Download Introduction to Astronomy

Announcements
• Projects are graded! Almost all were
quite good--congratulations!
• Test next week (all about stars)
• Second project is due in three weeks
So many things I would have done,
But clouds got in my way.
--Joni Mitchell
Black Holes
10 November 2006
Today:
• Special relativity theory (for high-speed
motions)
• General relativity: a new theory of gravity
• Black holes
• How to detect black holes
Special Relativity Theory
• A revision of Newton’s laws of
motion
• Especially important when
objects move at close to the
speed of light
• Proposed by Einstein in 1905
• Resolved apparent paradoxes
in electromagnetic theory
Albert Einstein,
1879 - 1955
Special Relativity Theory
• The “principle of relativity” (Galileo, Descartes) says that motion is
relative: There’s no way to tell who’s really moving, so long as the
motion is straight and uniform.
• But electromagnetic waves are predicted (and observed) to travel
at a fixed speed: 300,000 km/s.
• Before Einstein, physicists thought this meant that the principle of
relativity doesn’t apply to electromagnetic waves--just measure
the speed of light relative to you, and you’ll learn how fast you’re
really moving.
• Einstein proposed that the speed of light is fixed, regardless of the
motion of the source or the observer!
• Implications: Time itself behaves in bizarre ways, which become
noticeable only when objects move fast relative to each other.
Implications of Special Relativity
• The time interval measured between two events
depends on exactly how it is measured.
Amy
Beth
Speed = 4/5 speed of light
Alpha Cent.,
4 l.y. away
Amy stays home on earth, while Beth travels to Alpha Centauri
and back at 4/5 the speed of light.
Amy measures the time between Beth’s departure and return to
be 10 years (5 years each way), as we would expect.
Beth measures the time to be only 6 years! ( 10 x 1–(4/5)2 )
Implications of Special Relativity
• When you “add” speeds, the result is less than you
thought!
1/2 speed of light w.r.t. Beth
Beth
1/2 speed of light w.r.t. earth
Amy
Amy measures the cannon ball’s speed to be only 4/5 the speed
of light!
1
2
1+
1
2
+
1
2
.1
2
=
4
5
Implications of Special Relativity
• The speed of light (300,000 km/s) is a “Cosmic Speed
Limit”
Combining two speeds less than the speed of light
always results in a speed that is also less;
Photons and some other signals move at the speed
of light, regardless of the motion of the source;
It would take an infinite amount of energy to
accelerate a physical object up to the speed of light;
If a signal could travel faster than light with respect
to Amy, then it could travel backwards in time with
respect to Beth (who’s moving w.r.t. Amy).
Special Relativity
The mathematics of special relativity isn’t advanced-just basic algebra. There are many good books on
the subject, or you can learn more by taking Physics
2220 (Physics for Scientists and Engineers).
What about Gravity?
Newton: Force on the moon points toward where
earth is now.
Force
Einstein: That’s inconsistent with the Cosmic Speed
Limit! If the earth suddenly moves, the force on the
moon can’t change until 1.3 seconds later.
We need a new theory of gravity…
General Relativity Theory
• Einstein’s theory of gravity
• Especially important for
fast-moving objects and
for very dense objects
• Proposed by Einstein in
1915
Position
General Relativity: The Basic Idea
Time
The graph appears curved because space-time itself is
curved (distorted by the earth’s mass).
Why does the apple fall?
Aristotle: It’s seeking its natural place
toward the center of the universe.
Newton: The earth exerts a force,
pulling the apple downward.
Einstein: It’s moving along the
straightest possible path through
curved space-time.
Why do golf balls and bowling balls
fall at the same rate?
Because the trajectory is a
property of space-time itself,
not a property of the object.
Consequences of General Relativity
(Advanced mathematics required!)
• Inverse-square force
law isn’t exact; minor
corrections to solar
system trajectories
Mercury’s elliptical orbit gradually precesses, mostly due to
the gravitational pull of other planets. But a small part of the
precession (43 arc-seconds per century) is due to relativistic
corrections to Newtonian gravity.
Consequences of General Relativity
• Gravitational deflection of light
(twice the amount that Newton
would have predicted)
Arthur Eddington (tested
prediction in 1919)
Consequences of General Relativity
• Gravitational waves: ripples in
space-time curvature that propagate
outward from accelerating massive
objects (e.g., supernova explosions,
close binary systems)
Binary pulsar (in Aquila)
“LIGO” (Hanford, WA site)
Consequences of General Relativity
• Black holes: Objects so dense that not even light
can escape.
(2-D analogy of 3-D curvature)
Black Holes in Brief
• A spherical “horizon” surrounds the region from which
nothing can escape
• The radius of the horizon is proportional to the black
hole’s mass (surface area is 4πR2)
• For a solar-mass black hole, the horizon radius is 3 km
(only a few times smaller than a neutron star)
• Neutron stars, like white dwarfs, shrink with increasing
mass; maximum mass is 2-3 solar masses
• So a collapsing stellar core more massive than this
should form a black hole!
How to detect a black hole?
• Only through its gravitational pull on other objects!
• An isolated black hole would be virtually impossible to detect
• In a close binary system, a black hole can suck gas off the
companion star…as the gas spirals inward it becomes extremely
hot and emits x-rays
• Most famous example: Cygnus X-1. Binary system (8000 ly
away) of a blue supergiant star and a compact object, both 20-30
solar masses--too massive for a neutron star.
Dust ring (800 ly wide) swirling
into center of galaxy NGC 4261
More Black Hole Physics
• What happens if you fall into one? Nothing
special when you cross the horizon (unless
you try to turn around). But from then on,
you’re doomed. The equations say that when
you reach the center, your time stops. (The
equations don’t take quantum effects into
account.)
• Because black holes are perfect absorbers of
radiation, they also emit thermal radiation
from their horizons! Smaller black holes are
hotter. But for a solar-mass black hole, T is
only about 10–6 kelvin, so the radiation is
negligible.
Stephen Hawking