Common Telescope Formulas

Introduction

This page is an attempt to gather most of the formulas used with telescopes. I do not grant that all formulas here are correct, but I've been using most of them when building my own scope. Please always use the same units. I prefer working with millimeters. Some formulas are only applicable when one parameter is given in a certain unit that is then written next to the dimension, between square brackets, as in : D[mm].

General formulas

  • Definitions
    • Aperture: opening of the telescope (diameter of the objective). SYMBOL: D
    • Focal length of the primary: SYMBOL F
    • f-number: SYMBOL: f/ = F / D
    • Focal length of the eyepiece: SYMBOL: f
    • Apparent Field of View of the eyepiece: SYMBOL: AFoV
    • Minor axis of the diagonal (Newtonian scopes): diameter of the diagonal as seen from the primary (tilted at 45°). SYMBOL: d
  • Formulas
    • Magnification: SYMBOL: M = F / f
    • Field of View: SYMBOL: FoV = AFoV / M (this is an approximation)
    • Minimal magnification: SYMBOL: Mmin = D / maximal_eyepupil_opening.
      Young people achieve a maximal eye pupil of about 7mm, older people will fall down to 6mm or even 5mm.  Remember that the minimal magnification is that magnification at which there is still NO light that canNOT enter the eye pupil.
    • Maximal useful magnification: SYMBOL: Mmax = 2 * D[mm].
      This is not a strict value, but gives reasonably good results. With very good seeing, one can always try to go further!
    • Dawes limit = 116 arcseconds / D[mm]
    • Rayleigh limit = 138 arcseconds / D[mm]

Newtonian telescopes

  • Total illuminated field: SYMBOL: v = F * [(2 * π * FoV) / 360]

  • The FoV that appears in this formula is the maximal FoV you want to achieve with your scope (without vignetting etc.). This also means that you will have to take this FoV into account when baffling a tube, or when designing the light cage: at a height H in front of the primary mirror, you will have to add H * tan(FoV) to your primary diameter D to obtain the effective baffle diameter.
  • Height of the focal plane above the optical axis: SYMBOL: h = F * [ (d - v) / (D - v) ]

  • >Remember: h needs to be greater than D/2 + height_of_the_totally_racked-in_focuser + approx. 12mm. Use this formula when all but the height h is given (dangerous!).
  • General formula: F * d = h * D + (F - h) * v
  • Diagonal's minor axis: d = [h * D + (F - h) * v] / F

  • Use this formula when all but the diagonal's minor axis is given.

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