The idea of artificial gravity caused by rotation is based on a reaction to centripetal force, replacing gravity.
To simulate gravity, the spaceship needs to rotate, forcing the contents to pull towards the outer edge, creating a sense of weight.
In this case, the force is expressed by the formula:
F = mω²r = mg
It turns out that the angular velocity (ω) is established at the space station. In this case, at a distance (r) from the center of the ship, a force equivalent to the action of mg (weight) will arise.
From the above equation, it is clear that there are two options for influencing the value of simulated gravity:
• change in rotation speed (ω);
• change in circle radius (r).
The problem is that for a person who is standing on the floor of such a space station, the r values for the head and legs are different.
The legs and head are affected by various speeds and accelerations. At best, this can lead to the malaise. At worst, completely drain.
To avoid this, a very large r value is needed. The larger this value is, the smaller the deviations between the effects on the head and legs are (gradient).
These factors must be considered when planning such a system. To minimize the gradient, it is necessary to limit the angular velocity to 2 rpm.
If you translate this number into radians and substitute it in the original formula, you will be able to determine the minimum radius of a space station to simulate gravity equivalent to Earth.
g = ω²r
r = g / ω² = 9.8 (m / s²) / 0.209² (rad / s) = 224.3 meters
In general, the space station is very large. For comparison: the size of the ISS is 109x73x27 meters.
The main purpose of the ISS is to provide a laboratory for experiments, without the influence of gravity. Conducting research in space makes it possible to observe results that cannot be obtained on Earth.
There is another reason why in reality, there are no such stations. Only in science fiction, space programs are financed to a level sufficient for the construction of such impressive ships.