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Useful magnification to split double stars

Started by sawsatch, 11/17/2014 05:35AM
Posted 11/17/2014 05:35AM Opening Post
I read that it's 2.35 x the diameter of the objective according to Dawes Law.
How does one arrive at that number?
Posted 11/17/2014 10:31PM #1
The actual answer is "it depends on more than your aperture." Seeing, optical quality, and observer experience are often every bit as important. wink

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Posted 11/18/2014 04:26AM #2
Hi Stephen. Most fundamental rule of thumb is based on Rayleigh res (radians) being 1.22 wavelength/diam with assumption that two monochromatic stars of equal brightness are being observed and seen bright enough to of course look directly at the pair. Other assumptions are that effective wavelength is in the middle of the photopic visual ~0.55 um and that the eye resolves 1 arc-min (can just discern two dots separated by 1 acr-min as seen thru the eyepiece). Plug that in and an e.g. 6-inch telescope has a Rayleigh limit of 0.908 arc-sec (Rayleigh) 0.76 (Dawes) and 0.74 (Sparrow). These correspond to mags of 66, 79 and 81. But you really need around 4 times that mag to render the airy disc(s) comfortably resolved. That's why 1.5-inch theodolites typically have mag thru the eyepiece of ~60x. (This is bases on actual USE rather than theory!) So if we increase those 3 example mags by 4x it gives 264, 316 and 324 for Rayleigh, Dawes, Sparrow using a 6-inch scope. Your rule yields 358X...which is reasonably close to the 324. And I note that if we had assumed a wavelength of 0.5 um...the 324 becomes 356...virtually identical to the rule you cite. To ans your direct question though...I don't know who came up with that or how. Add to all this seeing, polychromatic, central obstruction, convolution...I wouldn't put too much stock in rules of thumb. In practice, I would crank up the mag until bright stars are quite comfortably bigger than dots. In fact, you will NEED to comfortably see fairly stable little Airy Discs on individual stars to even HOPE to have a good night splitting doubles to the capability of your scope! Tom Dey

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