Effects of time dilation on our observations of the Sun Forgive me if this question makes little sense -- I'm not a physicist, only an interested observer.
As I understand it, time is dilated in gravitational fields and the stronger the field the stronger the dilation -- the slower time flows. The sun is more massive than the earth, thousands of times more massive in fact (330k times afaik).
So, does this affect our observations of the sun? Is it taken into account when working out the physics that we're observing? When we watch a solar flare, are we watching it in slow-motion? Do solar winds accelerate up the gravity gradient towards us? Does this affect the measurements taken by SOHO (which is much further down the gravity well than we are)? And, does the Earth's constant acceleration affect these measurements too?
I realise that's lots of questions, but really I think it's just one: how does time dilation affect our observations of the sun?
 A: 
As I understand it, time is dilated in gravitational fields and the stronger the field the stronger the dilation -- the slower time flows.

The time dilation depends on the gravitational potential, which is approximately $-Gm/r$, not the gravitational field, which in Newtonian gravity would be $Gm/r^2$, and in general relativity isn't even an observable.

So, does this affect our observations of the sun?

Yes, but the effect is quite small. The effect is the potential divided by $c^2$, which for the sun comes out to be about 2 parts per million.

Is it taken into account when working out the physics that we're observing? When we watch a solar flare, are we watching it in slow-motion?

Very few observations are sensitive to an effect that small. Historically, people first tried to detect this for white dwarfs, which are much more compact and therefore have a bigger effect. You can detect such effects in sufficiently sensitive spectroscopic measurements, since the true wavelengths are known to very high precision.

Do solar winds accelerate up the gravity gradient towards us?

This depends on what you mean by accelerate.

And, does the Earth's constant acceleration affect these measurements too?

If by this you mean the gravitational potential of the earth, then yes, it can have a measurable effect on high-precision measurements. The classic confirmation of this was the Pound-Rebka experiment.

Does this affect the measurements taken by SOHO (which is much further down the gravity well than we are)?

What is generally detectable for spacecraft is the Doppler shifting of their radio signals, which can be thought of as a combination of kinematic and gravitational Doppler shifts.
A: A solar photon takes 8 minutes to reach Earth but has theoretically been travelling from the core to the corona of the Sun for maybe millions of years (no way to measure that) because in the sun's interior there are so many potential pathways for the photon to take that straight lines (available to it when it leaves) are not an option. It is said in $E=hf$ that the photon's energy is equivalent to its speed (the constant) and its frequency (level of vibration). On release from the body of the Sun, there would logically be a transition phase.
A physicist will have to provide further equations but as far as I understand it, gravitational effects do have an impact on the way we view light.
