Download HW10_Answers

HW #10 ANSWERS (Due 11/04)
1) Explain why a stellar core that has a greater mass than 4 solar masses, will not become a
neutron star, but instead become a black hole.
In a neutron star the neutron degeneracy pressure is holding up against gravity trying to
collapse the core of the star. When neutrons are packed very close together they act like
standing waves, which means they have can’t have just any energy. They can only have
certain specific energies (like an electron bound to an atom). When neutrons act like
waves, no two neutrons can have exactly the same state. This means that they can’t be
compressed closer together. This happens to electrons when a white dwarf is formed.
But the neutron resistance to compression isn’t infinite. If to much gravity is present it
will over come the neutron repulsion. When the core of a star has more than 4 solar
masses, the force of gravity is stronger than the neutron pressure. The core collapses.
Since there is no other repulsive force left in the universe to stop it, gravity collapse the
core to a singularity. This is a black hole.
2) The core of the star which becomes a black hole collapses to an infinitely small point
called a singularity. What we “see” as the outside of a black hole is not the singularity.
Instead this outer edge is called the Event Horizon. How is the Event Horizon defined?
The Event Horizon is the distance from the singularity where the escape velocity is
greater than the speed of light. Anything that passes closer to the black hole than the
Event Horizon will never return, because the escape velocity is greater than the speed of
light, which is the fastest speed in the universe. In general relativity the Event Horizon
can be defined as the distance from the singularity where time stops, relative to observers
outside of the Event Horizon.
3) Explain why the gravity becomes so extremely strong as you get close to the event
horizon of a black hole.
If you where to travel inside the Earth, the only mass that would have an effect on you is
the mass that is still interior to where you are located. Therefore, if you could go all the way to
the center of the Earth, the force of gravity would be zero at the center, since there is no mass
interior to your position. When a core of greater than 4 solar masses collapses into a black hole,
you can get extremely close to the center of the mass and still have all the mass interior to you.
This allows the force of gravity to become extremely strong.
4) State the two postulates of Special Relativity and explain what each means.
1) For objects moving at a constant velocity, all motion is relative. This means that there
is no object that is at absolute rest. It is impossible to tell if one object is at rest and
another is in motion. You can only say that something is in motion relative to something
else. That is the best that you can do.
2) The speed of light in a vacuum is constant for all observers. Everyone sees light move
at the same speed. It doesn’t matter how fast you are moving relative to somebody else.
Everyone agrees at all times on the speed of light.
5) In the 1990s show the X-files, Scully and Mulder once encountered a UFO and after the
flash of light realized that many minutes had gone by, even though it seemed like just a
couple of seconds. Mulder told Scully that when people encounter UFO they often lose
time. Sometimes hours go by that only feel like seconds. Scully replied that this is
impossible because “time is a universal invariant.” What would Special Relativity have
to say about this statement? (Note: universal means everywhere, and invariant means it
stays the same. So universal invariant means it is always the same, everywhere.)
Time is relative. It depends on your motion relative to someone else and also on the
amount of mass present. Time is not invariant. There is a universal invariant and that is
the speed of light. But it is the universally invariant nature of light that actually causes
time to vary. So Scully is wrong. (NOTE: On the X-files, the character Scully had
written a graduate thesis on Einstein’s relativity. Unfortunately, the writers on the show
apparently did not!)