• b. ultraviolet, gamma rays, blue light, radio waves;

• c. red light, radio waves, X rays, blue light;

• d. visible, ultraviolet, X-rays, radio

Light has properties

• a. of waves;

• b. of particles;

• c. none of the above;

• d. both a. and b.

What is the Law of Inertia?

• A body at rest stays at rest unless acted on by an outside force

• b. F=ma

• c. P^2=A^3

• d. Fg=mMG/R^2

Convert 742 km to millimeters

• a. 7.42 x10^8

• b. 7.42 x10^5

• c. 74.2 x10^8

• d. 7.42 x10^6

What is retrograde motion?

• a. “backward moving”/ or interrupted movement of a planet on the sky

• b. Clockwise rotation of the moon around the earth

• c. Rotation of planets around the sun

• d. Large elliptical movements of comets

This does not work for Light!

• If Galilean Relativity worked for light, we would expect to see light from a star in orbit around another star to arrive at different times, depending on the velocity of the star.

• We do not see this – light always travels at the same speed.

The Michelson-Morley Experiment

• Two scientists devised an experiment to detect the motion of the Earth through the “aether”– Light should move

slower in the direction of the Earth’s motion through space

– Detected no difference in speed!

– No aether, and the speed of light seemed to be a constant!

The Lorentz Factor

• It was proposed that perhaps matter contracted while it was moving, reducing its length in the direction of motion

• The amount of contraction was described by the Lorentz factor– At slow speeds, the effect

is very small– At speeds close to the

speed of light, the effect would be very pronounced!

Einstein’s Insights

• Albert Einstein started from the assumption that the speed of light was a constant, and worked out the consequences– Length does indeed contract in the

direction of motion, by a fraction equal to the Lorentz factor

– Time stretches as well, also by the Lorentz factor

• Moving clocks run slow• Moving objects reduce their length

in the direction of motion

Special Relativity

• Time dilation and length contraction depend on the observer!– To an observer on Earth,

the spacecraft’s clock appears to run slow, and the ship looks shorter

– To an observer on the ship, the Earth appears to be moving in slow-motion, and its shape is distorted.

• The passage of time and space are relative!

Possibilities for Space Travel

• Example: A spacecraft leaves Earth, heading for a star 70 light-years away, traveling at .99c– To an observer on Earth, it takes

the spacecraft 140 years to get to the star, and back again

– To passengers on the ship, it only takes 20 years for the round-trip!

• This means that high speed travel to the stars is possible, but comes at the cost of friends and family…

You see this every day!

• More distant streetlights appear dimmer than ones closer to us.

• It works the same with stars!• If we know the total energy output of a

star (luminosity), and we can count the number of photons we receive from that star (brightness), we can calculate its distance

• Some types of stars have a known luminosity, and we can use this standard candle to calculate the distance to the neighborhoods these stars live in.

Photons in Stellar Atmospheres

• Photons have a difficult time moving through a star’s atmosphere• If the photon has the right energy, it will be absorbed by an atom and raise an

electron to a higher energy level• Creates absorption spectra, a unique “fingerprint” for the star’s composition.

The strength of this spectra is determined by the star’s temperature.

Stellar Surface Temperatures

• Remember from Unit 23 that the peak wavelength emitted by stars shifts with the star’s surface temperatures– Hotter stars look blue

– Cooler stars look red

• We can use the star’s color to estimate its surface temperature– If a star emits most strongly in a wavelength

(in nm), then its surface temperature (T) is:

• This is Wien’s Law

Measuring Temperature using Wein’s Law

Spectral Classification

• Around 1901, Annie Jump Cannon developed the spectral classification system– Arranges star

classifications by temperature

• Hotter stars are O type• Cooler stars are M

type

• New Types: L and T– Cooler than M

• From hottest to coldest, they are O-B-A-F-G-K-M– Mnemonics: “Oh, Be A Fine Girl/Guy,

Kiss Me– Or: Only Bad Astronomers Forget

Generally Known Mnemonics

The Stefan-Boltzmann Law

• The Stefan-Boltzmann Law links a star’s temperature to the amount of light the star emits– Hotter stars emit more!

– Larger stars emit more!

• A star’s luminosity is then related to both a star’s size and a star’s temperature

A convenient tool for organizing stars

• In the previous unit, we saw that stars have different temperatures, and that a star’s luminosity depends on its temperature and diameter

• The Hertzsprung-Russell diagram lets us look for trends in this relationship.

The H-R Diagram

• A star’s location on the HR diagram is given by its temperature (x-axis) and luminosity (y-axis)

• We see that many stars are located on a diagonal line running from cool, dim stars to hot bright stars

– The Main Sequence

• Other stars are cooler and more luminous than main sequence stars

– Must have large diameters

– (Red and Blue) Giant stars

• Some stars are hotter, yet less luminous than main sequence stars

– Must have small diameters

– White Dwarf stars

The Family of Stars

Stars come in all sizes…

The Mass-Luminosity Relation

• If we look for trends in stellar masses, we notice something interesting– Low mass main

sequence stars tend to be cooler and dimmer

– High mass main sequence stars tend to be hotter and brighter

• The Mass-Luminosity Relation:

Massive stars burn brighter!

Massive stars burn brighter

L~M3.5

Luminosity Classes

Stellar Evolution – Models and Observation

• Stars change very little over a human lifespan, so it is impossible to follow a single star from birth to death.

• We observe stars at various stages of evolution, and can piece together a description of the evolution of stars in general

• Computer models provide a “fast-forward” look at the evolution of stars.

• Stars begin as clouds of gas and dust, which collapse to form a stellar disk. This disk eventually becomes a star.

• The star eventually runs out of nuclear fuel and dies. The manner of its death depends on its mass.

Evolution of low-mass stars

Evolution of high-mass stars

Tracking changes with the HR Diagram

• As a star evolves, its temperature and luminosity change.

• We can follow a stars evolution on the HR diagram.

• Lower mass stars move on to the main sequence, stay for a while, and eventually move through giant stages before becoming white dwarfs

• Higher mass stars move rapidly off the main sequence and into the giant stages, eventually exploding in a supernova