Question

Consider a space habitat that consists of a rotating cylinder. If the variation in g between one's head and feet is to be less than 1/105 g, then compared to one's height, h, what should be the minimum radius of the space habitat? (in terms of h)

The centripetal acceleration is proportional to the distance from the spin axis, r. If the feet are at r, then the feet of a person of height h would be at at 104/105 r = .9905 r

(r-h)/r = 0.99048
h/r = 1 - .99048 = .00952
R = 105 h