Transcript relativity1

What would happen to the Earth if the Sun
collapsed to from a Black Hole?
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1. The Earth would be
sucked into the black
hole
2. The Earth would be
shot out into
interstellar space.
3. Nothing. The Earth
would continue to
orbit like before.
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Nothing! The Earth would keep
orbiting like before.
Old
surface of
Sun
r
• It is only in close to the Black Hole where
gravity becomes extremely strong.
• The escape velocity of an object at the old
surface of the Sun (dashed circle) would
still be 400 miles/second.
• The difference is that the mass is all
concentrated at the center and you can
get closer to the mass now.
• Inside the dashed circle the gravity will
continue to increase until you finally reach
the Event Horizon where the escape
velocity becomes 186,000 miles/second.
Here’s why.
• Imagine there was a hole at the center of
the Earth. If you were able to travel down
and be inside the hole at the center of the
Earth, what would it be like?
What would gravity be like if you were in a
hole at the center of the Earth?
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1. Extremely strong
because the distance
to the center would
be zero
2. You would be
weightless
3. Extremely strong
because the mass of
the Earth would be
pulling from all sides
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There would be no net gravity. You
would float weightlessly.
Gravity
What if you only went half way to the
center?
On this side
of the line
there isn’t
as much
mass, but it
is closer to
you.
On this side
of the line
there is more
mass but it is
farther away.
Gravity
Mass
interior to
your
position
• The mass that is exterior to your radius
exactly cancel out. Only the mass interior
to your radius matters. And there is less
and less mass interior to you as you get
closer to the center.
• When you finally reach the center the net
gravity is zero.
Gravity is strongest at the surface of the Earth.
1/r2
Same thing would happen if you traveled to the
center of the Sun.
• NOTE: THIS DOESN’T MEAN THAT THE PRESSURE
INSIDE THE SUN IS LOW. IT ONLY MEANS THAT IF
THERE WERE A TUNNEL TO THE CENTER OF THE
SUN THE GRAVITY WOULD DROP TO ZERO!
• But with the Black Hole you can get closer to the surface
and not have overlying layers cancelling out.
If the radius shrinks then the surface is much
closer to the center of mass.
New radius
Much high
gravity at
surface
So a black hole is NOT an interstellar
vacuum cleaner
• Black holes are usually seen in binary
systems, where the material from the one
star is being transferred to the black hole
• As the material spirals in (accretion disk)
the hot gas glows and indicates a black
hole is present.
• The mass of the black hole can be
measured using Kepler’s 3rd Law.
• But PLEASE note. The black hole doesn’t
do anything differently to the companion
star, that a normal star of the same mass
would do. Mass is transferred for two
reasons:
• 1) The star and black hole are in a close
orbit, and the star that made the black hole
already was stealing gas from the
companion.
• 2) The companion evolves into a giant or
supergiant star, and the surface gets close
to the black hole.
So a black hole is NOT an interstellar
vacuum cleaner
It is now time to find out what is really
going on.
• To really understand a black hole we have
to abandon Newton. Newton’s Laws work
fine under normal conditions, but for things
like black holes and the Big Bang,
Newton’s Laws fail.
• We can only really describe these extreme
events the Theory of Relativity. This was
developed by Albert Einstein from 1905 to
1915.
We will begin with a series of thought
experiments.
• You are in a plane traveling at 500 miles/hour.
The flight attendant brings you some food and
as you start to unwrap your fork, you
accidentally drop it.
• What will happen?
Please make your selection...
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1. The fork will fly to the
back of the plane at
500 MPH
2. The fork will drop at
your feet
3. The fork will fly to the
front of the plane at
500 MPH
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The fork falls at your feet.
• This is because the plane is traveling 500
MPH, you are traveling 500 MPH and the
fork is traveling 500 MPH.
• Since you are traveling the same speed as
the fork, relative to you, the fork isn’t
moving.
• How would someone on the ground view
this forking event?
What will the person on the ground see
when the fork is drop? What path will the
fork take for the person on the ground?
500 MPH
What path will the fork take for
someone on the ground?
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1. They will see the fork
fly forward at 500
MPH
2. They will see the fork
drop straight down
3. They will see the fork
fly backwards at 500
MPH
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The person on the ground sees the fork traveling
forward at 500 MPH and dropping down. But since
you are traveling 500 MPH the fork lands at your
feet.
500 MPH
• Imagine you are in a car, traveling down
the highway at 60 MPH.
What does it mean to say “traveling down
the highway at 60 MPH”?
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1. It means that the car
is moving 60 MPH
2. It means the car is
moving 60 MPH
relative to the Earth
3. It means the car is
moving 60 MPH
relative to other cars
on the road.
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Right now, sitting still in your seat, you are
moving at an enormous velocity, relative to
other locations in the universe.
Right now, sitting still in your seat, you are
moving at an enormous velocity, relative to
other locations in the universe.
Right now, sitting still in your seat, you are
moving at an enormous velocity, relative to
other locations in the universe.
• You are moving about 700 MPH because the
Earth is spinning on its axis.
• You are moving 72,000 MPH as the Earth orbits
the Sun
• You are moving 528,000 MPH as the Sun orbits
the Galaxy.
