I’ve been reading Kim Stanley Robinson’s “Mars” books – I’m about 3/4 of the way through Blue Mars at this point – and I got to wondering about a theoretical space station. The idea I had is for an agricultural station. Something wheel shaped, rotating around a central axis to produce gravity on the inside surface of the drum, and angled so that the sun provides natural light for the inside of the wheel for half of the rotation. It’s a fairly standard Sci-Fi design, but the tricky part of this particular one is that I wanted the period of rotation to be 24 hours.
And that got me to wondering how big the station would need to be. Fortunately, a quick search turned up a fairly simple equation for calculating centrifugal force:
G = V2 / R
Where “G” is the gravity, “V” is the velocity of rotation and “R” is the radius of the station. The author there even gives a handy transformation of the function to calculate things in rotations per minute for any needed value:
acceleration = (RPM x 4 x π2 x R) / 602 feet/sec/sec
All we need to do is plug in our values for acceleration (32), RPM (1/1440) and solve for “R”:
R = 41,472,000 / π2 feet.
That puts the wheel at roughly 1590 miles across. This is going to be a damn big space station.