system
Given the following post, respond as if you're commenting on Reddit:
human
Are the shapes of galaxies we see distored by the light from different parts of it getting to us later than others?

Given that a galaxy is thousands of light years wide wouldn't the light from a nearer part of it reach us sooner than light from a further part of it? Why aren't the images of galaxies smeared sideways sometimes because the galaxy is moving sideways across the sky relative to us? Or are some of them like that?
gpt
The key number that determines how strong such smearing or distortion effects are is the ratio of the velocity of the object/material to the speed of light. The higher this ratio, the more the material moves in the time it takes for the light to travel, and the more the image we see (from the light emitted at a given time) misrepresents the current position of the object.

Let's calculate this ratio for galaxies. The typical velocity of material inside a galaxy (the stars and gas orbiting around the galactic center) is around maybe 200 km/s or so, depending on the galaxy (how big it is, where in the galaxy the matter is, etc). The bulk motion (how the galaxy is moving as a whole, separate from its internal motion) is also typically at the level of a few hundred kilometers per second (e.g, the Andromeda galaxy is moving towards us at 300 km/s).

The speed of light is roughly 300,000 km/s. The number of zeros is giving us an immediate clue how this ratio is going to go. The ratio of 300 km/s (for the sake of nice round numbers) to 300,000 km/s is 0.001, one part in a thousand.

So that's the level of distortion we might expect: one part per thousand. In practice, it's generally not even this significant. In a particular image of a galaxy, individual stars will have moved by one part per thousand in the image, but the overall shape and pattern of a galaxy won't really have changed by that much -- the stars at some location will have moved to a new location, but other stars will have moved in to take their place. It largely balances out. Features like spiral arms in galaxies (which are not a fixed collection of stars and gas -- stars move in and out of spiral arms naturally over the course of their orbits around the galactic center) turn out to have even lower velocities than the stars themselves. The pattern velocity of spiral arms, going from memory, is something like 3-4 times slower than the motions of the stars, so the spiral shapes we see in galaxies are even less distorted.

An alternative calculation we could perform, to check this answer, is this: the linear size of a large spiral galaxy is something like 100,000 light years -- i.e., it takes light 100 thousand years to cross from one end of a galaxy to the opposite side. Let's consider those sides as the 'back' and 'front', from our perspective as outside observers. The typical orbital period for a star around a galactic center is of the order of 100 million years. So we can consider the ratio of these two values: in the time it takes light to cross a galaxy, the stars will have moved roughly 1/1000th of a full orbit. The stars in the 'back' of the galaxy will truly be 1 part in 1000 further in their orbits, compared to the stars at the front, in the images we see of the galaxy.