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Units to cover: 55, 56, 59, 60 Homework 7 Unit 53. Problems 14, 18, 19, 20, 21, 22 Unit 26. Problem 12, 18, 20 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 electromagnetic 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 lightyears 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 L d= 4pB • 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: T= 2.9 ´106 K × nm • This is Wien’s Law l Measuring Temperature using Wein’s Law T= 2.9 ´106 K × nm l 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 B-A-F-G-K-M O- – 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 – • Other stars are cooler and more luminous than main sequence stars – – • The Main Sequence 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: L » M 3.5 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