Telescope Size, Design. A spy satellite orbiting 500 km above Earth is supposedl

Question

Telescope Size, Design.

A spy satellite orbiting 500 km above Earth is supposedly capable of counting individual people in a crowd in visual-wavelength images. Assume that the middle of the visual wavelength band is a wavelength of 550 nm. Assume an average person seen from above has a size of 0.8 m. Use the small-angle formula and the formula for telescope resolving power to estimate the minimum diameter of the telescope the satellite must carry. (Please give answer in meters).

Dmin = ______ m.

Explanation / Answer

Given,

Distance of satellite, D = 500 km

Wavelength, W = 550 nm

Rayleigh criteria of resolution, sin A (rad)= 1.22 (W/d)

sin A = 0.8/500000 = 1.6 x 10-6

d = 1.22(550 x 10-9)/(1.6 x 10-6) = 0.419 m or 41.9 cm

arc sec A = 114/Dmin

=> Dmin = 114/(arc sec A)

At 500 km, the angle of 0.8 m is tan-1(0.8/500000) = 9.17 x 10-5 degrees,

or 3600 x 9.17 x 10-5 = 0.330 arc sec

Then Dmin = 114/0.330 = 345.33 mm = 0.345 m

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