• Our Galaxy, the Milky Way, is moving toward the
Andromeda galaxy at about 240,000 MPH
• The Local Group of galaxies is falling into the
Virgo galaxy cluster at about 720,000 MPH
• Imagine you are in a car, traveling down
the highway at 60 MPH. (relative to the
ground.)
• A large semi-trailer passes you going 70
MPH relative to the ground.
• If you look over at the truck, how fast does
it look like the truck is going?
How fast does it look like the truck is
going?
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1. 10 MPH forward
2. 70 MPH forward
3. 10 MPH backward
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• Now the roles are reversed. You are in a
car traveling 70 MPH, and you pass a truck
which is going 60 MPH.
• What do you see?
How fast does the truck move this
time?
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1. 10 MPH forward
2. 70 MPH forward
3. 10 MPH backward
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• How about this?
• You are on the Earth and a friend flies
past the Earth in a spaceship which is
traveling 200,000 km/s. You decide to
signal your friend by shining a laser beam
past the ship. The laser beam is light, so it
travels at 300,000 km/s.
How fast does your friend see the laser
beam moving?
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1. 100,000 km/s
forward
2. 300,000 km/s
forward
3. 100,000 km/s
backward
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The Michelson-Morley Experiment
• The expectation is that the light traveling
with and against the motion of the Earth
around the Sun, should take more time to
complete the trip than the light beam
traveling perpendicular to the motion of the
Earth.
• This is what happens, for instance, when a
boat goes up and down stream in a river,
while a second boat goes across the river
and back. The crossing boat always wins.
• But not light!
The two light beams arrive exactly at the same
time.
• Light (in a vacuum) travels at the same speed,
300,000 km/s, no matter how you are moving.
• No matter what. Everyone in the entire universe
agrees that the speed of light is 300,000 km/s
• Think about this for a minute. What if semitrucks always traveled at 70 MPH, relative to
everyone. You stand next to the highway and
you see a car traveling at 60 MPH. And of
course you see the semi traveling at 70 MPH.
This is insane.
• If the person in the car is going 60 MPH
relative to the ground. And you see a
semi passing you at 70 MPH, then you
know the truck must be going
• 60 + 70 = 130 MPH relative to the ground.
• That’s what a person standing next to the
highway will measure. Not 70 MPH!
• Ask any highway patrol officer.
This is true for everything, EXCEPT
LIGHT.
• Light travels at the same speed for
everyone, regardless of your relative
motion.
How fast does your friend see the laser
beam moving?
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1. 100,000 km/s
forward
2. 300,000 km/s
forward
3. 100,000 km/s
backward
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Einstein’s two postulates of Special
Relativity (1905)
• 1) For objects moving with a constant
velocity (no accelerations) all motion is
relative.
• 2) The speed of light in a vacuum is
constant for all observers, no matter how
they are moving.
• Postulate 1, tells us that there is no such
thing as an absolute rest frame. There is
nowhere in the universe where you can
say, that thing is not moving. It has zero
velocity, absolutely. All you can measure
is relative motion.
• So, on a plane you do not feel like you are
moving. You look out the window and it
looks like the ground is scrolling past you
in the opposite direction that you are
sitting. Which is really moving? It is
impossible to say.
Consider a person on a train moving at 100 MPH
relative to the ground, and a second person on the
ground watching. Mr. Green throws the ball up in
the air.
100 MPH
Who will see the ball travel a greater
distance?
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1. Mr. Green (on train)
2. Mr. Red (on ground)
3. Both measure the
same distance
traveled.
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Mr. Green sees the ball move on the green
path and Mr. Red sees the ball move on the
red path
• Both Mr. Green and Mr. Red agree on the
time that the ball is in the air.
• But Mr. Green sees the ball travel a much
small distance than Mr. Red.
• This is because Mr. Green sees the ball
moving only in the up-down direction. Mr.
Red sees the ball moving up-down and
also to the right at 100 MPH.
• This means the measured speed of the
ball is much larger for Mr. Red than it is for
Mr. Green.
•
•
•
•
•
•
•
Here is how speed is measured.
Velocity = distance/time (example miles/hour)
V = D/t
We can rearrange this equation to read.
D = V*t
Both Red and Green agree on the flight time, t
Red sees a bigger velocity, vR > vG
• So this means that DR > DG
• That’s the way our normal world works.
But what happens when the ball is replaced by
light and the train is now traveling at nearly the
speed of light, c.
mirrors
V~c
Mr. Green sees the light follow the green
path and Mr. Red sees the light follow the
red path
• Clearly, Mr. Red sees the light move a
greater distance than Mr. Green.
• BUT… Here in lies the problem.
• This is light. Both Mr. Green and Mr. Red
agree that the light is moving at
c = 300,000 km/s
So,
DR > DG but vR = vG = c
DR/t = DG/t
How can this be?
How can this be?
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1. They have to
measure a different
velocity for light
2. The distance traveled
must be the same
3. The flight time must
be different.
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The Death of High Mass Stars
Quiz #8
• On the H-R diagram, a high mass star that is evolving
off the main sequence will become redder in color
and have and a constant luminosity. Write out the
equation for luminosity in terms of surface
temperature and radius. Then discuss which
parameter is primarily controlling the luminosity as
the star evolves.