Okay, a couple of quick questions regarding a story idea that's been percolating in the back o' me beedy widdle bwain for a while... I'd like responses from folks who can answer authoritatively re math & physics.
Story involves a large/mostly hollow spherical space colony/artificial world. Let's say it's about 1,200 miles in diameter, rotates on its north-south axis, ergo the "gravity" along the interior equator is Earth normal. Central light source in the very middle; hot but not unbearably so/no dangerous radiation.
Images below give a rough idea of what I'm talking about...
Question #1: How long would it take my protagonists to hit the interior surface if they arrive about 500 miles above the equator?
I know if the sphere had no atmosphere then theoretically my protagonists would fly along inside it...at least until the minimal mass of the hull of the sphere slowly pulled them toward it, or the light from the artificial sun pushed them away.
However...would the interior atmosphere still be relatively thick enough for humans to breathe all the way from the interior surface to the artificial sun?
Would the currents from this atmosphere push my protagonists along gently, or would they start dropping like a rock almost immediately?
Would they start slow and then begin picking up speed geometrically as they would on Earth (32ft p/s p/s)?
Question #2: How fast does this world (1,200 miles in diameter) need to be rotating for the equator to have one Earth gravity?
Would my protagonists be falling straight towards the interior surface, meaning whatever speed it was traveling at would hit them laterally like a freight train, or would they be gaining angular speed as they fell (perhaps due to wind currents) so they will be matching the angular velocity on impact?
For the sake of my story, would it be safer for them to fall in the direction of either interior pole rather than towards the equator? (I presume "gravity" would be considerably less due to angle of spin.)
For this particular story I'm looking more for plausibility than hard scientific realism here -- a handwaveum answer that lets my protagonists survive a freefall to the interior equator (into water, mushy vegetation, marshes, whatever) will work just as fine as a master's thesis in physics.