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What would happen to the Earth if the Sun collapsed to from a Black Hole?

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What would happen to the Earth if the Sun collapsed to from a Black Hole?

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- The Earth would be sucked into the black hole
- The Earth would be shot out into interstellar space.
- Nothing. The Earth would continue to orbit like before.

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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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- Extremely strong because the distance to the center would be zero
- You would be weightless
- 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.

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

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.

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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- The fork will fly to the back of the plane at 500 MPH
- The fork will drop at your feet
- 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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- They will see the fork fly forward at 500 MPH
- They will see the fork drop straight down
- 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

What does it mean to say “traveling down the highway at 60 MPH”?

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- It means that the car is moving 60 MPH
- It means the car is moving 60 MPH relative to the Earth
- 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?

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?

- 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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- 100,000 km/s forward
- 300,000 km/s forward
- 100,000 km/s backward

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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 semi-trucks 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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- 100,000 km/s forward
- 300,000 km/s forward
- 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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- Mr. Green (on train)
- Mr. Red (on ground)
- 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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- They have to measure a different velocity for light
- The distance traveled must be the same
- The flight time must be different.

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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.

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