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My basic question is, what would a fast lens with a huge zoom range look like?

This question has been asked and answered for photographers on the ground - the answer was basically (rightfully) "no one would ever pay for it or be willing to lug it around." But what if those limitations were removed? Image you're building a spacecraft for inspecting other spacecraft... you'd want a wide angle for target acquisition and/or proximity operations, you would need a large zoom for imaging details, and you'd need a fast aperture to get good images of the shaded side of the target (and since space radiation will significantly reduce the available ISO of your sensor). Changing lenses robotically wouldn't be an option due to the risk of contaminating your sensor or lens elements (reference here). Budget for a piece of hardware like this could easily be tens of millions of dollars, and the mass of the lens might be worth it (compared to simply having a second camera, doubling the risk of camera failure). A real example of a project working this problem is here.

So, what would that eventual lens look like? Let's baseline a full frame sensor to start with.

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Spacecraft that require such wide focal length ranges usually have multiple cameras. One for the wide field work and another for the narrow field work, just as they have separate cameras for various bands of the electromagnetic spectrum such as UV, Hydrogen Alpha, long infrared, etc. The "lenses" are often reflectors rather than refractors. The cameras are self contained independently of the reflectors they share with one another.

Note that of the six currently active instruments on the Hubble Space Telescope, the "Wide Field Camera 3" optical camera, installed in a 2009 servicing mission, covers a 164 by 164 arcsec (2.7 by 2.7 arcminute, about 8.5% of the diameter of the full moon as seen from Earth) field of view with 0.04 arcsec pixels. That's equivalent to about 28,000mm of focal length with a full frame sized 36x24 mm sensor cropped to a 4,100 x 4,100 pixel (16MP) 24x24 mm square. The "Advanced Camera for Surveys (ACS)" is another of the six instruments that includes three cameras itself. However the high-resolution "zoom" camera has been shut down since 2007.

Reflectors are much more efficient in terms of weight to total aperture and magnification that refractive lenses.

Spacecraft that have more traditional refractive lenses tend to be those pointed at the Earth's surface from low Earth orbit, where the weight penalty is not as much of an issue. They also don't tend to need to see wide angle views for target acquisition. They are close enough to the Earth's surface to use GPS satellites to determine their position and the precise direction that they are aimed.

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The front element would be 8-1/2" across. I doubt it could be made to zoom out to 10mm though. Many of its internal groupings would have to move close together, even overlap. 130 degree field of view... wow!

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