January 07, 2014 01/07/2014
Astromoical images are interesting because for some of the galaxies we see the light has taken 9 billion
years to reach us
People thought that 100% of the universe were stars, galaxies and dust (1960)
In the 30s he looked at a cluster of galaxies
He looked at those galaxies, how big they were and how they moved
They move in response to each other’s gravity
He used math to figure out how fast they were moving depending on their size
But when he measured he found that the rate they were moving at were much faster
2 reasons: calculations were wrong (the only assumption he used was the theory of gravity which was
Much of the galaxy cannot be seen with the telescopes we build
Most of what is in the galaxy cluster is invisible
Zwicky’s colleages though his “missing mass” idea was a bit nutty
He wasn’t really happy about that
His missing mass idea was shelved
Vera Rubin: ▯ Radio telescope
Looked at single galaxies and how fast clouds of gas were spinning around in those galaxies
The farther you are from the centre of galaxy, the slower you will orbit – Kepler’s Third Law
BUT this is not true for other galaxies In general, the things in the centre of the galaxy orbit slower, it then reaches a plateau
So either the law of gravity was wrong (not likely)
Or upto 90% of the masses of the galaxies was invisible
Invisible regardless of light/telescope
"In a spiral galaxy, the ratio of darktolight matter is about a factor of ten. That's probably a good number
for the ratio of our ignorancetoknowledge. We're out of kindergarten, but only in about third grade.
"Universe– 90% dark matter (it has gravity) , 10% stars..
Matter is that which produces gravity
Universe : 70% Dark energy, 27% Dark matter, 5% stars, galaxies
We can’t find 95% of the universe and even the 5% we can find, stuff is still missing
We can’t see 97.5%
49% luminating (light emitting) matter
To paraphrase the great physicist
We know that it isn’t likely that the law of gravity is wrong because this law has worked for many many
years and we use it successfully
There isn’t any other independent evidence to suggest the existence of dark energy/matter – and this is
why some people believe it’s the law of gravity that is incorrect
Dark matter: pulls things together
Dark energy: pushes things apart
We don’t know how big the universe is BUT we know how big the observable universe is
If the observable universe was a tank, it would hold atleast 340,000, 000, 000, 000, 000, 000, 000, 000,
000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000 liters of
water Jan 09, 2014 01/07/2014
You fall asleep on a train and when you wake up you see another train. Jan 09, 2014 01/07/2014
One of the trains is moving (yours or the other). How do you tell which one is moving?
Force against your body (when the train is starting/stopping/changing speed)
Watch for a fixed point outside the train
What if there’s no vibration, the train is moving at a constant speed and the windows are blacked out
Roll a ball and see which way it rolls but the earth is moving and balls roll staright
Airplane is travelling at 900km/h. You roll a ball up the aisle of the plane and it rolls at 10 km/hr
Clicker qs: How fast does the person on the plane see the ball moving? 10km/h
Clicker qs How fast does the person on the ground see the ball moving? 10km/h – this is relative to the floor
of the plane OR 910 km/h – this is relative to the ground
Who is correct?
There is no one correct answer
We can only measure motion relative to a given frame of reference
All motion must be described relative to something
I am moving relative to the people in the floor Jan 09, 2014 01/07/2014
Repeat the experiment with light instead of a ball
Airplane is travelling at 900km/h. Light is moving at speed ©. Someone shone a flashlight up the aisle
Clicker: If the beam of the light behaved the same way as the ball. What would a person on the ground
measure the speed to be? ©+ 900km/h
IT cannot be 900km/h because otherwise the light is moving at the same speed of the plane (that would be
weird – it wouldn’t shine down the aisle)
But reality doesn’t work that way – the answer is © in real life
No matter how the experiment is done, all observers measure the same speed of light.
Regardless of the movement of the plane
As long as you are measuring light, everyone will measure the same speed
With the ball the person on the plane and the person on the ground disagree at the speed of the ball
But with the light the movement of the person/source of light is irrelevant
The speed of the ball is different in different “frames of reference”.
The speed of light is invariant.
The speed of light is the same in all frames of reference. (any two observers in the same setting (vacuum)
The speed of light changes in water but ALL the people in the water will perceive the same speed
Tenets of Special Relativity
1. We can only measure speeds of objects relative to one another. (The laws of physics apply equally in all
2. The speed of light is invariant. Jan 09, 2014 01/07/2014
These two facts undo our thoughts about space and time
Jackie is moving away from you at 0.9©. You shine a beam of light at her (at speed ©), How fast does
Jackie measure the light to be moving? ©
You are moving toward Jackie at speed 0.9©. You shine a beam if light toward her. What speed does she
measure it to be moving? ©
This observed fact of nature has bizarre consequences.
