Are there gravity waves, akin to light waves? if so, what is the speed of gravity? if not, how does the mass of a distant object like the Sun affect the Earth?
we took Newton in physics and all that, but I don’t remember this question ever coming up. 
It’s thought so, yes
If so, the speed of light in a vacuum.
If not, no one knows. But no one has detected gravity waves yet (AFAIK.)
There is a Nobel Prize waiting for the person who answers these questions. Scientists have expectations of what is there (which Ludovic explains), but it’s still an unmeasured area.
When it comes right down to it does anyone know just how an alternating electrical current in a wire will induce a duplicate (except for magnitude) alternating current in a wire hundreds of miles away?
Yes, we have a set of equations that predicted it and which can be used to describe what will happen in each case but we also have a set of equations that describe the effects of gravity.
It appears to me that the completeness of the electromagnetic theory fools us into thinking we understand it. What we understand is the effect which is exactly what we understand about gravitation.
If the Sun were to explode at this instant, would we feel the gravitational result instantly or would it take 8 minutes to get here at the speed of light?
How gravity works:
Classical view: mass and energy distort the geometry of space-time. When the mass-energy configuration changes, the changes in the distortion propagate out at Einstein’s constant c. There are gravitational wave detectors that should be able to observe these.
Quantum view: massless unobservable particles (virtual gravitons, also at c) go from one particle to another, transmitting the gravitational force. There are also non-virtual gravitons that should be measurable in principle, but I think they are too low energy to be individually observable with current technology.
Newton’s theory of gravity is instantaneous and does not consider propagation.
It would take ~8 minutes for the earth to notice at which point it’d sail off into deep space.
The Sun exploding does not change it’s total mass-energy and would not affect us gravitationally at all. At least, until the mass-energy configuration is redistributed (that is, once it blows past us). The Earth will be caught in the in blast before its orbit changes.
Ture but I read that post as asking essentially what would happen if you removed the sun from the picture entirely in one go. POOF Gone
Nitpick: I wouldn’t call the first explanation the “Classical view”. That would be Newton’s theory. You probably meant “Einstein’s Theory” or “General Relativity View”.
And I pretty much agree with David, except that we haven’t yet been able to observe gravity waves (which we have for E/M waves).
John, there are a few different definitions for “classical”. It’s often used to mean “Newtonian”, but the more common meaning, among physicists, is “non-quantum”. By this standard, General Relativity is a “classical” theory. Even something like Hawking radiation, with quantum mechanical effects manifesting in a GR curved background space, is still “semi-classical”, since the gravitational field itself isn’t quantized in the theories used to describe it.
If the Sun exploded (which is possible, as opposed to just magically vanishing, which isn’t), we probably wouldn’t be flung out into space, but unless the explosion were perfectly spherically symmetric (which is unlikely), we’d feel some gravitational effect. That effect would take 8 minutes to reach us.
I would be willing to lay pretty long odds that humans (or our descendants) will never have the technology needed to detect individual gravitons. That’s the kind of thing a Type III civilization (that’s intergalactic-level) might do to show off. However, a stream of a great many gravitons travelling together would be a gravitational wave, and there is good reason to believe we currently have the technology, or are very close to it, to detect those. The estimate is that we’re about a decade away from postively and directly detecting gravitational waves, either with LIGO or LISA (my bet would be LIGO first, since LISA is dependant on NASA funding, which is in somewhat of a shambles at the moment).
Well, to be fair, we understand a lot more details about EM than we do about gravity. The fact that we know that the force is carried by the photon, and exactly how fast those travel, in particular.
With gravity, we’ve not even verified its speed, nor observed its particle. We think it travels at c, in waves, but if we were that sure about it, LIGO and LISA wouldn’t have been funded. And the graviton is just a name we’ve given to that hypothetical entity that we figure must be there somehow.
no doubt we have a lot more detailed explanation, and vocabulary, for the effects of EM than we have for gravitation. Just the same, I think we don’t really know why an electric field from an accelerating charge is accompanied by a magnetic field at right angles to the electric field. It just is.
If that were the only justification for LIGO and LISA, they would never have gotten off of the ground, nor, probably, should they have (there are a lot of experiments you could build with that money that would give more valuable results than that). But that’s analogous to saying that the purpose of a telescope is proving that light exists, and travels at c. Yes, you can use a telescope to do that, but once you have that, there’s a lot of other information you can gain using a telescope. At the very minimum, gravitational wave detectors will tell us a lot about the mass distribution of stars in our Galaxy, and how that distribution varies with location. More ambitiously, the descendants of LIGO and LISA will be able to measure the cosmological gravitational wave background, which will give us oodles of information about the state of the Universe at a tiny fraction of a second after the Big Bang (the earliest we can probe with light is about 300,000 years after).
It should take the full eight minutes.
Bah, of course we know why. They’re both artifacts of choosing this to be “space” and that to be “time”. They’re all part of the Faraday tensor, which is basically a gadget at each point of spacetime which measures a little bit of area in some plane at that point.