Download Black Holes

Gravity
(or, lies my physics class told me
about physical contants)
What physics 101 says
All objects falling toward the Earth have the same acceleration (free-fall) (neglecting air
resistance).
Weight (w) = mass x gravity.
Physics says: g = 9.81 N/kg = 9.81 m/s2 (a constant).
A good approximation and O.K. for physics problems, but
NOOOOOOOO!
What geologists say
Gravity varies from location to location on the Earth!
• Varies inversely with the square of distance from the center of the Earth (objects
weigh slightly less at higher altitudes than at sea level) (goes as r2)
• Varies with latitude (Earth is not precisely spherical; is flattened at the poles)
• Varies with subsurface geology
•Varies with the earths rotational speed
6-1 Newton’s Law of Universal Gravitation
Using calculus, you can show:
Particle outside a thin spherical shell: gravitational
force is the same as if all mass were at center of
shell
Particle inside a thin spherical shell: gravitational
force is zero
Can model a sphere as a series of thin shells;
outside any spherically symmetric mass,
gravitational force acts as though all mass is at
center of sphere
Watch the video that explains
acceleration inside the Earth.
Inside earth lecture
Video Lecture variations
of g due to rotation of
the Earth or variations
from Latitude.
Sorry, it’s the best I
could find.
Black Holes
Black Holes
The mass of a neutron star cannot exceed about 3
solar masses. If a core remnant is more massive than
that, nothing will stop its collapse, and it will become
smaller and smaller and denser and denser.
Eventually the gravitational force is so intense that
even light cannot escape. The remnant has become a
black hole.
Gravitational Lensing
Black Holes
• Black Hole and Neutron Star Dance
• Black Hole Geometry
Black Holes
The radius at which the escape speed from the black
hole equals the speed of light is called the
Schwarzschild radius.
Earth’s Schwarzschild radius is about a centimeter;
the Sun’s is about 3 km.
Once the black hole has collapsed, the
Schwarzschild radius takes on another meaning – it
is the event horizon. Nothing within the event
horizon can escape the black hole.
Escape Velocity
v  mass
radius
Earth shrunk down to 1 cm would give the correct proportions to prevent light
from escaping.
 = 300,000 km/s = c
Schwarzchild radius ~ 3 km x solar masses
Einstein’s Theories of Relativity
Special relativity:
1. The speed of light is the maximum possible speed, and it
is always measured to have the same value by all observers.
Einstein’s Theories of Relativity
2. There is no absolute frame of reference, and no
absolute state of rest. No preferred observer.
3. Space and time are not independent, but are
unified as spacetime.
“Spacetime tells matter how to move, and matter
tells Spacetime how to curve.”
Einstein’s Theories of Relativity
Special Relativity
As objects move faster
1.
2.
3.
Time dilation
Increase in Mass
Length contraction
Einstein’s Theories of Relativity
General relativity:
It is impossible to
tell, from within a
closed system,
whether one is in a
gravitational field,
or accelerating.
Einstein’s Theories of Relativity
Matter tends to warp
Spacetime, and in doing so
redefines straight lines
(the path a light beam
would take).
A black hole occurs when
the “indentation” caused
by the mass of the hole
becomes infinitely deep.
Question 1
The force of gravity can pull
on
a) a beam of light.
b) a massive object.
c) neutrinos.
d) antimatter.
e) All of the above are correct.
Question 1
The force of gravity can pull
on
a) a beam of light.
b) a massive object.
c) neutrinos.
d) antimatter.
e) All of the above are correct.
Gravity is described by general
relativity as a bending of space,
and all particles, including
photons, move through warped
space along curved paths.
Space Travel Near Black Holes
The gravitational effects of a black hole are
unnoticeable outside of a few Schwarzschild radii –
black holes do not “suck in” material any more than
an extended mass would.
Space Travel Near Black Holes
Matter encountering a black hole will experience
enormous tidal
forces that will both
heat it enough to
radiate, and tear it
apart.
Space Travel Near Black Holes
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshift as
it gets closer, so that time appears to be going more and
more slowly as it approaches the event horizon.
This is called a gravitational redshift – it is not due to
motion, but to the large gravitational fields present.
