Telescope Formulae

Lots can be calculated from Astro-images and your telescope, so let’s go through some simple(ish) formulae for observing the night sky. Unless stated otherwise, use measurements in millimetres, not inches.

I also made formula triangles if you prefer them 🙂

Magnification

Focal Length/eyepiece focal length = magnification

Magnification

The magnification can be worked out by dividing the larger focal length by the smaller. The Telescope’s focal length is written as fO, and is usually written on the telescope. The eyepiece is almost always labelled with its focal length (fe).

Focal Ratio

Focal length/aperture = focal ratio

F_ratio

The aperture is the diameter of the objective (the big lens or mirror), and the ratio is helpful for other calculations.

Field of View

Apparent field of view / magnification = True field of view

true_fov

The apparent field of view (a.k.a eyepiece field of view) is how much you can see through the eyepiece. It’s given to you from the manufacturers, and the true field of view (a.k.a telescope field of view) is how much you can see through the telescope. Fields of view are measured in degrees.

Exit Pupil

Aperture / magnification = exit pupil = eyepiece focal length /  focal ratio

Exit_Pupil

There are two formulae for the exit pupil. The exit pupil is where the light leaving the eyepiece converges, but this is best explained with a picture.

280px-exit_pupil_raytrace.svg

Star Magnitude Limit

Star magnitude limit = 2 + 5log(aperture)

This tells you the faintest thing your telescope can see, so you know what you can observe.  This equation depends only on your aperture (diameter of your biggest lens/mirror), because aperture is essentially how much light you’re letting in. For example, my telescope has an objective 76 mm aperture, so my magnitude limit would be:

2 + 5log76

=

2 + 5*1.8808

=

11.404

So something like Pluto (magnitude of 15) can’t be seen with my telescope, but I can see Venus (-4.4), mars (-3) and even Neptune(8) at its brightest.

Surface Brightness

Surface brightness is used throughout cosmology, and is a measurement of apparent magnitude (what we just discussed in the equation above) per unit area. It’s used for things called extended objects, which basically just nebulae, galaxies that cover a piece of the night sky. It can be calculated with this equation:

Surface Brightness = 2*(exit pupil^2)

Have fun using these and wrapping your head around them. Astronomy and cosmology has a lot more mathematics than you know, and this is just the beginning!

Happy Stargazing!

 

2 comments

  1. Great resource! This is very helpful. I’m really proud to own a telescope, but I have to admit I’m not all that proficient with using it. I’ve never really wrapped my head around all the technical details.

    Liked by 1 person

    • I’m glad you found this useful! I tend to struggle with remembering all the equations, but I think it’s just that I rarely get to use any 🙂

      Liked by 2 people

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