I apologize for this being way off topic, but there appears to be some smart folks here and I thought I would ask a few questions.
If a regular pendulum clock, which keeps quite accurate time, were taken from the Earth to the Moon and the correct time set into the clock and the clock was restarted, would the clock keep as accurate time as it did on Earth?
Would the clock's three weights have to be pulled up every 7 days as mine does?
Would the lower Lunar gravity make any difference in time keeping?
If so, which way and by how much?
If not, why not?
Hoyt W.
p.s. The Sun will rise in the East regardless of the above.
Looks like your question is how gravity affects a pendulum. A pendulum's movement is caused by gravity. Since a pendulum is just another falling object it should fall with the same acceleration as a free falling object (neglecting friction). An object on Earth will fall at 32 ft/sec^2. An object on the moon will fall with (I think) with 1/6 that acceleration, and
1/6 as fast. (An object in space, without gravity, will not fall at all). So a pendulum on the moon will keep time more slowly than on Earth. It seems like it should be 1/6 as fast, but I don't know exactly how the clock works, so maybe 1/6 isn't right.
So the clock time will slow down in direct proportion to reduced gravity. A pendulum about 1/36 (or so) of the length would set it right though, as the time is also proportional to the square root of the length.
It'll also stop working pretty quickly. The moon's atmosphere is a hard vacuum, and a dusty vacuum at that. Vacuum system lubrication is _difficult_ (many satellites lost because of it). Even low vapour pressure oils boil away in the vacuum and you're left with a sticky goo that jams mechanisms. Run the bearing clean and dry and you may get metallic welding instead. Then if you do find a bearing that works, the lunar dust is reputedly a real hazard for any long-term mechanism. With no air or moisture, there's not much to lay the dust and fine dust gets everywhere (Apollo suits started to show damage in just a few days)
They'd descend at exactly the same rate (in clock hand-movement terms) as on Earth. They may also need to be made heavier, as their mass would stay the same but they'd only have 1/6th of the weight - is this still enough to drive the clock ?
This usually shows up in about an 8th-grade science class.
The _stability_ of the time tick will be unchanged.
The _frequency_ will be lower. By a factor of about 2.42.
The weights have to be pulled up after the same number of cycles of the pendulum. Which will take about 17 days on the moon.
The frequency of a pendulum is proportional to the square root of the local gravitational constant.
Thus, since Lunar gravity is _less_ than that of Earth, the frequency will be lower. And the clock will run slower.
"How much?" The factor is the square root of the ratio of the gravitational field strengths. A quantitative answer is left as an exercise for the student.
The others are good references, but this might be simpler and to the point: Look at the period being proportional to the root of (l/g). This means that it is proportional to the length [gets longer as the root of the length increases, not important here since that won't change] and inversely proportional to the root of gravitational acceleration, g, as measured on that lump of dirt.
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the period will increase [slower clock] as the gravity decreases, and is measured by the root of that value [about 1/6th Earth's gravity.].
Look at it this way: It takes longer [for the pendulum bob] to fall the same distance on the moon.
So, was this your son's weekend homework assignment? :-)
Think tides. They would be much greater on the moon, due to the greater gravitational attraction of the Earth. The gravitational attraction of the Sun would have a greater effect as well - while it would be the same on the Moon as on the Earth, it would be greater proportionally to the Moon's own weaker gravitational force.
Other than those "outside influences", the pendulum should be just as accurate on the Moon as on the Earth. Slower, but just as accurate.
Jeweled bearings, sealed case. It should run *more* accurately in a vacuum. Remove air and you remove a whole set of variables.
24 hours unwinds the same amount of cord.
How complex is the mechanism? Does it drive three hands, or one?
Or is it just a pendulum, which can by itself be considered a clock. You can read time simply by counting the beats. Hands add nothing more than convenience.
John, I was agreeing with you up top that it would be less accurate, then at the bottom you said, in effect, that it would be just as accurate.
Did your fingers stumble or am I not understanding you? How could it be just as accurate if the pendulum has a slower cycle rate on the Moon? I am not trying to pick a fuss, but I fail to understand your point. And I do want to understand.
Accurate in the sense that it will be self-consistent; that is, an hour measured this week will be the same length of time as an hour measured last week, next week, or next year (assuming that you keep the clock wound).
Inaccurate, in the sense that each hour measured by the clock on the moon will actually be about 144 minutes long, and thus the deviation from "correct" time will grow continuously.
So a pendulum clock designed for use on Earth, moved to the moon, will keep time consistently, and could be considered accurate for lunar timekeeping, as long as those who use it are willing to agree on a new definition of "hour". Problems occur only when comparing the time shown by such a clock to the time shown by other timekeeping devices such as an Earth-based pendulum clock or a battery-powered digital wristwatch.
-- Regards, Doug Miller (alphageek-at-milmac-dot-com)
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I think maybe the terms "accuracy" and "precision" would be helpful here. You could say the clock has excellent precision, in that it will measure an hour almost the same exact way every time. However, its accuracy is poor, because it will not measure an Earth hour very well at all. Precision signifies how repeatable or closely matched measurements are to an average. Accuracy signifies how close those measurements are to the true value.
Father Haskell, you raise several interesting points. I understand the dry bearing wear problem in vacuum since I worked for Dr. von Braun for about 20 years before he was forced to leave Huntsville.
With the lower gravity on the Moon, dust would settle in the near area, but more slowly than on Earth, and not be blown about at all since there is no Lunar atmosphere of any significance. There are no winds on the Moon. [well, the Solar Wind, but that is another topic entirely] AFAIK, moisture has nothing to do with time keeping per se.
"24 hours unwinds the same amount of cord."
I assume you mean on the Moon as well as on the Earth. On the Moon, I now think the clock would unwind 1/6 of the cable per a real 24 hours. so we seem not to agree on that point.
IMHO, you have missed the point. I would agree with you IF the clock kept the same time on the Moon as on Earth, but I now do not think that it would and other reply posters seem to say that as well. I believe that it would take about 6 x 7 days for the clock to run down, assuming that it now runs down in 7 days here on Earth - or in that neck of the woods. In other words, the pendulum would move more slowly and there would be fewer pendulum cycles, or ticks, per real minute on the Moon. Ergo, the clock would be inaccurate and run slower and the hour and minute hands would correspondingly also move more slowly.
I think it matters not how complex the mechanism is or how many hands the clock has. The atmosphere and moisture are not factors because I had assumed the clock would remain inside a manned Lunar Lander of some kind. I did not state that assumption and that is my error. So forget about atmosphere and moisture - or lack thereof outside of the Lander. The clock would not be exposed to the Lunar environment - other than the lower gravity.
My Howard-Miller GF clock has 2 hands and 3 weights actually.
Thanks for clearing that up Doug. Consistency is a good clarification, STS, to the use of the single word of accuracy. I learn something new every day - or try to.
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