what kind of action cameras are good for 1080p video onboard a high moving object(more than 800kph)? I'm working on a project that will have a camera onboard the object for FPV as it moves in the air at very high speeds. What kind of frame rates are good to transmit and/or record onboard the flight, and what kind of characteristics in  action cameras should I look for. I know asking for 1080p can be hard but nowadays cameras have improved. DO suggest compromises in different areas and their effects on the transmitted video. I'm new to community so do help improve the question with edits and help me out. 

EDIT: This will be onboard a plane so under 100-200g with mount and casing(etc) should be ideal for each camera. 30-60 fps of 1080p is more than good enough for FPV as well as other onboard cameras. We aim to supply electricity as part of the electronics onboard, so any battery it has is more an inconvenience and can be bypassed to maintain electronic supply. FPV maybe live(low latency preferred), but other onboard cameras can be just recorded. I found most budget action cameras(60-200$) are around 64GB compatible and 1080p video consumes about 20-40MB/s depending on the camera. Budget is flexible but for 3-4 cameras I have about 700$ but I can stretch by little it if needed. Should I focus on 720p if data consumption limits my flight time, and/or is there any way to have them store onboard a larger data storage system(?)
Thanks a lot. Came here on the recommendation from photography stack exchange.
The usual solution here, used by many pilots is actually the ubiquitous GoPro. They are robust, housings are built for most purposes and the tech is tried and tested, and compatible with everything. Solutions already exist for continuous power.

And the new GoPro 360 cameras will give you views in every direction - may or may not be useful for your use case.

There are budget versions/copies, but GoPro are the most robust I have used for high-g, high exposure uses.

If you are expecting extreme temperatures, then make sure your housing has the temperature control you need. That's what everyone does for mounting cameras on fast/high aircraft :-)