Let’s look at motion on a train, from the perspective of two different observers.
Person on the train says the ball went up 1 m and came down 1 m in 1 s, for a speed of 2 m/s.
Person on the tracks (not moving with the train) says that the ball went up 2 m and came down 2 m in 1s,
for a speed of 4 m/s.
You were at point A when you threw it but as the train moved, you moved so you were at point B when you
The person saw the ball move up and down AND a little forward (so there more speed)
Clicker: What do the two observes agree on the ball’s motion? The time between throwing and catching
1. Again, what happens if we do this with light?
Clicker: If we repeat the experiment with a laser beam bouncing off a mirror on the roof of the train, what do
the two observers have to agree on? The speed of the light ray
Frame reference inside the train
Distance = time X speed
Time=distance/speed Jan 09, 2014 01/07/2014
Time = distance/©
Time = (1m + 1m)/©
Time 6.7 nanosec
Frame reference outside the train
Time = (2m + 2m)/ ©
We must ALL agree on the speed of light which allows us to disagree about the time
Because two observers moving relative to one another must agree about the speed of light, they must
disagree about the time between events!
Time literally flows at different rates for any two people in motion relative to one another!
This is called time dilation.
Observers in motion relative to one another also disagree about their lengths.
IF you have a barn that is 10m and if you have a ladder that is 20m long, if you move very quickly you can
fit the ladder into the barn but for a very short time
This is called length contraction.
You have two clocks that are in sync. You put one on a train and one on the floor. When you come back and
check more time will have passed on the clock on the floor/ Tutorial, Jan 13 01/07/2014
Alice is moving towards you at 50km/h. You throw a baseball in her direction at 50km/h. What does she see
the ball doing?
Moving towards her at 100km/h
Suppose that an object is moving with constant acceleration. What best describes its motion with respect to
In equal times its speed changes by equal amounts
What is the difference between speed, velocity and acceleration? If an object is moving with constant
velocity, can you say anything about its acceleration?
Speed: how fast something is going
Acceleration: change in velocity/time
Velocity: change in speed and direction
There is no acceleration
Feng is travelling away from you at 99% the speed of light when he turns on his flashlight. How fast will the
beam of light be going when it reaches you?
Speed of light is constant so ©
What is a “frame of reference”? When do two people share the same frame of reference? When do two
people share different frames of reference?
Speed of objects relative to one another
Suppose your friend is moving by you at some constant speed. Explain why your friend can equally say that
she is stationary and you are moving by her.
Depend on your frame of reference Tutorial, Jan 13 01/07/2014
In relativity, two people share the same frame of reference, if and only if:
They are not moving relative to one another (they don’t have to be stationary)
Two key absolutes:
The laws of physics are the same in references that are not accelerating (they can be moving but are not
The speed of light is invariant
Throw a bean bag up and down. The path of the bean bag is up and down.
Accoridng to the person throwing the bean bag it is going up and down.
The two paths agree
If the person tosses the bean bag up and down and walks forward. We see it moving forward AND going up
But the person throwing it only sees it going up and down. The two paths do not agree.
The person throwing it (Path A)
The path we see (Path B)
Path B has the greatest distance travelled
Assuming we don’t have a clock we need distance and velocity to figure out how much time has passed
(time = distance/speed)
If you ran at the same speed beside the person throwing it you would see it going up and down (same)
The person running and the stationary person would agree about how much time the bean bag has spent in
the air Tutorial, Jan 13 01/07/2014
If the bean bag had to travel at the same speed (light) the stationary person and the person running which
path would take more time:
Path B (longer distance would take more time)
Time runs more slowly in the reference frame of anyone moving relative to you
The faster the other reference is moving, the more slowly time passes within it
Suppose Laila is on a space ship moving past you at a constant speed close to the speed of light. How
would you view time (a clock) on Laila’s spaceship as it goes by?
Laila’s clock is ticking slower than yours (the faster the other frame of reference is moving, the more slowly
time passes within it for us)
For her, her own time is the same for herself
Suppose Laila is on a space ship moving past you at a constant speed close to the speed of light. What
would Laila see when she looks at your clock.
Your clock is ticking slower than Laila’s (in Laila’s frame of reference she is stationary and you are moving)
Astronauts on the International Space station are in orbit around the Earth, travelling at the speed of
7,660m per second. From our perspective here on Earth, how are the astronaut’s bodies again?
