G'day folks

A couple of questions from a perplexed Downunderite.

1. Foucauld's Pendulum is a great tool for showing the rotation of the Earth. I understand the pendulum's motion is related instead to that of the "distant stars".

But seeing as the distant stars are themselves not fixed, what provides the reference for the pendulum to swing in?

I suppose another way of looking at it would be this: Imagine we set up a pendulum which would last for 50 million years, the time it takes for the Solar System to complete a quarter lap of the Milky Way galaxy. What change would this cause in the pendulum's swinging?

2. A satellite is placed in a polar orbit around the Sun, such that the plane of the orbit is aligned with the centre of the galaxy. Will the plane of the orbit continue to point at the centre of the galaxy over that 50 million year quarter orbit? If not, how will the orbit change (assuming no effects from planets etc)?

i'm not quite sure i follow this. in what way is the motion of the pendulum related to the stars? Smithsonian Foucault's Pendulum FAQ

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The confusion comes from the misuse or "distant starts" to illustrate the idea of a nonrotating frame of reference.
It's a commonly used layman's way of describing something that isn't rotating with the earth, but you're right that is isn't completely true.

The pendulums motion is relative to a really nonrotating frame of reference, so if you have it swinging for long enough, yes it would show the rotation of the galaxy.

As for 2) I think you got it right, it will be useable to illustrate the galaxy's rotation.

Even the best pendulums have to be reset every so often, because they are perturbed by various factors in the environment, so it would be expecting a bit much for one to operate for 50 million years and return a piece of useable information.