Transcript Lecture 1

Black holes
Introduction to astronomy and physics
Astronomy - history
• Astronomy is among the oldest “sciences”,
if not the oldest:
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Stars were always visible and became important for
navigation
Phases of the moon were important for tides,
calendars
Seasons were important for agriculture etc.
Eclipses were seen as important omens
Astronomy and religion were long intertwined
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Classical Physics
Anything before 1905 can be considered
“Classical”
Classical means “no quantum mechanics” and
“no relativity”
Physics as a science could be tracked back to
the greeks
★Archimedes (buoyancy - things float)
★Atoms (things cannot be made of nothing)
★Geometry
★“Cosmology” (science of entire universe)
Greek insights
• The first “realistic” cosmology was derived by
the greeks
• Based on geometry:
★Circumference of earth from distance to the horizon
★Solar eclipses: size of the moon (1/4 earth)
⇒Distance to the moon (60 earth radii)
★Distance of the sun (much farther than moon)
⇒Size of the sun (much bigger than earth)
Earth’s radius - the
horizon
• Greeks were sailors
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They knew the earth
was not flat:
• You could sail
beyond the horizon
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They knew
trigonometry
They measured the
distance to the horizon
⇒Earth’s radius
The size of the moon
• Size of the moon: Lunar and solar
eclipses (earth’s shadow is bigger than
the moon’s)
• Lunar phases: the sun is about 500
times farther than the moon
Greek cosmology
• Sun and moon look like they are the same
size
• But the sun is 500 times more distant
• It must be 500 times bigger than the moon
• It must be 100 times bigger than earth
Greek
cosmology
• Sun is bigger than the earth
⇒Earth is unlikely to be center of
universe
⇒Earth must be orbiting around the sun,
not the other way around
• If earth is nothing special, maybe the
sun isn’t either
⇒Maybe other stars are just like our
sun?
Out of the dark
ages...
• Things were forgotten until
Copernicus
• First real modern
breakthrough in astronomy:
Tycho Brahe and Johannes
Kepler
★Precise measurements
⇒A revision of theory
★This is the scientific method
Science - what is and what isn’t
• Makes testable predictions
• If a prediction from a hypothesis is disproven,
the hypothesis must be abandoned (it can be
modified)
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Experiments must be repeatable
Must not add features that are not required (this
is called Okham’s razor)
★Physics and astronomy are science
★Evolution is science
A word on Astrology
• Example (Hemisphere’s magazine)
•Pisces (Feb 19 - March 20):
•“You must be doing something right, because your
financial picture looks rosy. Physically speaking,
there’s no need to pretend you’re a superhero. Pace
yourself. Around midmonth, lend an ear to those
around you; allow ample time for those thoughts to
seep into you subconsious”
• This fails on all grounds
Some important
things
• Physics measures things
• We measure distance, times,
temperatures
• We use those measurements to infer
other things:
★velocities (distance per time - how far can I
travel in one hour?)
★accelerations (velocity per time - how
much faster will I be traveling in an hour?)
Kepler’s laws (1571-1630)
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Planets orbit the sun on ellipses
Planets further out take longer (cube of
the radius goes like the square of the
time)
There is a relationship between how far
away the planet is to how fast it is
moving.
Saturn
Jupiter
Modern physics:
• Newton could be credited with the
invention of modern physics
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He invented calculus (along with Leibniz),
which is critical to almost all of physics
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He formulated the first real theory of
gravity
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He invented mechanics (Newton’s laws)
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He could explain Kepler’s laws
Gallileo (1564-1642):
• Gravity is a force
• Forces accelerate objects
• Gravity accelerates objects
• It accelerates all objects at the same
rate!
Newton’s laws
• Newtons first law
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An object in motion stays in constant
motion unless acted upon by a force
Newton’s laws
• Newtons second law
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A force accelerates an object and the
acceleration is proportional to the force:
F=m*a
The constant m is the mass of the
object
Force
Newton’s laws
• Newtons third law
• An accelerated object exerts a force
on the thing that is accelerating it with
equal strength but opposite direction
Force 1 Force 2
Newton’s laws
• Any object with mass M
attracts any
other object with mass M2, with a force
that is
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proportional to the masses (the heavier an
object, the more attractive it is)
proportional to the inverse square of the
distance (the further away you are, the
less pull there is from the object)
2M
M
1 3
1 1
Velocities
• Consider a train with some velocity v
Velocities
• Consider a train with some velocity v
• Condider a car at rest on the train
Velocities
• Consider a train with some velocity v
• Consider a car atop the train moving
backwards with the same velocity -v
Velocities
• Consider a train with some velocity v
• Consider a car atop the train moving
forward with the same velocity v
• It moves at twice the velocity, of course
Velocities
• Newton and Gallileo tell us:
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We are allowed to add velocities
together
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The car is moving twice as fast as the
train
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If the train is moving at the speed of
light, the car is moving at twice the
speed of light
Classical black holes
Escape speed
Newton predicts:
massive objects have
“escape speed”
If you throw a ball up, it
will usually fall back
down...
But: Rockets can
escape earth’s gravity
Question: How fast do
you have to throw the
ball for it not to fall
Escape speed
The escape speed from an object is
proportional to square root of the planet mass
inversely proportional to square root of planet
radius
e.g., moon: escape speed is 5,800 mph
e.g., sun: escape speed is 1,400,000 mph
Classical black holes
Rømer (1676):
Used Jupiter’s moons as a clock
Speed of light is finite (300,000 km/s)
Newton:
Light is a particle
presumption: it has mass
Classical black holes
Laplace (1795):
Make an object massive enough and
small enough: escape speed faster than
the speed of light
⇒ Light should not be able to escape
⇒ object would be completely dark.
⇒ It would be a “black hole”
No classical black holes:
A particle faster than the speed of light could
escape a “classical black hole”, so it would not be
all-consuming.
Maxwell (1864):
Light is an electro-magnetic wave
Has no mass
No classical black hole
Special
Relativity
• Maxwell’s equations
describe light as a wave
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Waves propagate at some
velocity
⇒ So: Light waves propagate
at the speed of light
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Symbol: c
c = 300000 km/s =
670000000 mph
Light waves
A moving light wave
• Newton and Gallileo:
• Consider a light wave moving with
velocity c
A moving light wave
• Newton and Gallileo:
• Consider a light wave moving with
velocity c
• Consider a car moving with velocity v
A moving light wave
• Newton and Gallileo:
• Consider a light wave moving with
velocity c
• Consider a car moving with velocity v
• To the car, the light is moving at velocity c
-v
Michelson-Morley
1887
Michelson-Morley
1887
• The earth is moving
around the sun with
velocity v
• We should be able to
measure the speed of
light as c-v
• Experiment: Not so!
• Conclusion: The
speed of light is
constant and always c
Maxwell vs. Newton
• Maxwell’s theory of electro-magnetism
agrees with constant, uniform c
• Newton/Gallieo theory of mechanics
does not agree with constant, uniform c