Resolving an elephant at 5 light years?

Question

I decided for chuckles to calculate the telescope aperture required to resolve an elephant at a distance of 5 light years and came up with a 9 million km mirror. I may have slipped up. Let resolution be defined as Dawes' at .116/m of aperture, and y'all can handle the trig and the size of the elephant any way you want within reason.

This is a tricky calculation with lots of zeroes so I thought I would throw it out for someone to double check.

I'll be there's more than one person out there who can crunch this so "best answer" may be reserved for the answer that includes a reasonable calculation of the thickness and cooling time of the pyrex. You can choose another substrate if you like. Don't forget to show your work! (within reason)

thanks.

Answer 1

I thought I'd add that, to get this resolution, you do not literally need a 6 million km diameter telescope mirror. It can be done with a phased locked array of just a few telescopes spread out in space over 9 million km. It's easier to do such a thing with radio waves (google "very large array") because the dimensional tolerances are larger, but has been done a few places for 10's of meters with visible light. Making it bigger it "just" a matter of refining the technology and putting it in space. There's still the issue of intensity, though; it would be nice to collect more than a few elephant photons. Some day ...

Answer 2

Roughly, the ratio of your telescope's aperture to the wavelength of light should be at least the ratio of 5 ly to the elephant's features. Let's say the wavelength of visible light is 500nm and you want to resolve features 10 cm. across. Then your telescope's aperture needs to be 5 x 10^20 x 500nm = 2.5 x 10^14m = 250 000 000 000 km. By comparison the solar focus is a spherical surface, centred on the Sun, 80 000 000 000 km. from the Sun; about 1/3 of this distance. If you located the eyepiece of your telescope at the solar focus on the opposite side of the Sun from the elephant, the Sun's gravitational field would act like the objective lens of a telescope. It would have a good enough resolution to make out the general shape of the elephant if your eyepiece was well constructed. We've already got the technology to carry out this experiment. But with today's fastest rockets it would take a couple of decades to get there. You'd need an ion propelled rocket costing about as much as the war in Iraq has since 2003.

Answer 3

Using back of the envelope calculations I came within an order of magnitude of your answer for the aperture.

So I'll focus on the Pyrex. Cooling time of 72 hours using 3 mirror blanks of 6 inch diameter and 1 inch thickness placed the appropriate distance apart in an equilateral triangle.