Permeability

The permeable force is the magnitude of the weakest stars seen with a telescope when viewed at its zenith . It can be evaluated using the Bowen formula:

m=5,5+2,5\lg D+2,5\lg {\Gamma }

{\ displaystyle m = 5.5 + 2.5 \ lg D + 2.5 \ lg {\ Gamma}}

{\ displaystyle m = 5.5 + 2.5 \ lg D + 2.5 \ lg {\ Gamma}}

, ^[1] where

D - telescope aperture in centimeters, ^[2]

$\Gamma$ ${\ displaystyle \ Gamma}$ $\ Gamma$ - the angular magnification of the telescope .

The permeable force depends on the magnification of the telescope, since as the magnification increases, the apparent brightness of the night sky background quickly decreases, which facilitates the visibility of weak stars.

More often in the literature there is another, simplified formula:

m=2,1+5\lg D

{\ displaystyle m = 2.1 + 5 \ lg D}

{\ displaystyle m = 2.1 + 5 \ lg D}

.

But the most accurate formula for assessing penetrating power is as follows:

m=2,5\lg {\frac {D}{\beta }}{\sqrt {\frac {Kt}{s}}}

{\ displaystyle m = 2.5 \ lg {\ frac {D} {\ beta}} {\ sqrt {\ frac {Kt} {s}}}

{\ displaystyle m = 2.5 \ lg {\ frac {D} {\ beta}} {\ sqrt {\ frac {Kt} {s}}}

, ^[3] where

$\beta$ ${\ displaystyle \ beta}$ $\ beta$ - diameter of the central maximum of the diffraction image of a star ( Erie disk ) in seconds of arc,

K is the quantum yield of the optical system of the telescope, equal to the ratio of the number of registered photons to the number of radiation hit the receiver (eyes or CCD .)

s is the brightness of the night sky background,

t is the exposure time.

This formula can be used to calculate the shutter speed required to obtain images of weak space objects in astrophotography.

Links

[1] Astronet> Telescope's permeability

[2] se.slovaronline.com

[3] Astronet> Optical Telescope

Permeability

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