Remember, the sun isn't on fire. It is a big fusion reaction, generating heat and light and other electromagnetic output.

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The sun isn't moving except relative to other objects. It is as true to say it is stationary as it is to say it is moving.

There’s nothing in space to push away layers of the sun like that, like a ball of hardened sand through water.

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There isn't a medium that the sun is moving through, nothing is dragging on its material like would produce "waves of fire" in its "path". The movement is imaginary- only real when you're measuring relative to other objects. No motion is universal, this is the big revelation of Einstein's theories of relativity.

No, the sun and the material in it does not feel any affects of the motion. As far as the sun and planets are concerned, there is no "ahead" or "behind" for the motion.

* For the nit-pickers out there: yes, there is tiny (and I do mean tiny) effect from galactic tides.

This doesn’t apply to Earth right? Especially since it does move - by revolving around the sun

No. As others have said. The sun isn’t on fire and space is mostly empty, nothing pushing on the sun to leave a trail behind it.

It does apply to earth. All motion is relative to something else. How fast are you going right now? You may be sitting still and think, I’m not moving at all. Ok, but the earth is spinning, so now how fast are you going? Ok, but the earth is also rotating around the sun. It’s also part of the solar system, which is moving, but it’s also part of the Milky Way, which is moving. But it also is part of the universe, which is expanding. So how fast are you going? The only way to answer it is to measure your speed “relative” to another object

Kinda sorta. Charged particles being emitted from the sun creates the heliosphere.

Well, in a way maybe - but not like you think. It’s called the Solar Wind and it shoots out equally in all directions (usually) rather than leaving a path. It’s not fire(there is no fire on the sun) but it’s ionizing & non-ionizing radiation of many different types.

there is a heliotail, which is a comet-like tail that is inflated by the solar wind of particles streaming off the sun, but it's more of a tail of the entire solar system than just streaming behind the sun like you might be thinking.

I see! Thanks for the explanation!

Not so much a blaze of fire, but the Sun does shoot out particles constantly (mostly electrons and protons) in the solar wind. There's also solar flares, coronal mass elections, and solar energetic particle events that occur rather frequently.

The Sun does have a heliosphere, though, and it interacts with the interstellar medium (yes, there is a non-trivial amount of mass in the spaces between stars). Heliopause occurs when the pressure of the solar wind matches the pressure of the interstellar medium (at about 100 AU).

As the Sun travels through this interstellar medium, it leaves behind a heliotail that is the direction opposite the Sun's motion in the galaxy.

https://en.m.wikipedia.org/wiki/Heliosphere

It applies to everything. If you fix earth in one universal place, the sun revolves around the earth. Nothing really makes sense, because there are phantom accelerations everywhere (because a more truthful model makes the sun stationary, since it is the much larger object, and experiences less acceleration than the earth does) but aside from those phantom accelerations, which are all real accelerations that the earth is experiencing, which we are applying to the rest of the universe to force earth to stay still, all the other math still checks out.

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At a surface level: No. If you're imagining, say, a firework and the trail it leaves, with "sun-stuff" behind it - there's nothing like that. This has been covered in detail by other posts.

At a more detailed level: Yes-ish. The Sun is constantly emitting particles - not just massless light but also massive particles, the "solar wind". As the Sun (and the entire solar system) move through space, this creates a "wake" or elongated "bubble" called the heliosphere. Notably, this is much larger than just the Sun - all the solar system's planets are well inside the heliosphere. This diagram demonstrates the effect.

The heliosphere is invisible and undetectable to the naked eye or any "human-level" interaction; you need special equipment to detect the differences between it and the surrounding interstellar medium. From a human perspective they would both "feel" just like empty space.

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Sorta, we have indeed measured our motion and the motion of the galaxy against the CMB. That's the biggest "rest state" we can measure against.

Why do comets leave a path of ice in its wake? Isn’t that a similar idea?

This was such a good answer! Thank you!

thank you!

Thanks. I’m paraphrasing the explanation from a book called “Why does E=MC2?” By Dr. Brian Cox and Dr. Jeff Forshaw. The book is written to explain the theory of relativity in a way normal people can understand, and talks about the implications of that theory on the real world. Makes a hard topic easy and fun to understand, so if you are interested I highly recommend it.

Awesome I’ll for sure put that on my TBR

The ice tail from a comet is because the sunlight pushes on the ice. The tail always points away from the sun, no matter which way the comet is moving.

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The heliotail isn't comet-like. It's made up of particles from the sun, but it points in four directions, like a four-leaf clover. It is not affected by the sun's motion around the galaxy.

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Thank you, good distinction.

The reason I relate it as such is because a comet’s tail doesn’t trail parallel to its trajectory, but rather parallel with the sun’s rays. As the heliotail’s orientation and shape are determined by the Interstellar Magnetic Field’s direction and strength

I thought the heliotail's shape was more determined by the pattern of ejection from the sun. Faster particles from the poles, slower from the equator, in a "puffing" sequence.

I think you’re right about shape, but I thought the overall orientation/direction was as I said - I’m very happy to be corrected if I’m wrong.