Astronomy 102 – Spring 2000
Tutorial #6: The Universe and its Gravity: Open or
Closed?
We are in the ultimate round of gravity versus expansion
saga…
In earlier episodes we found that gravitational pull is
in a constant battle with "push" by thermal pressure or quantum pressure.
Stars fates were decided by that battle. In the case of the universe as
a whole the situation is somewhat more complicated. The universe is expanding
not due to a constant pressure, but because all of its components had initial
velocities. It is therefore important to learn some of the basic properties
of gravity and how it "fights" initial velocities. It is also important
to see how our "naïve" understanding of gravity can lead us towards
the wrong description.
Get an object in your hand. It can be a pen, a calculator
or an eraser. Drop it from ~30 inches above your desk.
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What was the initial speed of the object? _____zero_____
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Was the final speed larger? ______yes_____
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What was the force that was responsible for that change in
speed? Gravitational pull by the earth
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Now throw the object upwards, to height of about ~30 inches.
As it was moving up, what happened to the object’s speed? The speed
is decreasing.
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What happened to the object when it reached the top? ____It
seems to stop for an instance, then moving downwards (it really is changing
speed all the time, though).____
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What happened to it right after that? ______Speed up as
it is moving downwards______
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Gravity was acting on the object throughout, and was responsible
for the object’s change of speed. Now imagine yourself as an astronaut
standing on a small asteroid and throwing the same object upwards (hey,
the astronaut Allan Shepherd brought a golf ball to the moon, so that’s
OK). Describe the motion of that object _________________If the object
is given an initial speed that’s very small it will go up & down as
on earth. _________________________________________________________________________________________________
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Now assume that you hurl the object from the asteroid with
all your might upwards. Describe the motion now: _________ If the initial
speed is large it will slow a bit at first, than slow less and less as
it is further from the asteroid. The asteroid will always slow it down
a bit, but never enough to make it return to the asteroid – even if that
asteroid was the only thing in the unliverse! The object is described as
having a velocity larger than the escape velocity. _____________________________________________________________________________________________________________
Note that the object may never return!
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Now consider a different situation: The whole class is standing
on a Very light asteroid (the mass of the asteroid is much smaller than
the mass of your class mates) and everybody jumps. If you jumped with an
initial velocity that is higher than everybody else’s is than you are affected
by their gravity (every body is attractive! Remember!?). Describe your
speed as a function of time: _________As the class is jumping the faster
ones are moving ahead of the peck, and slowing down a little in the process.
They are further from the center so the force slowing them down is smaller,
BUT all classmates closer to the center pull on them DESPITE OF THE
FACT THAT THEY ARE MOVING. The class mates closer to the center have larger
gravity due to their closeness, but less gravity because fewer class mates
pull on them. (this situation is analogous to that in the Olbers paradox
in which the 1/r^2 decline in light intensity is counteracted by the growing
number of shining objects). _____________________________________________________________________________________________________________
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Are you going to meet your peers again? What is it that will
determine your fate? _______The fate of the jumpers (all of them!) is
going to be determined by their jumping abilities AND their initial density.
(the asteroid is not a point, so the density can be determined for the
initial state). If the class is very densely packed and doesn’t jump high
they will all fall back again onto the asteroid. If they aren’t closely
packed they will fly away forever._______________________________________________________________________________________________________________
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Consider a universe made of objects that are hurled away
from each other. Assuming that there are as many slow objects as there
are fast objects, describe the expected DENSITY of the universe. A picture/diagram
will be helpful here. ________________As in 9, the effect is a density
that is decreasing in time, but not in space. However, unlike the class
examples of raisin breads, Adam, Eve and the snake, and growing balloons,
the objects are flying in ABSOLUTE space. That is: objects IN SPACE are
flying into EMPTY SPACE. The problems with this scenario are: 1. There
is no explanation of the microwave background radiation. Radiation coming
from the initial "asteroid" would go outwards, not come back to us in the
center. 2. There are strong reasons to believe that there will be different
abundances of matter at different distances, as in a huge supernova, but
that’s not what we see. 3. This solution is highly contrived, and is humanity
centered. It is not clear why we should be the center. (actually we are
not even the center. We are falling towards the "great-attractor," a fact
that can be discerned from red-shifts of nearby galaxies.). 4. Newtonian
cosmology, the theory that we used for this solution, was proven to be
inaccurate for distances of order of the solar system. Einstein’s theory
of gravity is still valid for these distances. ______________________________________________________________________________________________________
12. The universe is actually uniform in density, and as
shown above has many other properties hard to reconcile with a Newtonian
cosmology. In order to concoct such a universe with our naïve model
above we have to contrive an unbelievably complicated initial blast. The
idea described in Friday’s and Monday’s classes -- that space and the objects
in it are expanding at the expense of the original speed of objects in
that space – can better account for the uniform density of space. Explain
how: _________________See class explanations.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Note that the rate of motion of objects in an expanding-space
universe works exactly the same as the rate of motion in the universe that
you constructed in your imagination (although the density doesn’t).