The telescopes on some commercial surveillance satellites can resolve objects on

Question

The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 95 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 14 cm across. Assume first that object resolution is determined entirely by Rayleigh's criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 384 km and that the wavelength of visible light is 560 nm. What would be the required diameter of the telescope aperture for (a) 95 cm resolution and (b) 14 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b), i.e. is the military surveillance resolution accomplished? (a) Number Units (b) Number Units (c)

Explanation / Answer

lambda = 560 * 10-9 m

L = 384 * 103 m

D = 95 cm = 0.95 m

d = 1.22 * lambda * L / D

= (1.22 * 560 * 10-9 * 384 * 103) / (0.95)

d = 0.276 m

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d = 1.22 * lambda * L / D

= (1.22 * 560 * 10-9 * 384 * 103) / (0.14)

d = 1.87 m

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