Units to cover: 55, 56, 59, 60

1. Units to cover: 55, 56, 59, 60

2. Homework 7 Unit 53. Problems 14, 18, 19, 20, 21, 22 Unit 26. Problem 12, 18, 20

3. 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

4. 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

5. Light has properties • a. of waves; • b. of particles; • c. none of the above; • d. both a. and b.

6. 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

7. 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

8. 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

9. 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.

10. 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!

11. 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!

12. 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

13. 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!

14. 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…

15. 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.

16. 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.

17. 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

18. Measuring Temperature using Wein’s Law

19. 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 Spectral Classification

20. 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 The Stefan-Boltzmann Law

21. 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.

22. 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

23. The Family of Stars

24. Stars come in all sizes…

25. 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!

26. Massive stars burn brighter L~M3.5

27. Luminosity Classes

28. 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.

29. Evolution of low-mass stars

30. Evolution of high-mass stars

31. 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