Since I was a kid, I've wondered what would happen to the orbit of the
Earth if the Sun suddenly ceased to exist.  Would the Earth continue
to orbit around "nothing" for the 8 minutes or so that it would take
light to travel from the Sun to the Earth?  Intuitively, I have a hard
time picturing the Earth orbiting around nothing.  I would think that
it would instantly fly off into space.  But that would violate the law
that information can not travel faster than light.  I've tried
researching this on my own but get conflicting data.  Here are two
links, one from space.com that says the speed of gravity is near the
speed of light, and another that says that it is much faster.

http://www.space.com/scienceastronomy/gravity_speed_030107.html

http://www.metaresearch.org/cosmology/gravity/speed_limit.asp

My specific question is this:

If the Sun were made to vanish, would the Earth continue to rotate
around the spot where the Sun was until the last rays of light from
the Sun hit it?

All this is stuff even the experts don't agree on. :) You expect
someone (with all due respect to the wonderful researchers here) to
provide a more clear cut answer than that? :)

A 20% margin of error to boot :)

Thanks for the comment, Crythias.  I'm hoping that there is a
generally accepted answer in the physics community that not everybody
is already clued to.  I wouldn't have asked the question if I didn't
think it hasn't already been answered.  If mankind simply doesn't know
what will happen in this scenario yet, then I forget about it because
the answer isn't out there.

A lot of people in my generation still think Australia is a continent. :)

Hi bazuul-ga,
   Good question.  This was a topic that Einstein mulled over for
quite some time.  The end result was his theory of special relativity.
 In this, he calculated that the gravitational waves of which you
speak, travel at EXACTLY the speed of light.  Interesting eh?  If
you'd like to learn more about Newtonian physics, relativity, quantum
mechanics, and string theory, simply check out the NOVA website on the
PBS homepage. (http://www.pbs.org/wgbh/nova/elegant/program.html). 
They did a show not to long ago called the "Elegant Universe".  The
entire episode is available in streaming video at this website, and
you can watch it for free.  They address your particular question
(with some cool computer animations) in Chapter three of hour 1 ("A
New Picture of Gravity").  The entire video is explained in laymans
terms, so it's pretty easy to understand.  Enjoy!

Just noticed a mistake.... Einstein talked about this in his GENERAL
theory of relativity, not his thoery of special relativity.  FYI

Thanks Case1234, much appreciated.  I'll give it a go.

I think the mainstream opinion is that space is warped by gravity, and
it would unwarp instantly or at the speed of light if the source of
gravity was removed instantly. Some experiments have led to one
conclusion, and others to the other conclusion. None of the
experiments have been compelling.
 If a compact star passes though our Solar System at 0.999 c (with
respect to Earth) next year, we may have compelling data for persons
who servive. It is generally thought, the probability is very close to
zero for a nearby compact star to have a velocity of even 1% of light
speed, which may not br fast enough to produce compeling data
reguarding the speed of gravity.   Neil

The second website you provide is hardly a reputable source since it
is a metaphysical/cosmology website. However, much of the info on
there is pretty good, but I noticed a few incongruencies and
propagandish type material.
 
If gravity is a particle (the gravitron), then it would be impossible
to go faster than light, even if it had zero rest-mass (unless it were
like the theoretical tachyon, which cannot go below the speed of
light). But what in physics anymore is *just* a particle? haha.

I thought of a question similar to what you are asking, and it may
give another perspective on the subject. Imagine a long rod or bar. If
you push it, doesn't the other end also instantaneously accelerate
(assuming there is no compression of the material)? This is because
all the atoms have electrical forces (which are field forces, like
gravity) that repel each other, or the bonds themselves keep the
conformation of the rod (as in carbon fiber rods). So by pushing one
end of the bar, does that mean that force was instantaneously
transferred to the other end of the bar? This is a similar question to
yours, except instead of attractive forces it involves repulsive
forces or the forces of molecular bonds. (I realize that there will
always be some compression of the material though-- but could this
compression travel through the bar faster than light, since it is not
an actual object? What about sheering forces that travel faster than
the natural speed of wave propagation in a material? I'm almost sure
the answer is that the propagations still cannot travel faster than
light, since the reason for things not being able to travel faster
than light is not just that mass increases with velocity requiring
infinite energy, but also the component of time slowing for something
moving through space.

It seems that to fully answer the question, we'd have to know the
mechanism of how gravity works-- is gravity a particle, a wave, both,
or is it an actual effect of mass on space and time. (e.g., mass could
just instrinsically slow down time in space-- then, as an object
enters regions of more slowing of time, it loses rest mass, and gains
kinetic energy to maintain the total energy, thus creating the
gravity's force. This requires no particles at all, but it still
requires "info" to be carried through space....) It remains to be seen
how field forces work. In quantum mechanics, if a particle randomly
appears and then quickly disappears, as sometimes happens, does it
instantaneously exert effects on surrounding particles? My guess is
yes, just by its nature of coming into existence, the other particles
instantly respond to the loss of energy in the system and the addition
of mass into the system. How that happens, I have no idea.