The astronauts are aging more slowly than us January 14, 2014 01/07/2014
The speed of light is invariant
The laws of nature are the same for everybody regardless how they are moving relative to each other
Time literally flows at different rates for any two people in motion relative to one another.
Moving clocks run slow
Observers in motion relative to one another also disagree about their lengths
If someone is moving, you will see them shorter in the direction they are moving relative to you
The faster an object is moving relative to you, thshorter (in its direction of motion) you will measure it to
Twin Paradox (not really a paradox)
Imagine you get in a spaceship and travel to the star Vega at 99.9% of the speed of light
Distance from Earth to Vega 25 light years
Light year is a measurement of distance = distance light travels in one year
Light year is NOT a measurement of time
There is nothing a light year from the Earth – the Sun is a light minute away from the Earth
Stars are a few light years away from each other
One light year is in the middle of our solar system and another one January 14, 2014 01/07/2014
1 light year = 9.5 trillion km
Clicker: According to special relativity, if someone on Earth measures Vega to be 25 light years away, you in
your ship headed to Vega at 0.999c will measure the distance to be
Less than 25 light years (compared the person not moving relative to Vega)
In relativity, when someone is moving, they are shorter in the direction of travel as perceived by a person
who is not moving (relative to them)
The spaceship has shrunk in our perception
But the person in the spaceship doesn’t see themselves as short
Clicker: The person on Earth sees you travel 25 light years at 0.99c. They think your trip takes
A little more than 25 years
Nothing with mass can go the speed of light
Clicker: You measure the distance between Earth and Vega as only 1 light year. Thus, for you the trip to
Vega takes only:
About one year
If you were going much faster (than 0.999c) the answer would be less than one year
You can’t use this to go into the past because let’s say you do something that affects your existence – who
was it that went back
But you can go into the future
If you travelled to the center of our galaxy and back at the 99.999999% of the speed of light, you would age
8 days but the Earth would’ve aged 50,000 years
If you reach the speed of light it’s like time stops January 14, 2014 01/07/2014
If one person takes the subway regularly, vs one person stays at home the person in the subway ages more
slowly but this difference isn’t measureable
Everything in the universe can be described in terms of 4 forces
Four fundamental forces (everything that happens in the universe is due to these forces
Strong nuclear force
The strongest force in the world
Holds atomic nuclei together because two protons are both positive; they should repel but this force holds
Every force (apart from gravity) that is relevant to us is a form of electromagnetism
Makes atoms cling to each other
It’s range is infinite
Ex. friction, the force holding the tables together, etc.
Weak nuclear force
Breaks atoms together
Makes masses attract to one another
Gravity barely exits and yet it dominates
It’s range is infinite
Clicker: Do stars on one side of our galaxy feel gravity from stars on the other side?
The range of gravity is infinite
Every atom in the universe is feeling the gravity January 16, 2014 01/07/2014
Term Project January 16, 2014 01/07/2014
A common misconception people have about astronomy
Go deep into that misconception
What’s wrong with it and how can you fix it
Misconception: black holes are cosmic vacuum cleaners
Misconception: The sun is a planet
Find a way to resolve it the misconception without just telling them then answer
Has to be concise
Get right to the heart of what is wrong with the misconception
2% bonus on final grade
All of nature is shaped by four forces – of those gravity is the most weak force yet it is the most important in
astronomy because it acts over an infinite distance
Every star/atom feels the gravity of every other star/atom
Gravity does not cancel out (it only has a positive charge)
More mass = more gravity
Gravity is not very well understood
Clicker: Imagine a universe which is empty except for you and a baseball. If we ignore gravity, what will
ultimately happen to the baseball January 16, 2014 01/07/2014
IT will keep moving forever at a constant speed
Newton’s First Law (Law of Inertia)
Objects move with a constant speed and direction unless
Clicker: The moment the baseball loses contact with your hand, it stops :
Accelerating, changing speed, feeling a force
A force by your hand produces acceleration, acceleration is change of speed
Newton’s 2 Law:
Force = mass X acceleration
Clicker: After you throw the ball, what will happen to you?
You will move in the direction opposite to the ball’s direction motion, but slower than the ball
Human has a bigger mass than the ball so the force the ball exerts on the human has less of an effect –
human moves slower
Newton’s 3 Law
If one body exerts a force on another body, the other body will exert a force of equal strength but opposite
Every action has an equal and opposite reaction
What keeps the moon in orbit around the Earth?
