From: Stephen B. Gray <stevebg@roadrunner.com> To: math-fun <math-fun@mailman.xmission.com>; Gary <garybear9@roadrunner.com> Sent: Sat, December 18, 2010 7:05:39 AM Subject: [math-fun] A distant mirror I suggest a project to see if there is a mirror in space facing us 1000 light years from Earth. If it's out there and if it's big enough, we could peer at it and see what happened here 2000 years ago. Maybe some extraterrestrial civilization has taken pity on our ignorance of ~0 CE history in Palestine and elsewhere. To uncover history we might need to see details as small as a few meters, which implies a mirror diameter of X. Maybe someone could compute X. If X is large enough, the builders would (?) ....... many interesting questions. This notion is not suggested as something practical, just something that is "logically possible," showing that the information still exists, except for that created indoors or under the sheets. Steve Gray _______________________________________________ You will also need a large telescope mirror to view the Earth image 2000 ly distant. At 10^13 km/ly, this is 2 x 10^19 m. In order to see 1 m details, it will need to resolve an angle of 5 x 10^-20 rad. The standard diffraction limit for wavelength λ and aperture diameter a is λ/a. For λ = 500 nm, the required mirror diameter is 10^13 m = 60 AU. This is the size of Neptune's orbit. The distant mirror also needs to be at least this big. -- Gene