1. (will not be included in the 1st exam)
READING
Unit 26, Unit 27
(will not be included in the 1st exam) 

2. Most important is to prepare for the exam! This is your main
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

3. In other words, velocities add.
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.

4. 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.

5. 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!

6. The amount of contraction was described by 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!

7. Moving objects reduce their length in the direction of motion
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

8. Time dilation and length contraction depend on the observer!
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!

9. 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…

10. 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.

11. The Escape Velocity Limit: Application to Black holes
Also recall that nothing can travel faster than the speed of light, c, or 3108 m/s
If a stellar core is compressed so much that its radius is smaller than
(the Schwarzschild radius) then nothing can escape from its gravitational force, including light!
Recall that the velocity necessary to avoid being gravitationally drawn back from an object (the escape velocity) is:
Note that as R decreases, the escape velocity increases

12. 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

13. a. The luminosity of the Sun
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

14. a. Star C appears 4 times as bright as star D
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

15. 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

16. The light year is a unit of
a. time
b. distance
c. speed
d. energy

17. 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