Can Spanking Happen in Zero or Virtually No Gravity?

I think someone is confusing zero or low-gravity with non-atmospheric?
Yes, if we get into the pedantry of physics, an atmosphere is likely to need some gravity to stop it literally flying away, but low-gravity might well have a breathable atmosphere, so then the problem is only one of action and reaction.
If the spankee were secured in/on a spanking bench and the spanking bench were secured to the ground, then the spankee is going to stay in position until they are unfastened/derestrained.
So then to the spanker....
Velcro has been mentioned and a large rug or carpeted area (securely fastened down) under around and behind the spankee and spanking bench, with the pile made of velcro and the bottom of the spanker's footwear being also coated in velcro, would serve perfectly.
Lower gravity would't affect the impact of the hand or instrument used, in fact the lack of air resistance might make each strike harder.
What would change is the blood flow to the buttocks and that really would be interesting as to how and what. Likewise the rippling of the buttocks as each strike hits would be different.
If one were striking horizontally, then the action and reaction would be very similar to on earth, it's when one is striking downward or upward that the difference would be marked.
Impact utensils such as paddles and canes would work at least as well under these circumstances, but whips and floggers would not.

BlooDenim
If you were obliquely referring to me, do please use my name in the future, instead of as "someone." If I was addressing you, I'd extend the same courtesy.

A) No. I was not confusing zero or low-gravity with non-atmospheric. However that does bring up an interesting concept, as the moon has low gravity, and has an "atmosphere" but it isn't breathable. Kudos for thinking that up.
B) I just go to greater creative extents to make the required proposal by the OP work, while whittling away what I see doesn't work while staying within the stated parameters.

1) If you resort to using straps to restrain either one or both people, then you might as well have gravity, and the point of no gravity becomes moot. The only benefit of using restraints on a low gravity planet would be seeing ripples on the skin, as you pointed out. I can't express how uninteresting that is.

2) Since the circulatory system is a self-contained system (basically a closed hydraulic system), I don't believe it would be significantly affected by a lack of gravity. The heart wouldn't have to beat as hard since it wouldn't have a "down hill/up hill" course to pump blood, but I don't see how that would be significantly interesting, nor impactful on the proposed concept. Breaks in the capillaries from impacts, wouldn't become important until the sealed skin breaks, but the blood would still cling to the edges of the wound(s) and congeal to reseal the breaks in the skin as normal. Unless an artery was broken, but there aren't any arteries in the area of the buttocks to worry about.

3) Yes, if there were no air to cause resistance to the applied hand then the impacts would be harder, but "no air" means they would have to have breathing apparatus which, in turn would mean if the masks were dislodged then suffocation would occur. Lack of air, usually also means lack of air pressure, thus the participants would likely "bleed out" from eyes, etc as the circulatory system has a blood "pressure."

4) In my original reply, I was thinking "where is there no gravity?" which means in space (as you can't have a planet with no gravity). Having a space suit would be cumbersome, and subsequently cause large amounts of padding to inhibit the spanking to meaningless, thus being in open space, would require being inside sphere (like in a space station), and being located in the exact center of the sphere, would allow a) breathable pressurized atmosphere and b) zero gravity. However, the action of a spanking would still cause a tumbling fall in chaotic directions, so the sphere would need to be immense to avoid the same problems I pointed out earlier on a low gravity planet.
However the space station would have to be self correcting to keep the two participants at the center of the sphere, to avoid impacting with it's surface.

My use and understanding of "spanking" is the old fashioned form, as use of utensils would then be change the action to a cropping, flogging, or paddling.

Lonewulf If you were obliquely referring to me, do please use my name in the future, instead of as "someone." If I was addressing you, I'd extend the same courtesy.

Sir, you credit me with too much thinking. I was trying to contribute, not detract.
No offence was meant, but I will apologise in any case as I have no desire to cross swords with anyone on here.

