Telescope Science
by John Torae

Aperture

Aperture is the size of  the main optical lens of the telescope.  It can be specified either in inches or millimeters. “Light Grasp” which is how much light an optical system can pull is a function of the area of the aperture, so that, “Light Grasp” goes up and down in squares. 

For example, the Light Grasp of a 50mm pair of binoculars is 51, that is each ocular is 51 times brighter than you can see with the naked eye.  This is most apparent at night or in low light situations.  A 100mm binocular will pull about 4 times more light with a light grasp value of 204.

Light grasp can be calculated by the formula (A/38.495) where A is the area of the objective lens in square millimeters.

Little jump in aperture are significant jumps in light grasp.

Theoretical Minimum and Maximum Magnifications

One way to calculate the theoretical minimum and maximum powers for a given aperture is to use the following formulas:

  Minimum Power = D/6
Maximum Power = D/1.58

where D is the diameter of the objective in millimeters.

Limiting Visual Magnitudes

The brightness of a celestial object can be measured by the “magnitude scale.” On this scale each magnitude is about 2.5 times fainter than the one below it.

For example, a fourth magnitude star is about 2.5 times dimmer than a third magnitude star, and about 6.3 times fainter than a second magnitude star.

The full moon is about magnitude -12 and the Sun, which is about a million time brighter than the Moon, is a magnitude -27.  With dark transparent skies, the dimmest star you can see with the unaided eye is about magnitude 6.

To calculate the limiting visual magnitude possible with a particular aperture and assuming transparent dark skies, use the following formula:

  LVM = 2.7 + 5 * (LOG10D)

where LVM is the Limiting Visual Magnitude and D is the Diameter of the objective in millimeters.

Dawes Limit and Resolution

One measurement of an optics resolution is Dawes Limit.  Dawes Limit can be calculated with the formula:

  Theta = 115.8/D

Where Theta is Dawes Limit and D is the diameter of the objective in millimeters. Atmospheric conditions rarely allow the value of theta to be better than 0.5.
To calculate the size of the smallest lunar feature visible from an optic, using Dawes Limit use the following formula:

  Size = (2*theta*3476)/1800

where Size is the smallest resolvable lunar object in kilometers and theta is the value of Dawes Limit.

Aperture Calculator

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