The force of gravity is exerted on both the earth and moon January 16, 2014 01/07/2014
Clicker If we could shut off gravity, what path would the moon follow?
Going in a straight line (upwards/forward)
It is the Earth’s gravity that makes it turn into a circle
The moon is already moving upwards
For it to go ▯ there would have to be another force
Newton’s Law of Gravity
Gravity is a force that depends on the masses of the two objects/ the square of the distances between them
Clicker: If the distances between two stars triples, the force of gravity between them:
Decreases by a factor of 9
From 1687 until 1916, Newton’s description of gravity held sway
Einstein question’s Newton’s logic
Although we agree with Einstein, we agree neither was completely correct
How do you know if you are moving?
You can only tell if you are moving relative to something (Einstein)
He wanted to know that how can you know for sure that you are feeling a force of gravity
Feel our own weight? (we feel our weight on our feet because the floor is pushing up – it’s a consequence
of gravity but it’s not gravity) January 16, 2014 01/07/2014
Jump? (you come back down)
Clicker: Imagine you’re in a spaceship, far from any object with mass (no gravity). The spaceship
accelerates upwards. You let go of a baseball at shoulder height. What happens to the ball?
You do feel something when you accelerate (you need force to accelerate so you feel pressed against your
It falls towards your feet
TO make it hover and accelerate along the ship there needs to be a force to make the ball move with the
Doesn’t matter if the ball is inside or outside the ship
But if there is no gravity what is pulling the ball down
The Equivalence Principle
You have no way of knowing if the force of gravity is acting on something
Ex. you are sitting in your living room and your cup falls. You have no way of knowing if its because of
gravity or the room is being pulled up
In a small area of space the effects of acceleration is indistinguishable from the force of gravity or if
someone is pulling the room up
No experiment can distinguish a gravitational force from a corresponding acceleration of the whole
The equivalence of acceleration and gravity has profound consequences
Jackie falling down while you are being pulled up are indistinguishable
General relativity does away with gravity and replaces it with curved spacetime
Anytime with mass bends space and time (more mass = more bending)
Objects follow the straightest possible path through curved spacetime January 16, 2014 01/07/2014
If you send two people to walk on the surface of the Earth in space they would meet up; we would say it’s
because of the Earth’s curvature. Not because of gravity.
IF satellites do the same thing we would say it’s because of gravity
No gravity just bent space time
Clicker: If everything follows a curved spacetime, which of the following would you expect from general
relativity, but not from Newton’s theory of gravity.
Light bends as it approaches massive objects
Gravity and space time curvature is not the same thing space time curvature is Einstein’s alternative
to gravity. Tutorial January 21, 2014 01/07/2014
Clicker : The red ball is sitting in an accelerating train. Ignoring the effects of friction, how does the ball
react to the train’s acceleration? Relative to the train floor, the ball
Accelerates right (because the train is moving to the left)
Clicker : Madhula is feeling weightless. Which of the following is the most correct? She is in free due to
Moving at constant velocity in an empty universe with no gravity
Clicker : Which escape velocity below is the highest? The escape velocity
On the surface of the Earth
Clicker: Ike just passed the event horizon of a black hole. At the moment he passes through he will:
The event horizon of a black hole is not a physical boundary and there will be no sudden change due to
crossing the event horizon
Replaces gravity with curved spacetime
What does “escape speed” of Earth mean? What determines the escape speed of the Earth at its surface?
The escape speed is the speed an object needs to go to get out of the Earth’s orbit
Determined by mass of the planet
Can the escape speed of a body be larger than the speed of light? If so, what can from such a body?
Yes (blackhole) – blackholes can have a higher than light escape speed
Escape speed is determined by mass and gravitational pull
The higher the gravitational force, the faster it needs to go to escape Tutorial January 21, 2014 01/07/2014
What is the “Schwarzchild radius” of a black hole? What is special about the Schwarzchild radius?
The distance from the centre to the event horizon
The closer you are to the event horizon, the faster you need to travel faster (than the speed of light to
What is the “event horizon” of a black hole? What is special about the event horizon? What is physically
located at the event horizon?
It is not physically located anywhere
The closer you are to the event horizon, the faster you need to travel faster (than the speed of light to
Black holes are dangerous and suck up matter?
