Homework Help: Science

Posted by Jjong on Saturday, January 21, 2012 at 3:41am.

If the variation in g between one's head and feet is to be less then 1/100 g, then, compared to one's height ,what should be the minimum radius of the space habitat?

Science - drwls, Saturday, January 21, 2012 at 7:46am
Let the habitat radius be R and the person's height be H.

Assume that the "gravity" is established by rotating a cylindrical or wheel shaped space station, with radius R. The actual value of g will be deterimned by the rotation rate, w.
g = R w^2.

g(head)/g(feet) = 1.01
= R(head)/R(feet)
= (R + H)/R = 1 + (H/R)

H/R = 0.01
R = 100 H (or higher)

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