You are correct about zero atmosphere meaning breathing apparatus and the spankee trying not to hold their breath or just breathe normally, as one strives to do in scuba gear, whilst being punished would prove trying if not impossible!

About using velcro, I was trying to make spanking possible in low gravity, so if such would emulate gravity effectively, then we win? Well that was what I thought.

I was talking about a low-gravity with atmosphere planet. (Other planets are available).
Ok, "Where there is no gravlty" Spanking in free space would be as I think was said, laughably impossible. In a space station, we are back to restraints or similar impossibility, though at least we could have freedom to breathe and wear what clothes (or lack of) that we wanted.

Regarding the circulatory system, I will not stand firm as I have no medical qualifications, but I was reliably informed (I read it in one of my many forays into space exploration) that zero gravity changes much about the circulation as the heart, arteries and veins are designed to work under Earth's gravitational pull and do not function as normal in space. That is why I would be very interested in research to see how bruising or even redness/blushing happens in zero gravity.

Spanking does by and large mean application of hand to bottom, but is extended to cover many forms including usage of utensils, were this not so, then the term "Hand-spanking" would be a tautology.
Such is a personal preference and certainly not worth arguing about, but I do take your point about cropping, caning, flogging, paddling etc.

I do hope we haven't deviated from the hopefully amusing OP?

Using straps is not the same as having gravity. One big difference is that you can orient spanker and spankee in some pretty creative positions that are not really practical in one-gravity. For example, imagine the spanker on a spanking bench...no different, right? But there would be no reason the spanker couldn't be hovering over the spankee's back, parallel to the spankee's torso, head to tail, and striking "down" so that the spankee's sacroiliac would be close, the sit spots a little farther, and the back of the thighs at the edge of what the spanker could reach. You might be able to do something like that in one-g if you built a shelf over the spanking bench for the spanker to lie on, but it would be quite awkward. In microgravity, easy-peasy.

Long term, in microgravity, there are numerous changes to the body. Body fluids tend to pool in the head and feet (and hands, somewhat). That's why astronauts have a perpetually slightly stuffy nose on orbit, and why they like spicy food up there (easier to taste when you're nose is a little stuffed up). There is very little difference on the circulatory system, although cardiovascular fitness drops more rapidly in microgravity than in one-g in the absence of exercise. That's why you see astronauts working out at least an hour a day, more likely an hour of cardio plus an hour of resistance exercises using bands similar to a bowflex machine.

I don't have a lot of data, but I don't believe contusions (bruises) work much differently in microgravity than in one-g. I would guess reddening of the buttocks works the same way.

Spanking in vacuum...it's just not going to happen if participants are wearing spacesuits. Someday we may have skin tight spacesuits which would allow a spanking, but not in the foreseeable future. Since we can't breath very long in a vacuum, the effect of no air resistance on spanking implements is likely moot.

But here's an interesting possibility. It's definitely possible to expose only parts of the body to vacuum for short periods. Imagine that you get a "hickey" over any exposed body part. Now, imagine the seat of a spacesuit being out, or perhaps a hole in the hull of a vehicle that gets sealed by a butt (the great master Robert Heinlein actually did a story based on this). I would expect any spanking on that exposed body part to be greatly amplified by the "hickey" effect.

Finally, I just want to say every current space vehicle has internal restraints and velcro everywhere. The last time I was in a Shuttle cockpit, some walls had little 2" squares of velcro every 8-10 inches or so, forming a big grid. And of course everything from pens to operator manuals to schedules also had velcro all over them. Since it's pretty much impossible to get any work done if you're floating away from the worksite, there are portable restraints that lock into the walls on the ISS. In the lab, every rack has a bunch of sockets running along the edges, a socket every inch or two. There are grab bars that span the rack and can be plugged in on each side, there are foot restraints that can be plugged in at the bottom or the top, the whole inside of the vehicle is just coated with this stuff. There will always be a way to rig up some sort of restraint to keep a spankee from floating away, if that's a concern.