Earth Designs
Posted in cross stitch on 12/25/2009 12:07 am by admindesign a telescope to meet their needs. could you test your design by observing stars from earth?
astronaunts observing from a space station need a telescope with a light gathering power 15000 times that of the human eye, capable of resolving detail as small as second of arc and having a magnifying power of 250. design a telescope to meet their needs. could you test your design by observing stars from earth?
To gather 15,000 times as much light as a human eye, the aperture must have 15,000 times the area of a human eye. In the dark, a healthy human can have a pupil diameter of 8mm. Since A=pi*r^2, you can calculate the light gathering area of the pupil, then multiply that up by 15,000.
The formula for diffraction-limited resolution is:
angular resolution (radians)= 0.1384/D, where
D = telescope diameter in m
And the conversion:
1 arcsecond = 4.84813681 × 10-6 radians
So either the factor of 15,000, or the resolution requirement, will place a constraint on the minimum diameter of your design.
In terms of magnifying power,
magnification = focal length of objective / focal length of eyepice.
So this ratio must be 250.
Finally, Hamal, also known as alpha Cassiopeiae, is 6.88 milliarcseconds in diameter and appears to be large due to its proximity. Obviously, 6.88 milliarcseconds is much smaller than one arcsecond (i.e., one thousand milliarcseconds), so no, the resolution of a scope such as you describe could not be tested by viewing stars. Especially when considering atmospheric turbulence that blurs seeing.
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