# Measure an angle in the sky from a photo?

Let's say I have an picture of the sky or of an landscape and I want to measure an angle in the celestial sphere. Is there any software for that? In real life I would use the empirical hand gestures or a theodolite.

• Digital or film? Do you happen to know details like the lens or field of view of the camara it was taken with? Do you see stars in the image that you recognize? There's a big difference between a FITS image from a known telescope and an image cut from a magazine.[object Object] – James K Aug 17 '18 at 19:19
• I am referring to digital images. I know (and can set) all the above parameters, as I am taking the photos with a DSLR. Ideally I would like to measure angles in the sky with a daylight photo. – theshepherd Aug 17 '18 at 20:54
• iraf or pyraf. Check it out. – Kornpob Bhirombhakdi Aug 20 '18 at 11:30

Assuming low distortion (not a fisheye lens), the image is a gnomonic projection of part of the celestial sphere. If $r$ is the distance from the image center in pixels, $p$ is the pixel scale in radians per pixel, and $\theta$ is the angular separation from the center in radians, then
$$rp = \tan \theta$$
For example, I used the measurement tools in GIMP and Stellarium on two bright stars near the center to verify the central image scale of 112 arcsec/pixel or 0.54 mrad/pixel. The edges of the 2320x1740 image are 1160 and 870 pixels away from the center. Solving for $\theta$, the edges are 0.56 and 0.44 radian away from the center, so the image's angular dimensions are 64 by 50 degrees from edge to edge.