54°12.0' N; 4°25' W

                               Astronomical Formulas

                                                  Useful Calculations

                           Formula                                                                                                                                 Example

                           F/Ratio = Telescope Focal Length / Objective Diameter                                                 1000mm (FL) / 200mm (OD) = F/5

                           Magnification = Telescope Focal Length / Eyepiece Focal Length                                1000mm (FL) / 10mm (EPFL) = 100X Magnification

                           Exit Pupil = Eyepiece Focal Length / Telescope F/Ratio                                                 10mm (EPFL) / F5 = 2mm Exit Pupil

                           Telescope Resolution = 116 / Objective Diameter (mm)                                                  116 / 200mm (OD) = 0.58 Arc-Seconds

                           Actual Field of View = Apparent Field of View / Magnification                                        80deg / 40X = 2 Degrees

                           Aperture Gain = (Objective Diameter / Eye Pupil Diameter) ²                                                         200mm / 7mm ²  =  816.33 x

                           Mirror / Lens Surface Area = (pi r ²  )                                                                                    100mm x 100mm x 3.14 = 31,400mm

                           Minimum Useful Magnification = Objective Diameter / Eye Pupil Diameter                   200mm / 7mm = 58 x  Magnification      

                           Maximum Useful Magnification = Objective Diameter (mm) x 2                                       200mm x 2 = 400 x  Magnification

                           Limiting Magnitude = 5 x Log₁₀ (Objective Diameter (cm)) + 7.5                                      Log(20) = 1.3 so (5 x 1.3) + 7.5 = 14 Magnitude

                           Lunar Feature Resolution = (2 x Dawes Limit of Scope * 3476) / 1800                           2 x 0.58 x 3476 / 1800 = 2.24 km (For a 200mm Scope)

                           Magnification to Split a Binary Star = 480 / Binary Angular Separation                           480 / 34 =  14.12 x Magnification    

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Definitions

F/Ratio; is the measure of a telescopes speed.

Magnification; is the factor an object appears nearer (larger) than it actually is.

Exit Pupil; is the diameter of the object that is seen at the eyepiece.

Telescope Resolution; is the absolute minimum resolvable distance between objects (Dawes Limit).

Actual Field of View; is the true field of view seen in the sky.

Apparent Field of View; refers to how wide a field of view an eyepiece will provide.

Aperture Gain; the gain in light capture compared to the average human pupil (7mm).

Surface Area; the total volume of the mirror or lens (in mm).

Minimum Useful Magnification; the minimum magnification before light is wasted that could enter your eye.

Maximum Useful Magnification; the maximum magnification before further magnification degrades the image.

Limiting Magnitude; is the faintest object detectable using the telescope.

Lunar Feature Resolution; is the smallest resolvable lunar feature in km (3476 diameter of the moon, 1800 angular size of moon).

Magnification to Split a Binary Star; magnification of telescope required to split a binary star (eg shown is using Albireo 34deg separation).