time base calibration

But not impossible to make. See Wikipedia, art. "gridiron pendulum". Ask on rec.crafts.metalworking for tips on making it.

I enjoyed reading the following on that subject:

Jon

An old HP 5328A counter with option 010 will do this without breaking a sweat. You should be able to pick one up for no more than a couple hundred USD on ebay.

I don't know the answer to that---but I do know it would have to be calibrated and adjusted for its geographical location. The gravitational acceleration can vary by up to 1% over the surface of the earth.

I think that most pendulum clocks had an adjustment screw to allow this correction.

Let's look at the problems with gravitational measurement with the mass-on-a-spring approach.

suppose you have a suspended mass of 1kg and a spring constant of 1.0m/kg

A 1ppm change in gravity will result in a position change of 1x10^-6m, or about 0.001mm.

I suspect that you could design a system to measure that deflection pretty accurately---probably using lasers and interferometry.

The problem is that you have just built youself a nice seismograph. Now you have to add some very good low-pass filtering to your results. You will also have the same temperature corrections problems as you would with a pendulum.

In any case, it's probably worthwhile to look at the specs of the Worden gravity meter. It can measure gravity changes with a resolution of one part in 100 million (10ppb).

Here's a page about the construction of a simple gravity meter:

Mark Borgerson

Maybe, but you can also use multiple cycles, which is also going to reduce the problem you mention below, as it both increases the mechanical tolerance, and shifts the sample time longer than typical earth shudders.

A simple optical gate will have a fast aperture time, whilst laser schemes take time to resolve, and probably do not like too much velocity.

A laser scheme that was able to track the full cycle and deliver many samples per cycle, would be nice (but sounding rather costly)

-jg

Yes, - but perhaps a calibrate in-situ could simplfy that - ie a deliberate (but slow) thermal cycle could be run to check time/temp profiles.

The other question is would this Gravity deviation be once a day, or twice a day as Tides are. And what shape would the deviation take ? Tides are close to sine, but that's a close to resonant response.

-jg

Yes, or 10us over 100 swings, or 100us over 1000 (etc)

Good point on the rotation. Possible solutions : Run the pendulum for only 100-1000 cycles, so the rotation effect is reduced. [even a wider slot-sensor for the impulse sense, than the time sense ?]

Or, build a tracking table, that servo-corrects the pendulum sensors, so the swing slices them always at 90' ?

A camera is another possible sensor, but could that give enough sample points to infer the time with enough precision. (Frame rates are slow)

-jg

Sorry, I didn't look at the price! I use the Jupiter units I got from Timeline.

If you need the higher frequency than the Jupiter's 10 KHz, you could multiply it up with a phase locked loop.

Don

Twice in 24 hours. It's quite surprising at first, but the sign of the effect is the same at noon and at midnight, always pointing upward. The tidal force tries to pull the earth apart in the direction pointing to the moon (or sun), and squeezes it together orthogonal to that. It wants to turn a circle into an ellipse.

Not really. The pendulum can have its plane of rotation fixed. The classic precision pendulum is built that way, resting on knife edges protruding from both sides of the arm.

Years ago my older brother described a similar system. I never saw it. He said that recording the seismometer data and adding all the recordings together, synchronized with the hammer strikes, resulted in the reflections rising up out of the random noise. I wish I had seen it.

I ran across a mention of very accurate pendulum clocks that were used to synchronize transmitting stations for early LORAN. These were Shortt Clocks. The Shortt clocks were used until the 1950's. A Google search for Shortt Clocks turns up interesting information on building one.

Don

Stunningly brilliant. Thanks for the link.

I haven't done the math but given that the sun and moon create tides of very roughly the same amount, the 100:1 sun/moon ratio looks a little strange to me.

This does look measurable to me, with some care.

There are commercial gravitation meters that could easily measure the changes here. They use masses and springs, I think.

Good load cells are phenomenally linear and stable over time and temperature. A load cell and a weight, in a reasonably temp-stable environment and with a good 24-bit delta-sigma adc, could be data logged for a month or so. Signal analysis of the data should easily pull out the solar and lunar signals.

John

Interesting idea, John. Given, that the [land-]surface of the earth lifts up by as much as 60cm when the moon passes over, one should think that with a 24bit converter, resolving as little as a 10millionth this effect could be noticeable with a loadcell.

Rene

Thought: why measure the vertical component, a small variation on top of 1G? Rotate the sensor 90 degrees and measure the horizontal (east-west) G force. That will go positive and negative as the sun and moon circle the Earth (which, as we now know, is the center of the universe.)

You could do that with a load cell, or a stationary pendulum with, say, a capacitive displacement sensor, which is simple and can be incredibly sensitive.

OK: a vertical metal plate hanging from a couple of steel wires, capable of swinging east:west. It's between two fixed plates, forming two capacitors, with a very small clearance. Add a little electronics and it should be easy to measure the sideways deflection caused by the earth and the moon... and a lot of seismic stuff for extra fun.

John

Hmm, because that was the original challenge?

That, of course, describes a seismometer. Which will measure all kinds of things, including the passage of cars nearby, people walking around near the apparatus, and of course earthquakes. Using one to measure the tidal force would shift the burden from mechanical precision to signal processing.

Not doubting the numbers, but it would seem that 60 cm. movement on a regular basis would be causing temblors every time the moon passes overhead.

Was it?

Except that conventional seismometers are AC coupled and don't work down to microhertz.

John

Not really. We're talking about 60 cm compared to about 600000000 cm. That's a 1e-7 change. And we're talking about an effect that works the same way on *everything* under the sun (and moon), and with very small gradients. So there's no relevant force building up between neighboring rocks. It's not like some external force were kicking the continents upwards from below twice a day, which would tend to damage the place where such kicks hit.

One slightly famous, inadvertant measurement of earth tides occured in the huge particle accelerator LEP at CERN (Geneva, Switzerland). This machine, though 27 km in circumference, had to be tuned and monitored so precisely that they found they had to compensate for the deformation of the underground tunnel by tidal forces (in addition to the lake's water level and movement, and the ground currents of a high-speed train line nearby).