They can suck up matter that is close (not sure how close)
But something can orbit it
If you are at the event horizon and you are going at the speed of light. You will not get sucked in, you’ll be in
orbit – you won’t be able to enter, you will drop back outside
If you take the sun and replace a blackhole with the same mass the Earth WILL NOT get sucked in –
people will die because no sun but we won’t get sucked in
The force of gravity depends on mass
As long as the mass doesn’t change, Earth’s orbit does not change
1. Do the following situations feel different?
A) You are on Earth feeling 9.8m/s acceleration
B) you are on a spaceship that is accelerating at 9.8m/s 2
No Tutorial January 21, 2014 01/07/2014
2. Do the following feel different?
A) You are in free fall towards the Earth (no physical object pushing against you except gravity; you feel
B) You are travelling at a constant velocity in an empty universe with nothing in it
No they feel the same
3. How would Newton explain why a satellite is orbiting Earth?
The satellite is moving less than the escape speed so the gravitational force is making it orbit the Earth
The satellite is moving and the gravity makes it turn
4. How would Einstein explain why a satellite is orbiting Earth?
Curved spacetime causes the satellite to turn
The curve changes the direction
The curve is created by mass
Gravity depends on the mass and distance – greater mass = stronger gravity
Mercury feels the gravity of the sun more than Pluto even though the range of gravity is infinite, the
strength of the pull decreases with distance January 21, 2014 01/07/2014
General relativity replaces the idea of gravity – it gives the same prediction
Objects influence one another by bending space and time (rubber sheet)
Anything travelling through the space has to alter its path due to the bent space
Clicker – If everything follows a curved spacetime, which of the following would you expect from general
relativity, but not from Newton’s theory of gravity.
Light bends as it passes near massive object
Bending of light due to bent spacetime – gravitational lensing
The blue galaxy is behind the yellow but the light of the blue galaxy is coming towards us and encounters
the bent space of the yellow galaxy and it bends around the yellow galaxy – this enables us to see it
The yellow galaxy is focusing the light of the blue galaxy towards us
General relativity enables this
Dark matter has matter therefore it curves space
Anything with mass curves space
We can measure dark matter
The blue galaxy light bends but the mass of the yellow galaxy is not enough to bend it in the way it does
therefore dark matter must be there to distort it in that way
If I throw a water bottle into the air it won’t orbit It’ll hit the Earth. However, if you throw the water bottle fast
enough (where the ground is not there) it will orbit elipse
At vorbite ball “misses” the far side of Earth and complete an orbit
The slowest speed in which you can throw it so that it orbits the Earth – minimum speed (depends on the
height you throw it from)
If we just throw it faster it will miss the Earth by an equal distance on all sides (it becomes a circle where the
Earth is exactly in the centre) January 21, 2014 01/07/2014
If you throw it really really fast you can escape Earth’s gravitational pull (it won’t make an orbit) – escape
Minimum speed to orbit : v=v orbit
Elliptical orbits :orbitv black hole
An object with an escape speed of © is a black hole
A black hole bends spacetime infinitely – you’ve bent space as much as it can bend or more
Anything that that such a density that its escape speed has reached the speed of light
You can go in but never come back out
If you fall into a blackhole, the person outside would think your time has stopped – it wouldn’t seem like that
to you it has stopped
No one knows what happens inside a blackhole
At the end of a black hole, space itself is whirling into the blackhole at the speed of light
A black hole has nothing significant in it
It just has what it was formed from
People say at the centre of the blackhole there is something called “singularity” the density is infinite – but
we don’t really know what’s in there
There is no physical boundary
The sphere is a the point where the escape speed = © (the speed of light event horizon
Inside the circle (event horizon) the escape speed is the speed of light: escape ©
Outside the escape speed is less than © : v escape
There is nothing worse than the singular the event horizon is what it keeps us away from it
There are theories
At the event horizon of a black hole © =v escape January 21, 2014 01/07/2014
Clicker: If you are just outside the event horizon of a black hole, can you get away from the hole?
Yes, if you move quickly enough
The radius of the event horizon (i.e the size of the black hole) is called the
Schwarzschild radius: R SchwarzchildM/c 2
The distance from the singularity to the event horizon
Clicker : If we add mass to a black hole, the black hole will:
It gets bigger
Clicker : If we replaced the Sun with a black hole having exactly the same mass as the Sun, what would
happen to the Earth?
Earth would continue to orbit as normal, but it would get very cold
If it has the same mass, the curvature would be the same January 23, 2014 01/07/2014
One single star is able to output the same amount of light as the entire solar system
Supernovae is probably the second most biggest explosion
There is so much light you can see it as a flicker of light from the other side of the observable universe
This galaxy is 12 million light years away, so technically this star blew up 12 million years ago but we just
see it today
Clicker: Which of the following would allow us to locate a black hole today?
We could look for