Jan 8 2008, 07:28 PM
This thought keeps nagging at me, so I wanted to share it -- figuring the specs comes down to solving some problems in quantum mechanics, which is way out of my expertise, but the idea intrigues me:
Let's say we had an occulting element that was at a good distance from a very large light-gathering telescope. I'm tentatively picturing an occulting element like a fan blade: A central rotating hub with two (or so) wires connected by ballast weights to the hub. Obviously, in space, once you got the rotation going, it would keep going.
The observation event would involve the occulting element passing in front of the object to observe. Let's say Pluto, for example. If the trajectory worked out just right, you could have the planet occulted by a wire crossing the planet first in one dimension, then later by a wire at right angles to that one. If you were collecting photometry data of the planet during those two (or more) events, you could produce an image with pixels as fine as the wire appears to be from the distance between the telescope and the occultor. If the wire were 0.5 mm thick and the distance about 1 AU, the resolution would be extraordinary. And in principle, photometry could be performed with several broadband filters, producing multispectral images with great resolution of distant objects.
Now, for all the problems I've avoided mentioning: There is a direct tradeoff between resolution and time over which you integrate the photometric data. The goal would be to make the occultation last as long as possible, but with objects in different solar orbits, that would be tricky. You'd also want as much light gathering as possible, although you wouldn't necessarily need good resolving power (not even as good as a backyard telescope). The kicker upon which I can't comment is what QM does to light wrapping around the wire and hitting the sensor anyway. Presumably, there's something predictable about that, and maybe it could be divided out in the analysis, without complicating the mechanism. Having the wires be thicker (more like fan blades) would mean that light could only bleed around one edge at a time, rather than two.
It seems like in principle, high resolution multispectral images could be made even of extrasolar planets, even if we had to cover a square kilometer of the Moon with light-gathering telescopes to get the signal-noise high enough.
I don't know what the theoretical limits are, but it seems like we could have Voyager-like images of other solar systems without venturing outside our solar system.
Feb 23 2008, 07:16 PM
It looks like no one else is sure either. It sounds like an interesting idea to me, though.. you could try submitting it to physics professors and seeing what they thought.. or.. to other people with similar knowledge, wherever they may be
Feb 25 2008, 06:11 AM
I did one bit of work on the theory:
Supposing the goal were to achieve a resolution of 10 km on a Moon-like object orbiting Epsilon Eridani.
With a mirror covering 100 m^2 on our end, the number of photons striking the mirror from any given 10 km x 10 km patch on the remote object would be about 5.5 per second. That includes all wavelengths.
To get reasonable signal/noise to compute albedo, you'd need to collect data for about 10 seconds. So the occulting element would have to slide across the face of the remote object at an apparent rate of 1 km/sec. Any faster, and you'd lose your signal.
Thus if the occulting element were orbiting the mirror at a distance of 1 AU away, it would need to have a radial velocity of just 1.5 mm per second. Off the top of my head, just about any orbital configuration anywhere remotely near the Sun would exceed that by many orders of magnitude.
So alternatives would be:
1) A "one-piece" assembly with the occulting element and the mirror connected by a beam, and the beam set to rotate at the appropriate rate. But because the beam would have to be vastly shorter than 1 AU, the velocity control would have to be vastly greater still.
2) Time the observation so that the occulting element were in retrograde motion (or stop motion) relative to the mirror in the right time and place for the occultation. Seems to require unachievable precision.
3) Launch the two elements outside of the Sun's gravitational influence so that their trajectories can be controlled in "zero G". This is probably unworkable, as even the galactic acceleration due to gravity would prohibit the incredible control needed.
4) Achieve greater precision by having the occulting element be a ballistic/rotating element fired backwards from the main body, correcting for the forward motion by the main body. So, imagine a large fan blade rotating so that the ends of the tips on one edge almost exactly cancelled out the forward motion of the main body.
All of that said, you lessen the precision requirements considerably if you tolerate resolution of just 100 km per pixel. Or if you greatly increase the amount of light gathering. (Note: Resolving power is much less important. A lot of passive light-gathering mirrors along the ground track would contribute additively.) You would tighten them up again if you also wanted to perform any kind of multispectral imaging. And I'm completely omitting quantum mechanical effects from my analysis, since I lack the requisite knowledge to take it into account.
The Moon is a pretty good baseline, because it is lit by enough solar energy to be right in the habitable zone of the Sun, and its low albedo would probably be about equalled or bested by any interesting object.
All of this looks very challenging for even the near future, but since cruise time to any such objects will be even more prohibitive, this does seem to be the direction forward, whenever it does happen. Decent resolution of extrasolar targets should eventually be achievable, with good spectral resolution to allow basic compositional mapping. Given any high-priority star systems, we could obtain three or so snapshots, capturing the worlds in various moments in their relative rotation (to get lucky with some of them, we'll have to be unlucky with others), perhaps mapping an entire star system's worlds with about six passes of occulting elements.
Feb 26 2008, 04:01 AM
A 100 m mirror working in visible light has a theoretical resolution of approximately 500 nm/100 m = 5x10^-9 radians (500 nm is the wavelength of the green light). At a distant of 1 AU (150x10^9 m), this translates into 750 m. Based on my rudimentary optical knowledge, this means that anything smaller is essentially invisible to the telescope. Note that a distant object (even a small planet) is not a point source to such a telescope, rather it is a diffraction circle of approximately 5x10^-9 radians wide (=0.001 arcseconds) and your mask needs to cover this definite size.
This is a "lo-fi" version of our main content. To view the full version with more information, formatting and images, please click here