Transcript 8Oct_2014
READING Unit 26, Unit 27 (will not be included in the 1st exam) Homework 5 Most important is to prepare for the exam! This is your main assignment. Look through the lectures and read the corresponding chapters. The homework will help you a bit with this. Unit 6, problem 7, Unit 8, problem 10 Unit 10, problem 8 Unit 12, problem 6, problem 8 Unit 14, problem 7, problem 9 Unit 15, problem 7 Unit 18, problem 7 Unit 26, problem 10 Galilean Relativity • Galileo noted that the speed of a thrown object depends on how fast and in what direction the thrower is moving – If the thrower is moving in the same direction as the throw, the projectile goes faster – If the thrower is moving in the opposite direction, the projectile goes slower • In other words, velocities add. 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… General Relativity: Mass Warps Space • Mass warps space in its vicinity • The larger the mass, the bigger “dent” it makes in space • Objects gravitationally attracted to these objects can be seen as rolling “downhill” towards them • If the mass is large enough, space can be so warped that objects entering it can never leave – a black hole is formed. The Escape Velocity Limit: Application to Black holes • Recall that the velocity necessary to avoid being gravitationally drawn back from an object (the escape velocity) is: Vesc 2GM R • Note that as R decreases, the escape velocity increases • Also recall that nothing can travel faster than the speed of light, c, or 3108 m/s • If a stellar core is compressed so much that its radius is smaller than 2G M RS c2 (the Schwarzschild radius) then nothing can escape from its gravitational force, including light! Gravitational Redshift • Photons traveling away from a massive object will experience a gravitational redshift. – Their frequency will be shifted toward the red end of the spectrum Which of the following factors does *not* directly influence the temperature of a planet? • • • • a. The luminosity of the Sun b. The distance from the planet from the Sun c. The color of the planet d. The size of the planet Star C and star D are equally luminous. Star C is twice as far away from Earth as star D. How do the brightness level of stars C and D compare? • • • • a. Star C appears 4 times as bright as star D b. Star C appears 2 times as bright as star D c. Star D appears 2 times as bright as star C d. Star D appears 4 times as bright as star C The speed of light in vacuum is _____________ • • • • a. 300,000 m/s b. 300, 000mph c. 300, 000 km/s d. 300, 000, 000 mph The light year is a unit of • • • • a. time b. distance c. speed d. energy How do the wavelength and frequency of red light compare to those of blue light • a. Red light has a longer wavelength and higher frequency than those of blue light • b. Red light has a longer wavelength and lower frequency than those of blue light • c. Red light has a shorter wavelength and higher frequency than those of blue light • d. Red light has a shorter wavelength and lower frequency than those of blue light