The probe itself, however, does not experience any such
shifts; time would appear normal to anyone inside.
Question 2
The event horizon of a
black hole
a) is the point where X rays emerge.
b) is the physical surface of the hole.
c) defines the outer edge of an accretion disk.
d) is measured by the Schwarzschild radius.
e) extends for millions of miles into space.
Question 2
The event horizon of a
black hole
a) is the point where X rays emerge.
b) is the physical surface of the hole.
c) defines the outer edge of an accretion disk.
d) is measured by the Schwarzschild radius.
e) extends for millions of miles into space.
The event horizon is the surface of an
imaginary sphere around a collapsed object
inside of which nothing, including light, can
escape.
Space Travel Near Black Holes
Similarly, a photon
escaping from the
vicinity of a black
hole will use up a lot
of energy doing so; it
can’t slow down, but
its wavelength gets
longer and longer.
Space Travel Near Black Holes
What’s inside a black hole?
No one knows, of course; present theory predicts that
the mass collapses until its radius is zero and its density
infinite; this is unlikely to be what actually happens.
Until we learn more about what happens in such
extreme conditions, the interiors of black holes will
remain a mystery.
Observational Evidence for Black Holes
The existence of black
hole binary partners for
ordinary stars can be
inferred by the effect the
holes have on the star’s
orbit, or by radiation from
infilling matter.
Observational Evidence for Black Holes
Cygnus X-1 is a very strong black hole candidate.
Companion Star
• Its visible partner is about 25 solar masses.
• The system’s total mass is about 35 solar masses, so
the X-ray source must be about 10 solar masses.
• Hot gas appears to be flowing from the visible star to
an unseen companion.
• Short time-scale variations indicate that the source
must be very small.
Observational Evidence for Black Holes
Cygnus X-1, in visible light
and X rays
Question 3
Cygnus X-1 is
a) NASA’s latest X-ray orbiting telescope.
b) a millisecond pulsar with three planets.
c) the strongest X-ray eclipsing binary system.
d) a likely black hole binary star system.
e) the first gamma-ray burster spotted in X rays.
Question 3
Cygnus X-1 is
a) NASA’s latest X-ray orbiting telescope.
b) a millisecond pulsar with three planets.
c) the strongest X-ray eclipsing binary system.
d) a likely black hole binary star system.
e) the first gamma-ray burster spotted in X rays.
Cygnus X-1 is an X-ray source with one
visible star orbited by an unseen companion
of at least 10 solar masses, and very rapid
changes in the signal indicating a small
source.
Observational Evidence for Black Holes
There are several other black hole candidates as well,
with characteristics similar to Cygnus X-1.
The centers of many galaxies contain supermassive
black holes – about 1 million solar masses.
Observational Evidence for Black Holes
Recently, evidence
for intermediatemass black holes has
been found; these are
about 100 to 1000
solar masses. Their
origin is not well
understood.
Question 4
If the sun was replaced by a
one-solar-mass black hole
a) Earth’s orbit would not change.
b) Earth would be pulled into the black
hole.
c) X rays would destroy Earth.
d) Earth would be torn apart from the tidal
force.
e) life would be unchanged.
Question 4
If the sun was replaced by a
one-solar-mass black hole
a) Earth’s orbit would not change.
b) Earth would be pulled into the black
hole.
c) X rays would destroy Earth.
d) Earth would be torn apart from the tidal
force.
e) life would be unchanged.
The force of gravity depends only on mass and distance, not
the type of matter, or its size.
Summary
• If core remnant is more than about 3 solar masses,
collapses into black hole.
• Need general relativity to describe black holes;
describes gravity as the warping of spacetime.
• Anything entering within the event horizon of a black
hole cannot escape.
• Distance from event horizon to singularity is
Schwarzschild radius.
Summary
• Distant observer would see object entering black
hole subject to extreme gravitational redshift and
time dilation.
• Material approaching a black hole will emit
strong X rays.
• A few such X-ray sources have been found, and
are black hole candidates.
• Calculate the event horizon for a sun with a
mass equal to 4 solar masses.
• Sun: Mass= 1.99 x 1030 kg
• Mean radius = 6.96 x 108 m