Ask An Astronomer 
Here are the answers to selected questions. . Questions may have been edited for clarity or brevity. Click on a link to move directly to the answer.
Almost all celestial rotation in our solar system is from West to East, or counterclockwise when looking down from the North pole. All planets orbit the Sun in this direction; the Sun itself, as well as all but two planets rotate in this way. This is not too surprising, since the angular momentum associated with all this rotation is the same as the total angular momentum of the primordial solar nebula from which the sun and all planets formed.
The two exceptions are Venus and Uranus. Uranus' rotational axis is tilted by slightly more than 90 degrees with respect to its orbital plane, i.e. it is rotating "on its side". Venus is the only planet in the solar system that truly exhibits reverse rotation, spinning in the opposite direction to its orbital motion.
It is thought that this anomalous rotation was caused by a collision with a very large asteroid, or even a planetoid, early on in the history of our solar system. The collision would have destroyed the asteroid, but the impact could have changed the orientation of the orbital rotation axis.
The easiest way to calculate the distance from the earth to the sun is by
using the known distance to one of the other planets. It takes a few
steps though.. so bear with me. Take Venus for example; we can use radar
signals to find the distance to Venus. Signals sent from earth will
bounce off the surface of Venus and then travel back to earth where we
can detect them. Because radar travels at the speed of light (a quantity
that is well known from laboratory experiments) you can easily calculate
the distance between Venus and Earth at any time.
distance = 0.5*(time for radar to travel both ways)*(speed of light)
Now that we know the distance to Venus we can calculate the distance from
the Earth to the Sun using trigonometry. Both Venus and Earth travel in
almost perfect circles around the earth, so this is a fairly easy
calculation. It might help to envision the situation if you draw two
concentric circles on a piece of paper to represent the orbits of the
Venus and Earth. Now imagine that the earth is set at one position in its
orbit, as Venus travels along its orbit there are two points where the
Venus-Sun line and the Earth-Sun are perpendicular (90 degrees apart).
From our perspective on earth this is the point where Venus is the
farthest it will get from the Sun. By keeping track of Venus over time we
determine exactly when this will happen. When this happens we make the
radar measurements mentioned above and we also measure the angle between
the Sun and Venus at this point (here's where the trigonometry comes in!).
It turns out that the distance from the Sun to the Earth is:
(distance of Sun-Earth) = (distance of Earth-Venus)*(cosine(angle))
This is how we get the distance of Sun-Earth to be 92,955,830 miles! This
is also known as one astronomical unit (AU)
Many people struggle with the idea that looking farther out means
looking farther back, at least in the temporal sense.
Presumably, you already get this point, or at least part of it.
Just to make sure we're on the same page though, along with anyone
who might stumble across this, let me put it this way:
The light emitted by the birth of the
universe comes from... well, everywhere. The early universe was a
boiling sea of high energy particles. These particles were packed
closely enough to keep light trapped basically right where it was
sitting. In other words, the universe was opaque.
However, the universe was expanding, which means the boiling sea
of particles was cooling off, as all expanding substances do,
and eventually, the whole shebang cooled to the point where light
could escape, which it did, from every point in the
universe at once.
So let's imagine you're sitting in a spaceship in the middle of all
of this, watching the universe become transparent. (With appropriate
radiation shielding, or some sort of super-robot body. Use your
imagination.) What you'd see in the first instant is all the now-free
light rushing at you from the nearby part of the universe, naturally,
the light that's had time to reach you. Wait five minutes longer,
and you're still seeing light, just light that had to travel farther
to get to you. But all this light was emitted at the same time, so
you conclude that the light is five minutes old, and you're seeing
something that happened five minutes ago.
Hopefully, you see where this is going. Wait around a few billion
years, and you're still seeing light from that same event, way back when,
but which was emitted so far away that it took all of those several
billion years just to reach you. So by virtue of the long unfathomable
distances between, you get to look back in time.
The key to your question may be in your understanding of the place in
time and space from which the light was emitted.
If the light had been emitted immediately, i.e. at the same
instant the universe was created as a tiny little speck, then all the
light would certainly have raced past us by now. But we're not looking
at some cosmic firecracker, the burst of light that was produced
by the explosion that started it all, in fact we can't, precisely
because the universe was too bright for the light to move
around for the first few hundred thousand years. (Well, too energetic,
anyway. Hopefully, this makes sense.) By the time the universe was
transparent, it was also very big, such that we can look out to long
distances at times long ago.
