so is Lorentz contraction a completely different effect than the length contraction due to time dilation that has almost the identical formula? Do they stack? It is my understanding that time dilation causes length contraction in the radial direction where lorentz only affects in the direction of motion.

I don't know how to address your question about "completely different" and "stacking" of the effects and your apparent distinction between "radial" and "direction of motion". I see that your original post is trying to envision relativistic effects for the perspective from Earth that is revolving around the center of our galaxy, so I will try to get to that. But, envisioning how things will appear in relativistic conditions is very hard.

Concerning "different" and "stacking", it is necessary to remember that the Lorentz Transformations were developed as an

*explanation* for the

*observed experimental result*, that the velocity of light does not

*appear to* change when taken in any direction, at any speed. So,

*all* of those equations in Special Relativity Theory need to be applied to appropriate observations to predict how those observations would appear to a different observer traveling at a different speed. In that sense, they "stack" so that both length measurements and time

*interval* measurements need to be recalculated with those equations in order to adequately explain all observable changes in perceptions between two observers. Conceptualizing how to do this is not trivial for us, because we are not used to the effects at such high speed differences.

Astronomy forces us to try to envision some of these effects to make sense of our observations, because some of the speed differences that we see are sufficient to create observable effects. But, even the Lorentz Transformations are not sufficient to explain all of our observations. So, we have added the Theory of General Relativity to explain the effects of

*extreme *gravity on apparent measurements in our observations (as well as the relationship between mass and energy). But, even that is not enough to explain the Hubble observation about the

*observable* universe

*seeming* to be expending away from us in all directions at the same rates, with the rates only a function of distance from us here on Earth. So, to make that consistent with the theories of Relativity, we have added

*assumptions* that there is a lot of "dark matter" that we cannot see, to "explain" the

*apparent extra* gravitational forces that are needed to make our galactic orbital velocities match our equations. And, we have added an

*assumption* that there is an unknown force called "dark energy" that

*somehow* makes space itself expand, so that

*two places in space can be moving apart faster than the speed of light *even though no matter can be moving

*through* space any faster than the speed of light.

It is important to remember that all of these theories about measuring lengths and time intervals and masses and energy levels are

*just mathematical tools that work to *__quantitatively__ __describe __our observations in a manner that seems to work.

__Why__ that math describes our observations is

__not__ explained by those theories.

There is a similar situation in the very tiny, "quantum world", where we find that sometimes light particles (photons) and sub-atomic particles (e.g., electrons) behavior must be described by the mathematics for particles, and other times we must use the mathematics for waves in medium. Google and read the discussions about the "double slit refraction paradox" which seems to challenge the concept of cause and effect, even suggesting time-travel to explain apparent violations. I point this out to help you realize that even successful mathematical quantitative

*description* of some physical process does not actually help us understand

*why* it works as described.

So, to your question about observational differences between conditions when the Earth is on one side of the galaxy vs the other side, and radial vs linear directions, all I can suggest is this: First, the situation regarding differences in apparent measurements as a function of which side of the orbit we are on in the galaxy is basically the same situation that was done with the Earth's position in its revolutions around the sun, which led to the Lorentz transformations and the Theory of Special Relativity. We don't expect to see any differences due to speed, except frequency shifts in light sources, e.g., red shifts. But, when you add in the other theories and their mathematical descriptions, and then

__postulate__ some physical phenomenon occurring at great distance and great speed differential, and then ask what it

*should *look like, it gets extremely difficult to actually apply the mathematics of all of those theories and assumptions to answer such a question.

There are a lot of people employed to try to apply the math to observations, in the hope of actually getting a better understanding of the physics underlying our observations of our universe. But, it is very difficult work, requiring a lot of familiarity with the theories, math and conceptual visualization, then extensive, difficult computations to test whether what those theories predict we would see is what we are seeing.

I am not one of those people doing that type of work, and i don't get the impression that there are any others on this forum who do that type of work. So, I don't expect the folks here to just supply the answers to all of the questions that we come up with as we try to ponder "How can all of this be?"