I am trying to make an astronomical clock. I need a reasonably inexpensive method of turning a clock shaft 360 degrees in one sidereal day (about 23.93447 hours), and a way of turning the shaft 360 degrees in one Lunar tidal day (about 24.84111 hours).

I did stumble over a quick and dirty way to do it here:
http://adsabs.harvard.edu/full/1988JBAA...98...89M
http://adsabs.harvard.edu/full/1987JBAA...97..348M

Basically one takes a dirty cheap quartz kitchen clock movement, and swaps the quartz oscillator for one that will turn the hour hand at the desired rate. You use three separate movement, but that's OK, they are cheap.

What I want to know is if anybody knows a good source of oscillators?

In the design, the author uses a 24 hour movement for the mean solar day hand, and 12 hour movements for the sidereal and lunar hands.

I gather that the standard oscillator for a 12 hour movement is 0.032768 MHz (2^15 Hz) since it can be easily binary divided into one second.
If I have done my math correctly, this means that a sidereal 12 hour movement would need a 0.032858 MHz oscillator, and a lunar 12 hour movement would need a 0.031658  MHz oscillator.

(this will make a sidereal movement that does 360 degrees in 1/2 a sidereal day, but a 2:1 gear train can turn it into the desired 360 degrees in 1 sidereal day).

Anybody have a source?

There are any number of ways to generate fairly exact frequencies, including tunable oscillators (quartz and other) and direct digital synthesis, starting with a "round number" oscillator. You could, for example, start with a microcontroller running on a 16 MHz clock, and have counted down output, once per "sidereal second" -- on average -- to advance the second hand on a clock.
What I don't understand is what you're actually trying to do. There's no one single type of oscillator, rather there are many, many different types suitable for many different applications. If it's a telescope drive that you're after, a kitchen clock mechanism is probably not strong enough. If you're trying to drive a microcontroller in the multi-MHz range, then you'll want a different type than if you're trying to drive that, and so on. Even for modding a kitchen clock, you probably need to match the crystal capacitance to the one that it normally uses.

In any case, you don't necessarily need to find a crystal at the right frequency. There are any number of tunable (VCXO) crystal circuits. Most of these are easier to work with in higher frequency versions, performing suitable division. You can also get crystals custom cut at any frequency that you like. You can also just get a kit: http://www.mtmscientific.com/sidereal.html

Thank you!

Basically, I'm trying to make a crude kindergarten version of this
http://www.negspace.com/wordpress/category/celestia/
but looking more like the Stage Five here:
http://www.almagest.co.uk/middle/astclk.htm

So there will be a Sun hand, a Moon hand, and the spinning ring with the zodiac on it. The Sun hand will spin 360 degrees every 24 hours (1 mean solar day), the Moon hand will spin 360 degrees every 24.84111 hours (1 lunar tidal day), and the zodiac will spin 360 degrees every 23.93447 hours (1 sidereal day).

I was planning on using high-torque clock movements, since the zodiac ring will be larger than an average clock hand.

I was trying to cut costs and accommodate my relative lack of skill by using inexpensive kitchen quartz clock movements. I toyed with the idea of calculating new gearing and using a rapid prototype service like Shapeways to cut new gears, but discarded that as impractical (I would not only have to make new gears, but make ones that would fit into existing pivot holes). The "replacing the oscillators" trick looked like a relatively simple solution, if I could find a source of appropriate oscillators.

I have been told that I could save myself a lot of grief by biting the bullet and using an Arduino to drive three stepper motors. I am looking into this, though it will significantly raise the part cost, and I would have to program the control code, plus figure out a way to allow setting the hands.

If you can find high-torque movements, everything will probably be strong enough, but it's not necessarily easy to replace the oscillator in any given movement. You may need to physically look at it first to see if this is possible.

Creating all of the necessary gearing through shapeways is a neat idea, but potentially expensive, as are stepper motors. A possible compromise would be to use the *motor* from the digital clock movement, but to drive the motor directly from a microcontroller. That would save quite a bit on motor cost, and you wouldn't need to add stepper motor drivers.
(And, you don't need to use an Arduino, there are cheaper ways, starting with a bare microcontroller like the ATtiny2313, and $5-$22 in parts for a parallel port, serial, or USB programmer.)

Thank you, these are good leads. I'll explore them.
Thanks again!