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Simple rule of thumb: The resolving power of a telescope is a function of aperture (diameter of primary lens or mirror). A telescope with an aperture of 100 mm
by Florin_Andrei 14y ago
Simple rule of thumb:
The resolving power of a telescope is a function of aperture (diameter of primary lens or mirror). A telescope with an aperture of 100 mm (4") has a resolving power of 1 arcsec. Then 200 mm of aperture buy you 0.5 arcsec, and so on.
What is the minimum size of detail to distinguish those objects? Let's say 10 cm - kind of blurry, but intelligible.
What's the distance to them, from a telescope in low orbit? It's approximately the semi-major axis of the orbit of the Moon - 384,000 km.
arctan ( 10 cm / 384000 km ) = 2.6 * 10^-10 radian = 5.4 * 10^-5 arcsec
The aperture you need to get that kind of resolving power is:
100 mm / (5.4 * 10^-5) = 1800 m
You'd need a telescope with 1.8 km of aperture to see the Moon lander with 10 cm linear resolution. Scale down the aperture if you're content with less resolution, the function is linear.
Please note this is for a scope in vacuum, above the atmosphere. Air turbulence will reduce its resolving power dramatically, requiring some kind of adaptive optics to dynamically counteract the blur, which typically is not 100% efficient.