Intriguing question. If you just spin the liquid about an axis, then the equipotential surface would make a cylindrical mirror.
That could be useful e.g. as a solar concentrator to focus the sun's rays on a central heater along the axis.
But - can't see how you'd use that as a telescope. You can use a spherical surface with a suitable corrector secondary mirror - that's a Schmidt camera. But don't think you can do much with a cylindrical mirror as a telescope.
That then leaves the option of spinning it around several axes simultaneously.
E.g to have two "pails" tethered to each other in a tether spin around a common center of gravity. And simultaneously they are rotating around the line joining them together.
If the tether was very long and the spin rapid, perhaps that could give a reasonable approximation to a parabola, and with a very slow tether spin rate, stay pointing in one direction long enough to do some useful observation.
But you have issues there of the gyroscope effect, your spinning mirror would try to keep a single axis in space and it's axis of spin is continually changing so it would tend to tilt, so that would distort its shape. And - perhaps coriolis effects.
There is one thing you could do, that is if you have a way to do continuous acceleration e.g. with an ion thruster, and then spin around an axis orientated along direction of travel. That would create a parabolic mirror.
Idea is briefly outlined here: Page on archive.org
Wikipedia has an article on this, but the cites are extremely low quality and it reads like one of those articles you find sometimes that may be mainly "made up" by the author of the article, with one of its main cites a long rambling discussion in a google group.
Liquid mirror space telescope
I've just posted to its talk page about this.
Rereading your question - I see you talk about spinning it up then freezing it. In that case, I think best solution is just to set it spinning at the same time that you are accelerating.
E.g. suppose you were launching it to GEO or to Earth Sun L2 etc - use ion thrusters or some low thrust continuous acceleration, for long enough to spin it up and then freeze it, using that idea of spinning around an axis along the direction of thrust.
I'd have thought that might be your best chance of a good parabolic mirror using this method. It's an idea....
E.g.? A thin film of mercury, over a thin layer of tough mylar sheet, a bit like a solar sail - a bit like a parachute in appearance - and then set it spinning as well, then let it freeze. Once it is in shape, slowly stop accelerating, and at same time slowly reduce the rate of spin.
(Just to stop accelerating while maintaining the same spin rate would flatten it out into a flat disk shape, and even if it is already frozen at that stage, hard to imagine something so thin being so strong it doesn't tear apart from the continuing spin when you stop accelerating unless you despin it at the same time).
Could that work? ... How do you spin it up or spin it down? Maybe - to enclose it in a bubble of air and rely on air friction??
Or - maybe an easier way - a parabolic surface beneath it? Which you need as support anyway.
So what about this idea?
Just have a good parabolic template already, and make this as a shell on top of it. Place a mylar sheet and then a thin film of mercury or other liquid metal over the mirror first. Then accelerate the mirror along its axis and at same time spin it up. When the perfect parabolic affect is achieved, then let it freeze. Then slowly decelerate and spin down at the same time.
When done you have a thin film perfect parabola mirror lying on top of your template. Which you then just lift off gently, apply another layer of mylar and more mercury, and repeat.
It might be a way of bulk making lots of thin mirrors in quick succession. Not at all worth doing for one mirror, but perhaps this might be a useful technique if you want thousands of these mirrors for some reason. For a truly giant telescope perhaps using optical interferometer?
Just sharing a few thoughts - no idea if it is possible or not.
That could be useful e.g. as a solar concentrator to focus the sun's rays on a central heater along the axis.
But - can't see how you'd use that as a telescope. You can use a spherical surface with a suitable corrector secondary mirror - that's a Schmidt camera. But don't think you can do much with a cylindrical mirror as a telescope.
That then leaves the option of spinning it around several axes simultaneously.
E.g to have two "pails" tethered to each other in a tether spin around a common center of gravity. And simultaneously they are rotating around the line joining them together.
If the tether was very long and the spin rapid, perhaps that could give a reasonable approximation to a parabola, and with a very slow tether spin rate, stay pointing in one direction long enough to do some useful observation.
But you have issues there of the gyroscope effect, your spinning mirror would try to keep a single axis in space and it's axis of spin is continually changing so it would tend to tilt, so that would distort its shape. And - perhaps coriolis effects.
There is one thing you could do, that is if you have a way to do continuous acceleration e.g. with an ion thruster, and then spin around an axis orientated along direction of travel. That would create a parabolic mirror.
Idea is briefly outlined here: Page on archive.org
Wikipedia has an article on this, but the cites are extremely low quality and it reads like one of those articles you find sometimes that may be mainly "made up" by the author of the article, with one of its main cites a long rambling discussion in a google group.
Liquid mirror space telescope
I've just posted to its talk page about this.
SPINNING THEN FREEZING
Rereading your question - I see you talk about spinning it up then freezing it. In that case, I think best solution is just to set it spinning at the same time that you are accelerating.
E.g. suppose you were launching it to GEO or to Earth Sun L2 etc - use ion thrusters or some low thrust continuous acceleration, for long enough to spin it up and then freeze it, using that idea of spinning around an axis along the direction of thrust.
I'd have thought that might be your best chance of a good parabolic mirror using this method. It's an idea....
E.g.? A thin film of mercury, over a thin layer of tough mylar sheet, a bit like a solar sail - a bit like a parachute in appearance - and then set it spinning as well, then let it freeze. Once it is in shape, slowly stop accelerating, and at same time slowly reduce the rate of spin.
(Just to stop accelerating while maintaining the same spin rate would flatten it out into a flat disk shape, and even if it is already frozen at that stage, hard to imagine something so thin being so strong it doesn't tear apart from the continuing spin when you stop accelerating unless you despin it at the same time).
Could that work? ... How do you spin it up or spin it down? Maybe - to enclose it in a bubble of air and rely on air friction??
Or - maybe an easier way - a parabolic surface beneath it? Which you need as support anyway.
So what about this idea?
Just have a good parabolic template already, and make this as a shell on top of it. Place a mylar sheet and then a thin film of mercury or other liquid metal over the mirror first. Then accelerate the mirror along its axis and at same time spin it up. When the perfect parabolic affect is achieved, then let it freeze. Then slowly decelerate and spin down at the same time.
When done you have a thin film perfect parabola mirror lying on top of your template. Which you then just lift off gently, apply another layer of mylar and more mercury, and repeat.
It might be a way of bulk making lots of thin mirrors in quick succession. Not at all worth doing for one mirror, but perhaps this might be a useful technique if you want thousands of these mirrors for some reason. For a truly giant telescope perhaps using optical interferometer?
Just sharing a few thoughts - no idea if it is possible or not.
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Robert Walker
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