Would they have to be designed specifically for lunar gravity to maintain a 60Hz frequency for the purposes of a timepiece? Could one bring a crystal oscillator watch to the moon and keep accurate time?
How would solar power acquired on the moon affect timepieces plugged into an electrical socket on the moon? I'm guessing no difference here, or would there need to be something to account for in regards to the power grid?
The days when clocks work on the 50/60 Hz of the mains supply are long gone. Unless you have an old one. The trouble with them is the electricity companies were supposed to ensure that over a day there were the correct number of cycles in a day or whatever period was defined. So sometimes the frequency was allowed to vary slightly from nominal due to load and other factors in the generation process.
As
@Wayne Mack points out below most crystal based clocks use a 2^15 (32,768) based frequency. this is to make it easier to generate a one second period (divide by 2 - 15 times). However it's quite common to use higher frequencies derived from the microprocessor used in the system. This allows the reading of the clock to be synchronized to the instruction that take the sample of the clocks registers. Plus gives the opportunity for more decimal places. So if the u Processor had a crystal of 32,678,000 for instance, it would be easy to get a millisecond timer and so on for higher frequencies. It would take the uP only a few instruction cycles to read the time.
Again as Wayne points out crystals vary their frequency with temperature and to some extent variations in voltage across them. These are usually specified in parts per million per degree. It's possible to get crystals with an accuracy of +- 200 or even better.
On the moon the main problem would be the low temperature and it's almost certain a temperature controlled crystal would be needed (Just ensure it oscillates) These can be incredibly accurate (and expensive). 0.5 ppm isn't uncommon - since the temperature is controlled, variations caused by that are negligible - but they do consume more power. Phase loocked loops are also employed sometimes to multiply these frequencies inside the microprocessor. So the base frequency of the crystal might be 25MHz, but using a "PLL" the actual clock rate inside the chip could be many multiples of that frequency.
From my reading, I believe the oscillation frequency of a crystal is largely controlled by the make up of the crystal. Gravity does not seem to be a significant affect, "Acceleration effects including gravity are also reduced with SC-cut crystals as is frequency change with time due to long term mounting stress variation." Temperature and heat dissipation may be a more pronounced affect, "In a real application, this means that a clock built using a regular 32 kHz tuning-fork crystal keeps good time at room temperature, but loses 2 minutes per year at 10 °C above or below room temperature and loses 8 minutes per year at 20 °C above or below room temperature due to the quartz crystal." Atomic clocks appear to be a viable alternative, "Due to aging and environmental factors (such as temperature and vibration), it is difficult to keep even the best quartz oscillators within one part in 1010 of their nominal frequency without constant adjustment. For this reason,
atomic oscillators are used for applications requiring better long-term stability and accuracy."
Reference:
Crystal oscillator - Wikipedia
I once had to design a product to monitor the G forces involved when cars were driven into a wall. I had quite a time trying to find out if the forces would affect or even prevent the crystal working. Most of the people I asked were bemused by the question and I couldn't understand why no one would give me a straight answer (These were mostly the front line sales people).
Eventually I got through to a crystal designer who also seemed bemused.
"What are we talking about here?" he asked. What G forces are you expecting?
"Ooo, about 100G," I said.
After he stopped laughing, which I thought was a bit insensitive, he replied.
"Well our crystals are used in smart armaments. They get to well over 1000G."
Licking and ticking was mentioned.
