Could a circular space station simulate the Earth's gravity by spinning at a certain velocity? (I have seen something like this in A.C. Clarke's 2001)
Asked by: John Dowson
Answer
Short answer is yes.
Here is the long version:
Earth's gravity, simplified to what happens at the
surface, says that the earth pulls at anyone with
a force given by:
F = mg
If F is in Newtons, and m is in kilograms,
g has the value of roughly 9.81 N/kg, and
it is called the acceleration of gravity.
Now, if we set a cylindrical space station in
rotational motion at a certain angular velocity,
anything that moves with it will need a centripetal
force to keep it rotating with the station. In
other words, the 'floor' will have to push a person
standing in it with a certain force, pretty much
the same way the floor has to push every person
up on earth. The magnitude of this force is given
by:
F = m^{2}r
Where m is the mass of the object, is the angular
velocity of the space station and r is the radius
of the space station.
Now, if we want to simulate Earth's gravity, we
require that these two forces be equal.
So:
mg = m^{2}r
^{2}r = g
Or
(2/T)^{2}r = g
T = 2 sqrt(r/g)
Where T is the period of rotation.
Given the size of the space station, it is then
possible to figure out how fast it must be rotated.
Let me give a few figures here.
For a radius of one mile, the space station would
have to rotate with a period of about 80.5 seconds.
For a 10-mile radius space station, the period
increases to about 4 minutes 15 seconds.
When you quadruple the radius, the period only
doubles. So, it would seem that a rather fast
paced rotation is required.
There is one caveat, however. Anything in motion
inside the space station will be subject to what
is called 'coriolis forces', which would not be
experienced due to gravitational forces. The direction
of the force is always perpendicular both to the
axis of the space station, and the direction of
motion, and its magnitude is
F = (2)/T * v * sin()
Where T is the period of the space station,
v is the velocity of the body in motion, and
is the angle between the axis and the
direction of motion in the body. So, the faster
the station rotates, the more the effect will
be. So, one should try to make the station
larger to minimize coriolis effects.
Answered by: Yasar Safkan, Ph.D. M.I.T., Software Engineer, Istanbul, Turkey
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'