Transcript 8Oct_2014

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
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
– 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
• 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
Einstein’s Insights
• Albert Einstein started from the
assumption that the speed of light
was a constant, and worked out the
– 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
– 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
• 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 
• Note that as R decreases,
the escape velocity
• 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 
(the Schwarzschild radius) then
nothing can escape from its
gravitational force, including
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
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