Back in the early days of the space program, every country who was developing rockets to send up to space needed to test the survivability of those rockets. Instead of sending up people right at the start, pretty much every country in the space racer was sending up animals as a lower-risk alternative. There were a couple of cats sent up to space, but dogs and monkeys were preferred, generally because they could be better trained than cats. The French sent a cat called Félicette into low orbit on October 18th, 1963; Félicette had a successful 10 minute flight (5 minutes of which were without gravity) and survived her round trip.
Cats, in general, do not like zero gravity, as this video from the Air Force of yesteryear proves. They find it just as disorientating as people do in their first time in zero gravity. But if you were to put a cat in space, their hair should behave more or less the same as people’s hair in space.
On the ground, the force of gravity helps pull all hair - short or long - towards the ground. As you might expect, this is particularly noticeable for long-haired cats and long-haired people. People and cats with short hair would be less inclined to say that their hair points downward, and might notice less of a change. In both long and short haired cases, the lack of gravity will mean that each hair will float freely away from your head. This doesn’t usually change the appearance of people with very short hair by very much, but people with medium to longer hair notice a dramatic change in the way their hair behaves - their hair will tend to expand outwards into a cloud around them.
This is Marsha Ivans, an American astronaut, in space, and the most dramatic case of space-hair I could find. (Normally, she looks like this.) If you apply the same principle to cats, your medium to long haired cats will come out looking much more Pomeranian-y than usual, as their hair puffs out around them. Short haired cats will look a little bit fluffier, but it won’t be as extreme a change.
As far as how loose cat hair would behave once shed in space, we can once again look to how the astronauts take care of their own hair. Astronauts have to use a vacuum as part of their shaving routine to make sure that sharp pieces of hair don’t start floating around the space station, and they also have to be careful when washing their hair to not let the loose hairs escape their towels. There are two reasons for this precaution. First, wandering hairs can clog up the intake of the air filtration system on the space station. To keep the filters clean, the astronauts would have to be very conscientious about vacuuming out the filters, and they would probably need replacing more frequently, given the way that cat hair can work its way into fabric. Secondly, and more of a direct problem for the health of the astronauts, loosely floating hairs can float directly into the eyeballs of the astronauts, causing significant irritation. They can also be inhaled. Neither eyeballs nor lungs like foreign particles very much, and the irritation from either of those could keep the astronauts from doing all the science they have to do while in orbit.
So both the cats and the astronauts will probably be happier if we leave them safely on the ground. The cats will be much happier with gravity around, and the astronauts will be happier without cat hair in their eyes.
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