#### 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.
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
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 3108 m/s
• If a stellar core is compressed
so much that its radius is
smaller than
2G  M
RS 
c2
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
```