Our space ship has lost power, what happens now....

[Rive]

This gave me pause for thought, and might be relevant to the OP, so I brought it up in the physics subforum.

You've managed to open a nice can of worms there

And on that, I wondered how aggressive the Dzhanibekov Effect would be on a ship half a kilometre long? Would it impart enough force to be structurally damaging?

Usually 'classic' spaceships with that rocket-like longer-than-wide shape are supposed to get some really nasty gravity at both ends, and to make that worse it won't match the original so the structures and internal orientation/equipment are not expected to handle it properly.
The expected long walkway/transport corridors along the ship axis becomes deep wells, to start with.
If it's not some 'classic' but a well-thought 'design for emergency' kind of ship, then things can be different, of course.

 

[Melbourne Guy]

If it's not some 'classic' but a well-thought 'design for emergency' kind of ship, then things can be different, of course.

It is not classic, more a large rectangular box, @Rive, but damage like this hasn't happened for centuries. As one character muses as he plans to scupper his troop carrier, "Ships were either retired and scrapped, or they suffered catastrophic failures, or, if they were naval vessels, they were destroyed in combat."

Specifically, the lose of artificial gravity is so uncommon that nobody designs for it anymore.

 

[Rive]

Then that crew is just ... screwed. Some corridors are now wells: some are chimneys, and they are without climbing tools. Some decks might be partially accessible if they are lucky, but for most areas it's like an upside down house (built in a rolling barrel)...

 

[Melbourne Guy]

Then that crew is just ... screwed

Plot spoiler...they are rescued

But the ship is operating in microgravity, so it's not as bad as all that, plus, the surviving crew are in localised pockets of surviving infrastructure. And I only need to keep them alive for a relatively short amount of time before they are saved. Still, most of the seven hundred and sixty crew do die, so I guess your observation holds, @Rive!

 

[AlexB23]

I'm about 25,000 words into my latest novel and the story arc is coming together nicely, but one aspect I need thoughts on please is what would happen inside a spaceship that has been grievously damaged in battle to the point that it has been abandoned by the fleet as a 500m long wreck.

Specifically, there is no power so the only light is from emergency globes and there is no gravity (my novels have AG), and I am wondering what happens to the air?

I'm assuming that in zero gee it would need fans to circulate, but does that lead to adverse effects on the few crew who survived? Or would it not matter much, as the ship's heat drains away and the crew freeze to death...

Well, assuming your spaceship is computerized, an error code can be displayed on the screens inside the ship displaying what systems are damaged. There is a technology called a bistable LCD that can display the last data on the screen without requiring a constant electric current. My alien race has that technology and more advanced forms during the 21st century through 31st centuries.

For retaining an atmosphere inside the ship, I am not sure. Maybe a special foam inside the walls that can expand and cover the holes in the ship.

 

[DaveC426913]

There is a technology called a bistable LCD that can display the last data on the screen without requiring a constant electric current. My alien race has that technology and more advanced forms during the 21st century through 31st centuries.

My Kobo eReader has that technology...

 

[Lren Zvsm]

There would be another concern beside the air. The spaceship, having lost all power, would be moving at the speed it was moving when it lost power and in the same direction FOREVER unless help came. Would its trajectory lead it into enemy territory? How easy would it be for the rescuers to know the direction in which the crippled spacecraft had been knocked off course when it lost power?

 

[DaveC426913]

There would be another concern beside the air. The spaceship, having lost all power, would be moving at the speed it was moving when it lost power and in the same direction FOREVER unless help came. Would its trajectory lead it into enemy territory? How easy would it be for the rescuers to know the direction in which the crippled spacecraft had been knocked off course when it lost power?

Well, yes. But I think the OP is looking in the shorter term. Of course, if they don't ever get power back, they're gonna die long before they have to worry about where they're headed.

 

[AlexB23]

My Kobo eReader has that technology...

That is nice. :) Hopefully one of these days we could get HD full color bistable displays in real life.