# For a very large rotating space ship, how deep would the 1g centripetal force effect be?

Assuming some devastating event will destroy every habitable planet in the system and we have to evacuate. We build a fleet of spaceships 200 miles long and 50 miles wide. Everything from earth we don't take with us will be vaporized so we need to simulate all the interconnected layers of the oceans as well as surface life here on earth. Assuming the cylinders are hollow in the middle, with a hydrogen ramjet principle for thrust. At less than 1/10 g acceleration, would the aforementioned 50 mile wide cylinders have the required 1g simulated gravity for 3 miles of depth for ocean life to survive on this ship?

• Also, are you requiring that the cylinders (assuming you meant that the spaceships were cylindrical) have constant simulated gravity for some region of depth? Because that's impossible. May 26, 2017 at 23:37
• It is not necessary for the cylinders to be propelled. They will keep rotating at constant speed without any thrust. May 28, 2017 at 8:33

The effective "gravity" goes by $$g_{eff}(r) = \omega^2 r \;,$$ where $\omega$ is the angular frequency with which the ship turns and $r$ is the radius at which you measure the effective acceleration.
Obviously it will only be exactly $1\,\mathrm{g}$ at one radius, and it varies linearly as you move away from that point. It is up to you do determine how much slop you are happy with, and from there figure out the necessary size of the craft.
• So to conclude, the thickness can range from $50 \times 1.03=51.5$ miles ,(where you would feel $1.03g$) to $50 \times 0.97=48.5$ (where you would feel $0.97g$). So total thickness of livable spaces 3 miles May 30, 2017 at 13:16