The accuracy of observation over vast distances.

[0Tun0]

When observing objects outside of our galaxy, how does one determine from which direction the original object was located relative to the observer when the positions of the original object, the various gravity fields its emissions travel through, and the observer are constantly shifting?

When dealing with objects that are millions and billions of light years away, how precise can our different approximations be when we cannot compare from other vantage points of even 1 light year from our current position?

[Romanus]

Though I'm no expert, AFAIK astronomers pay little attention to the "original" position of extragalactic objects--partly because it is indeed impossible to determine without more detailed parallactic or (very) long-term data, and partly because it has no impact on "current" observations, which are of course past observations.

[Andrew D]

When dealing with objects that are millions and billions of light years away, how precise can our different approximations be when we cannot compare from other vantage points of even 1 light year from our current position?

They aren't very precise at all. The distance from Earth to Andromeda, the closest major galaxy, is only known within .06 Mly. That's 60,000 light years. You could call that margin of error astronomical.

[George]

When dealing with objects that are millions and billions of light years away, how precise can our different approximations be when we cannot compare from other vantage points of even 1 light year from our current position?

The accuracy is limited by the method being applied to the object.

Type 1A supernovae, for instance, were the breakthrough objects in getting any reasonable accuracy for those very distant galaxies. Astronomers also use different techniques that enhance the accuracy of these measurements. Using numerous filters, for instance, improves accuracy.

[antoniseb]

When observing objects outside of our galaxy, how does one determine from which direction the original object was located relative to the observer when the positions of the original object, the various gravity fields its emissions travel through, and the observer are constantly shifting?

When dealing with objects that are millions and billions of light years away, how precise can our different approximations be when we cannot compare from other vantage points of even 1 light year from our current position?

The original post is not about distance, but about the changing directions of the photons. The answer is that we can get confirmation by looking at such objects as the Einstein's Cross the scale of the deviation from true direction that object night have. We can also tell similar things from the weak lensing surveys we use to locate dark matter in Galaxy clusters. The answer is that in most cases, the variation in direction of the photon doesn't change more than an arc-second or two over a 12 billion LY flight.