Which would be the whole story, if the universe had stopped
expanding once it turned transparent. It did not, however, so the
answer is a little more complicated (though if you made sense of
the above explanation, you should be in good shape). It turns out
that your second assumption--that the universe expands more
slowly than light speed--is wrong.
Which might sound like a joke at first, but I assure you I'm serious.
Objects are constrained to move at velocities less than light
speed, but space itself may stretch as fast as it wishes, over great
distances. Of course, if the space between two points is stretching
faster than light, then those two points are prevented
from ever trading information, and might as well belong to entirely
separate universes.
So our universe effectively has some maximum volume,
namely, that volume which is expanding away from us more slowly than
light speed. It just happens that this volume still encompasses
light that was emitted in the earliest years of the universes
existence. Presumably, this light will eventually disappear
over the edge from our perspective, never to be seen again.
Before we jump in, let's first correct a bit of trivia in
your question. While dark matter has implications for cosmology--the
way the universe will behave/has behaved on very long timescales--the
evidence of its existence is independent of the concept of an
expanding universe.
Now, as for your question itself. There is something of a boundary to
the universe, the Cosmic Microwave Background. It represents a point
in the universe's history at which the universe was opaque, therefore
we can't see anything beyond it. But we can't exactly measure how much
it recedes every year, since it's a few billion light-years away, a
distance that's not going to change by a measurable amount over the
course of our lives.
Still, you haven't found a fatal flaw in cosmology, because there are
always other tools at a scientist's disposal. I invoke the power of
Doppler shift (or redshift, if you prefer). While we can't necessarily
measure giant distances with high precision, we can usually get a
reasonably precise measurement of the spectrum of an object. You may
be used to thinking of a spectrum in terms of prisms and rainbows and
such, and it's not far off. However, the spectra astronomers use tend
to be much more detailed, to the point where we can make out
individual spectral lines.
Without going into overly boring detail, a spectral line is a
particular wavelength of light (a very specific shade of red, for
instance) that is preferentially emitted by an individual atom. You
can learn more:
here,
along with a bunch of other quantum physics stuff, if you're
interested.
Back to Doppler shift, when an object is in motion, the spectral lines
emitted by the atoms move around to different wavelengths. It's
similar to the effect that causes a train's whistle or an ambulance's
siren to change pitch as it goes flying past you. If an object is
moving towards you, the light gets shifted toward shorter wavelengths;
if it's moving away, the light is shifted toward longer
wavelengths. These effects are called blueshift and
redshift, respectively. (Though, to be sure, if light is
already blue, it will get blueshifted toward violet or
ultraviolet, and if light is already red, it will get redshifted
toward infrared. It gets confusing if you put too much thought into
it, so just think about it in terms of what effect it has on yellow
light.)
Knowing this, Edwin Hubble (the guy the telescope is named after) went
out and measured the Doppler shift of several nearby galaxies. If you
assume the universe is not expanding, you'd expect to see a
more or less even distribution of blueshifts and
redshifts. Surprisingly enough, he found that almost all of the
galaxies he measured were redshifted, meaning every galaxy is
traveling away from us. Even more evidence has been amassed today, and
we know that galaxies very far away are extremely
redshifted. So we know beyond a shadow of a doubt that everything in
the universe seems to be moving away from everything else. And if this
is the case, the universe must be expanding, as it's hard to imagine a
way to make things get farther apart without actually increasing the
extent of space they cover.
To get mathematical for a moment, prior to Hubble's measurements,
Albert Einstein had formulated his theory of General Relativity,
coming up with an equation that described the entire universe. He was
unsatisfied, however, when he realized that his equation predicted
that the universe must be either expanding or contracting. He was able
to create a solution in which the universe could be stable, but upon
the announcement of Hubble's discovery, he changed his mind, calling
the alteration the biggest mistake of his career.
So, one of the greatest minds of all time predicted a universe that
was expanding, and one of the first guys to go looking found he was
right, as has everyone who's gone looking since. And hopefully, that's
all the answer you need.
Thanks to Alex McDaniel, David Lai, Shawfeng Dong, Gabe Prochter, Ian Dobbs-Dixon, Jay Strader, Justin Harker, Karrie Gilbert, Kyle Lanclos, Laura Langland-Shula, Lynne Raschke, Marla Geha, Michael Kuhlen, Nick Konidaris and Scott Seagroves