If you found out a way to produce a smooth icy surface on an ice moon like Ganymede, Enceladus, or Callisto, what kind of challenges would someone face if they tried to start ice skating? I figured you'd have problems with traction or staying glued on the surface in a low gravity world. Would this be possible?
First of all, the surfaces of these moons are relatively smooth; that is to say, given the resolution of our images of their surfaces, they look smooth from a distance but that isn't to say that the surface is ragged or textured in some way. If you look at pictures of the Earth from a distance for example, the oceans look smooth but they still have waves and in some cases quite choppy surfaces that just don't appear at that resolution.
That said, assuming for the sake of argument you could find a pocket of the surface that is smooth enough, there are a number of other challenges that would make ice-skating difficult. The issue with weight in the lesser gravity is actually the easiest to fix, just like bouyancy in scuba diving, you simply wear weights. You could even use skates that are already weighed down so that traction is better.
Of more concern is whether or not your skates could actually move on the surface. Enceladus for instance is supposed to have an ice coating of actual water, but it would be very cold on that surface. One of the reasons why skaters move so gracefully over smooth ice is that the friction of the blade actually melts the ice it travels over, and that ice either becomes slush on the surface or re-freezes, which is why ice skating rinks have to be regularly resurfaced.
On Enceladus however, it is so cold that the ice would probably re-freeze (if the friction had any effect at all) so quickly that it could freeze your skate in place on the ice. Given that the temperatures on that moon are estimated to be around -201oC, it's even doubtful that there would be enough energy in the friction of the blade over the ice to heat it up to above 0oC, and therefore get it to melt. As such, your problem may not actually be too little traction, but too much.
Finally, and perhaps most importantly, given that Endeladus has no atmosphere and is so cold, you'd have to be on the surface in a full space-suit. This is going to be bulky, heavy and may solve your weight problem in its own right, at least in part, but it's also not going to be super flexible and allow the movement that one needs to stay balanced on the ice.
So assuming that the surface really is smooth enough (and it probably isn't), that the skate doesn't stick to the ice (and it probably will), you're still going to be in the exact opposite of a figure skating costume while on the ice, reducing your ability to skate normally (let alone do anything acrobatic or artistic) to almost zero.
Let's take you at your word
We'll assume whatever technology is necessary to produce your skating rink has been provided. A nice dome, temperature control, a Zamboni, the works. What's left over is the gravitational difference between the moon and Earth. Would someone be able to ice skate?
Yup, no problem. But there are some gotchas.
An adult ice skating on a moon will weigh about the same as a child ice skating on Earth. So, from a very simplistic perspective, traction isn't the problem. The three primary problems are the adult's (a) mass, (b) height, and (c) strength. (You shouldn't be surprised that these three issues are tightly interrelated.)
The problem with mass is that it takes the same amount of force to move it around on a moon (or in space) as it does on Earth. All that's missing is the gravitational component that sometimes works in your favor and sometimes doesn't. Skating on a moon means the adult will experience the weight of a child. Since children can skate just dandy on Earth, the weight of a child (an adult) on the moon can skate, too.
But the mass is another issue. If the skater gets moving too fast, they may not be able to stop because the mass is still there and requires the same stopping force as it would on Earth. But, with less weight, the edge of the skate may no longer hold the mass of the adult in place.
Another problem is height, which in this case is a fancy word for "leverage." Remember all that mass we were just talking about? In an adult, a lot of that mass is a long way off the ground compared to a child. Attributed to Archimedes is the phrase, "Give me a place to stand and with a lever I will move the whole world." He wasn't kidding, leverage is a power multiplier, meaning a little force goes a long way. An adult's height could lead to the skater's feet stopping as expected, but their torso not stopping with them. The usual consequence is a sore bottom (but, with the lower weight, it won't hurt as much as your pride).
This is probably the greatest problem. An adult obviously has substantially more strength than a child (assuming equal weights, moon vs. Earth). That means an expected hop-and-spin might just land you in the bleachers. Or an expected turn might turn into an unexpected full stop. However, skaters would quickly learn how to "pull their punches" and exert less strength. The real problem is when they get back to Earth and all those atrophied muscles suddenly keep them from skating.
What this means is that an adult on a moon must skate like a child on Earth: slower, gentler, and with less self-consciousness.
It would depend on the temperature and the gravity.
Iceskating works (and ice is slippery) because of a very thin layer of liquid water on its surface. It's a combination of temperature differences at the interface and pressure applied on the ice's surface that make it possible to skate on ice.
If the gravity is weak enough that a skater's weight doesn't produce enough pressure, and/or the temperature is low enough, it can become physically impossible for ice to melt when the skates' blades come in contact with it. When that happens the ice stops being slippery and behaves like other types of rocks.
You could probably imagine workarounds in some edge cases, for instance by heating the skates' blades to overcome too low a pressure applied on the ice or too low a temperature.